md nastran r3 release guide

MD Nastran R3

Release Guide

CorporateMSC.Software Corporation2 MacArthur PlaceSanta Ana, CA 92707 USATelephone: (800) 345-2078Fax: (714) 784-4056

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Con t en t s

MD Nastran R3 Release Guide

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Preface to the MD Nastran R3 Release Guide xiv

A Word About Prerelease Features xv

List of Books xvi

Technical Support xvii

Internet Resources xix

1 Overview of MD Nastran R3

Overview 2

Local Adaptive Meshing 2

Advanced Integrated Nonlinear (SOL 400) 2

Contact 3

Explicit Nonlinear (SOL 700) 4

MD Adams Integration 4

Optimization 4

Aeroelasticity 5

SCA User Defined Services 5

Symbolic Subsitution 5

List of Errors Resolved 6

List of Example Problems for the MD Nastran R3 Release 6

List of MD Nastran Documents Released with MD Nastran R3 7

2 Adaptive Meshing

Local Adaptive Mesh Refinement 10

Introduction 10

The Adaptive Mesh Refinement Loop 14

Refinement by Regular Subdivision 15

Location of New Grid Points 20

Hanging Nodes and Multipoint Constraints on Hanging Nodes 23

Selection of Elements to Refine 27

Refinement Criteria 28

Propagation of Refinement 37

Table of Contents


==

iv

Transference of Analysis Data Between Unrefined and Refined Meshes 42

Detection of Geometric Features and Material and Superelement Interfaces

49

User Interface 55

Output 68

Guidelines and Limitations 71

3 Advanced Integrated Nonlinear and Contact

SOL 400 Performance Enhancements 76

SOL 400 Advanced Heat Transfer 77

Outline of New SOL 400 Heat Transfer Capabilities 77

BCONTACT=ALLBODY 95

Introduction 95

Benefits 95

Input 95

Output 95

Limitation 95

Example 95

Linear Perturbation and Brake Squeal Analyses in SOL 400 98

Introduction 98

Input 98

Output 99


Examples - Examples of Case Control Approaches 100

Examples of Linear Perturbation and Brake Squeal Analyses 102

SOL 400 Materials and Elements 109

Introduction 109

Benefits 110

Advanced Integrated Nonlinear Analysis 111

Input 111

Output 113


Enhancements to Connector Elements 118

Introduction 118

CBUSH Enhancements in SOL 400 118

Inputs 119

Outputs 119

Example 119

Nonlinear CWELD and CFAST Elements in SOL 400 120

vContents

Inputs 121

Outputs 121

Supported Output Requests 122

Limitations 122

Example 122

Adaptive Time Stepping Scheme Enhancements for Quasi-Static Analysis

128

NLADAPT Bulk Data Entry 128

Results Output 131

Contact and Adaptive Time Stepping Enhancements for Transient

Dynamic Analysis 133

Enhancements for Dynamic Contact 133

Enhancements for Dynamic Time-Stepping 136

Progressive Failure Analysis with a Micromechanical Module 138

Introduction 138

Definition of a Composite 138

Output 140

3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface

and Edge-to-Edge 141

Introduction 141

Benefits 142

Moment Carrying Glue 142

Input 142

Limitations 142

Examples 143

Improved Flexibility in Contact (for Shell only in MD Nastran R3) 145

Input 146

Examples 147

In-Plane Shell Edge-to-Edge Glue 147

Input 147

Limitations 147

Examples 147

Beam-to-Beam Contact 151

Input 151

Examples 152

General Shell Edge(-to-Edge and -to-Surface) Contact 155

Input 155

Limitations 155

Examples 155

Optimize Contact Constraints 157

Input 158


==

vi

Limitations 158

Examples 158

GLUE Control 158

Input 158

Limitations 159

Breaking Glue 159

Input 159

Limitations 160

Miscellaneous Items 160

Explicit Nonlinear - SOL 700 162

Introduction 162

New Capabilities in Explicit Nonlinear - SOL 700 162

Advanced Fluid Structure Interaction (FSI) 162

Parallel FSI 165

Advanced Composites 166

Smooth Particle Hydrodynamics (SPH) Method 167

Sheet Metal Forming (SMF) with Spring-back 167

Integrated Fan Blade Out (FBO) and Rotor Dynamics (RD) simulation 169

Analysis Chaining 172

New Materials and Elements 174

Support for FAA Hybrid II and III Dummy Models 174

New SOL 700 Bulk Data Entries and Parameters 175

Arc-Length Methods (Pre-release) 183

Introduction 183

Benefits 183

Method and Theory 183

Inputs 184

Outputs 184

Limitations 184

Analysis Chaining 189

Introduction 189

Input 189

Analysis Type 189

Examples 190

Legal Chaining Type 193

Limitations 194

4 Implicit Nonlinear

Implicit Nonlinear - SOL 600 196

Support of Large Grid and Element IDs 196

viiContents

Multiple RFORCE Entries in the Same Subcase 196

BCONTACT Case Control Command Clarification 197

Generalized Alpha Dynamic Integration Method 202

MATVP Material Property Entry 202

MATSMA Shape Memory Alloy Material Property Entry 203

Nonlinear Elastic Orthotropic Materials 203

Composite Integration Methods to Reduce Computer Time 203

New SOL 600 Bulk Data Entries and Parameters 205

5 NVH and Acoustics

NVH Enhancements 208

ACMS with Acoustic External Superelement Creation 208

Multiple RANDOM Looping 208

Sparse OUTPUT4 Format for External Superelement Creation 208

Binary op2 and op4 Compatibility Robustness 208

Merged Superelement Results 209

Enhancements to the Frequency Response Function (FRF) and FRF

Based Assembly (FBA) Feature 210

Introduction 210

Names for FRF Components 210

Interchangeable COMPID/COMPNAME Fields in All Bulk Data Entries Meant

for FBA Use 210

User Load Specification in the FBA Process 210

Responses to Unit Loads and User Specified Loads 210

Connection of Scalar Points and Explicit Connection of Coincident Grid Points

212

Flexible Connection of Degrees-of-Freedom 212

Release of Connection Degrees-of-Freedom 212

Grounding of Connection Degrees-of-Freedom 212

Handling of Displacement (or Local) Coordinate Systems at Connection Grid

Points of FRF Components in the FBA Process 213

FRFs for PLOTEL Grid Points 213

Summary of the Enhancements 213

Enhancements to ADAMSMNF Case Control Command 214

6 Numerical Methods and High Performance Computing

Linear and Nonlinear Contact Analysis 216

Introduction 216

Benefits 216


==

viii

Inputs 216


Demonstration Example 217

High Performance Iterative Solver Now Available for Nonlinear Transient

Analysis 219

Introduction 219

Benefits 219

Inputs 219

Outputs 219


Matrix Based Iterative Solver Now Available for Nonlinear Static Analysis

221

Introduction 221

Benefits 221


Inputs 222

Outputs 222


Demonstration Examples 222

Factor Matrix Caching for Lanczos and Nonlinear Transient Analysis with

NLAUTO 225

Introduction 225

Benefits 225


Inputs 225

Outputs 225



New TAUCS Indefinite Solver Improves Lanczos Performance 228

Introduction 228

Benefits 228


Inputs 228

Outputs 228



Shared Memory Parallel (SMP) Scalability Improvements for Static

Analysis 230

Introduction 230

Benefits 230

ixContents


Inputs 230

Outputs 230

Guidance and Limitations 230


New MAXRATIO Information Output 232

Introduction 232

Benefits 232


Inputs 232

Outputs 232



Example Input Data 233

Example Output 235

New SPARSESOLVER MDTSTATS Information Output 236

Introduction 236

Benefits 236


Inputs 236

Outputs 236



Example Input Data 237

Example Output 239

7 Upward Compatibility

TEMPERATURE Case Control Command 242

Improvements in Fluid Eigenvalue Analysis 244

FLUID GRID Points and Partitioning 245

Distributed Memory Parallel (DMP) Diagnostic Messages 247

System Information Message (SIM) 6916 248

8 Optimization

Enhancements in DRESP3 250

Introduction 250

Benefits 250


==

x

User Inputs 250

Output 255


Examples 257

Topometry Optimization 260

Introduction 260

Benefits 260

Input 261

Output 263


Example 1 - Three-bar Truss (tomex1.dat) 263

Input 265

Output 267

Example 2 – Car Model Topometry Design 267

Topography (Bead or Stamp) Optimization 269

Introduction 269

Benefits 269

Input 269

Outputs 272


Example 3 – A Square (togex1.dat) 273

Input 274

Output 274

Permanent Glued Contact Modeling in SOL 200 275

Input 275

Example 4 - A Solid Beam (topoug5.dat) 275

Input 276

Output 277

Randomization of an Input Data File 278

Introduction 278

Benefits 278

Input 278

Output 279


Random Elimination of Element Types 280

Introduction 280

Benefits 280

Input 280

Output 280


xiContents

Enhancements in SOL 200 Optimization 281

Introduction 281

Benefits 281

Input 281

Example 282

Output 284

Guidelines 286

Limitations 286

Optimization of Nonlinear Structural Responses (Pre-release) 290

Introduction 290

Benefits 291

Theory 291

Implementation 294

Input 295

Outputs 298

Examples 302

References 307

9 Aeroelasticity and Rotor Dynamic Improvements

A New Aerodynamic Interpolation Method 310

Introduction 310

Inputs 310

Outputs 310


Examples 311

External Spline Server 313

Introduction 313

Inputs 313

API Changes 313

Sparse Matrix Format 314

Upgrading an Existing Spline Server 314

Blade Vibration Analysis 315

10 SCA User Services

User Defined Services 318

Introduction 318

Example 318

Requirements 320


==

xii

The 2005 New Template

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å Preface to the MD Nastran R3 Release Guide

å A Word About Prerelease Features

å List of Books

å Technical Support

å Internet Resources


Preface to the MD Nastran R3 Release Guidexiv

Preface to the MD Nastran R3 Release Guide

This Release Guide contains descriptions for both the MD Nastran R3 and MD Nastran R2.1 versions,

and supersedes the MD Nastran R2.1 Release Guide.

xvPreface

A Word About Prerelease Features

MD Nastran R2.1 contains a number of features that have been labeled as “prerelease.”

A prerelease feature or enhancement is defined as a feature or enhancement that has not yet completed

MSC’s exhaustive verification and validation (V and V) testing and qualification process. Therefore,

prerelease features are to be used at the client’s own risk.


List of Booksxvi

List of Books

Below is a list of some of the MD Nastran and MSC Nastran documents. You may order any of these

documents from the MSC.Software BooksMart site at http://store.mscsoftware.com/.

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ç Installation and Operations Guide

ç Release Guide

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ç Quick Reference Guide

ç DMAP Programmer’s Guide

ç Reference Manual

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ç Getting Started

ç Linear Static Analysis

ç Basic Dynamic Analysis

ç Advanced Dynamic Analysis

ç Design Sensitivity and Optimization

ç Thermal Analysis

ç Numerical Methods

ç Aeroelastic Analysis

ç Superelement

ç User Modifiable

ç Toolkit

ç Implicit Nonlinear (SOL 600)

ç Explicit Nonlinear (SOL 700)

ç MD User’s Guide - Application Examples

ç Topology Optimization

ç SCA Service Guide

ç User Defined Services

xviiPreface

Technical Support

For help with installing or using an MSC.Software product, contact your local technical support services.

Our technical support provides the following services:

• Resolution of installation problems

• Advice on specific analysis capabilities

• Advice on modeling techniques

• Resolution of specific analysis problems (e.g., fatal messages)

• Verification of code error.

If you have concerns about an analysis, we suggest that you contact us at an early stage.

You can reach technical support services on the web, by telephone, or e-mail.

tÉÄ Go to the MSC.Software website at www.mscsoftware.com, and click on Support. Here you can find

a wide variety of support resources including application examples, technical application notes, training

courses, and documentation updates at the MSC.Software Training, Technical Support, and

Documentation web page.

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United States

Telephone: (800) 732-7284

Fax: (714) 784-4343

Frimley, CamberleySurrey, United Kingdom

Telephone: (44) (1276) 60 19 00

Fax: (44) (1276) 69 11 11

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Telephone: (31) (18) 2543700

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Madrid, Spain

Telephone: (34) (91) 5560919

Fax: (34) (91) 5567280


Technical Supportxviii

bã~áä Send a detailed description of the problem to the email address below that corresponds to the product you

are using. You should receive an acknowledgement that your message was received, followed by an

email from one of our Technical Support Engineers.

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The MSC Institute of Technology is the world's largest global supplier of CAD/CAM/CAE/PDM training

products and services for the product design, analysis, and manufacturing markets. We offer over 100

courses through a global network of education centers. The Institute is uniquely positioned to optimize

your investment in design and simulation software tools.

Our industry experienced expert staff is available to customize our course offerings to meet your unique

training requirements. For the most effective training, The Institute also offers many of our courses at our

customer's facilities.

The MSC Institute of Technology is located at:

2 MacArthur Place

Santa Ana, CA 92707

Phone: (800) 732-7211

Fax: (714) 784-4028

The Institute maintains state-of-the-art classroom facilities and individual computer graphics laboratories

at training centers throughout the world. All of our courses emphasize hands-on computer laboratory

work to facility skills development.

We specialize in customized training based on our evaluation of your design and simulation processes,

which yields courses that are geared to your business.

In addition to traditional instructor-led classes, we also offer video and DVD courses, interactive

multimedia training, web-based training, and a specialized instructor's program.

Course Information and Registration. For detailed course descriptions, schedule information,

and registration call the Training Specialist at (800) 732-7211 or visit www.mscsoftware.com.

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xixPreface

Internet Resources

MSC.Software (www.mscsoftware.com)

MSC.Software corporate site with information on the latest events, products, and services for the

CAD/CAE/CAM marketplace.


Internet Resourcesxx

Chapter 1: Overview of MD Nastran R3 MD Nastran R3 Release Guide

1 Overview of MD Nastran R3

� Overview


Overview2

Overview

MSC Software is proud to release MD Nastran R3. This release of MD Nastran significantly advances

the multidiscipline capabilities available to you. The following sections briefly describe some of the

major and minor enhancements to MD Nastran R3.

Local Adaptive Meshing

MD Nastran R3 introduces adaptive remeshing in linear statics (SOL 101) and Advanced Nonlinear

(SOL 400). This enhancement allows you to specify a region of the mesh to remesh during the simulation

based on various criteria. If any of the activated remeshing criteria is met, the element, and possibly some

neighboring elements, will be subdivided. The results from the original mesh will be mapped on to the

new mesh and the analysis will continue. The three basic remeshing criteria are:

• Error Estimate – this criterion uses an estimation of the stress error in an element and compares it

to a maximum allowable value.

• Regional – in this case, a sphere or cube is defined and any element that is within the sphere or

cube is remeshed.

• Contact Status – this criterion monitors the contact status of an element. If contact is detected,

the element will be subdivided.

Remeshing can provide you with an automated way to refine your mesh in areas of stress concentration

and contact. The result is much more accurate results without the need for multiple models of various

refinements.

More information on the local adaptive meshing capabilities can be found in Adaptive Meshing (Ch. 2).

Advanced Integrated Nonlinear (SOL 400)

MD Nastran’s Advanced Integrated Nonlinear module is designed as the multidiscipline solution

sequence. Unlike the traditional MSC Nastran solution sequences, this module can host multiple

analyses to perform a full event simulation, such as brake squeal analysis or engine thermal cycling. The

basic solver requirements for these event simulations are the ability to chain individual analyses together

where the results of one analysis are used as the initial conditions for a subsequent analysis. Examples of

this are thermal analyses and structural analyses and the ability to perform perturbation analyses at any

point during the event to extract required information such as frequency response.

With this release, SOL 400’s analysis chaining capabilities include the following types of analyses:

• Linear static analysis (New)

• Nonlinear static analysis (Released in R2)

• Nonlinear transient analysis (Released in R2)

• Normal modes analysis (New)

3CHAPTER 1

Overview of MD Nastran R3

In addition to extending the analysis capabilities of MD Nastran, there has also been a focus to enhance

the performance. With MD Nastran R3, new adaptive time-stepping routines have been implemented in

the nonlinear solutions. These routines both increase the robustness of the solution and also reduce the

number of steps taken for a complete step.

Numerical Methods has always been a focus for MD Nastran. In the first two releases, new numerical

solvers were integrated. The MD Nastran R3 release continues this focus by making the CASI solver

available for nonlinear transient analyses and implementing a new matrix-based solver for unsymmetric

problems. Examples are, heat transfer with advection and structural analysis with friction, damping, or

follower forces.

For structural analyses with composites, a new optional module is available in SOL 400 for progressive

failure analysis. You can now calculate micro-mechanical damage for both the matrix and fiber directly

from MD Nastran.

More detailed information on these enhancements to SOL 400 can be found in Advanced Integrated

Nonlinear and Contact (Ch. 3).

Contact

The general 3D contact capabilities released in MD Nastran R2 included iterative touching contact in

Linear Statics (SOL 101) and the Advanced Nonlinear (SOL 400) and glued contact in all linear solution

sequences. For MD Nastran R3, the contact capabilities have been enhanced to include beam-to-beam,

shell edge-to-edge, and moment-carrying glue contact.

With beam-to-beam contact, beam element contact is detected and load transfer is passed from one beam

to the other. You can also specify a beam “radius” to increase the displacement accuracy. This

functionality is critical in many industries including the biomedical field where devices such as

pacemakers are modeled with wire leads using beam elements.

The shell edge-to-edge and moment-carrying glue options are included to ease the process of assembly

modeling. The edge-to-edge contact option works with both touching and gluing contact. With edge-

to-edge gluing, surfaces defined using shell elements do not need to have mesh congruency at the

boundary. This dramatically reduces the amount of model pre-processing required to create complex

assemblies. The moment carrying glue option allows shell-to-shell, shell-to-solid, beam-to-shell, and

beam-to-solid connections. Using this technique, moments generated on one mesh will be transferred

through to the other mesh automatically.

• Direct complex eigenvalue analysis (New)

• Modal complex eigenvalue analysis (New)

• Brake Squeal Analysis (BSQUEAL Command) (New)

• Steady state heat transfer analysis (New)

• Transient heat transfer analysis (New)


Overview4

In addition to the advanced contact functionality, enhancements have been made to increase solver

performance with contact models. The adaptive time-stepping routines have been implemented for

dynamic analyses and there are also new computational tools and procedures for all contact analyses.

More detailed information on these enhancements to SOL 400 can be found in Advanced Integrated

Nonlinear and Contact (Ch. 3) and Numerical Methods and High Performance Computing (Ch. 6).

Explicit Nonlinear (SOL 700)

As a complement to the Advanced Integrated Nonlinear solution for multidiscipline analysis,

MD Nastran also includes an integrated LS-Dyna based explicit solver. This solution was officially

released in MD Nastran R2.

For MD Nastran R3, the Eulerian solver used in MSC.Software’s Dytran solver has been fully integrated

into MD Nastran’s SOL 700. This combination of LS-Dyna and MSC.Software technology provides a

best-in-class solution for traditional impact and crash problems involving fluid-structure interaction.

This FSI solution has also been implemented for high performance computing using the distributed

memory parallel technique.

Through the use of SOL 700 analysis chaining, you can now model complex problems including:

• Pre-stress structures such as engine fan for bird strike (Implicit-to-Explicit)

• Event simulations involving multiple drop tests (Explicit-to-Explicit)

• Manufacturing processes with spring back (Explicit-to-Implicit)

For crash analysis, MD Nastran R3 adds the FAA Hybrid Dummies to the previous dummy models

included in the R2 release. Micromechanical progressive failure analysis components are included MD

Nastran’s SOL 700.

Other enhancements to MD Nastran’s Explicit Nonlinear solution are described in Advanced Integrated

Nonlinear and Contact (Ch. 3).

MD Adams Integration

The integration of Motion and Structural analysis continues with MD Nastran R3. With this release, you

can save your flexible body model and mode information directly in the MD Nastran database for import

into MD Adams. This new storage mode eliminates the need to save an intermediate Modal Neutral File

(MNF) file.

More information on the MD Adams integration can be found in Enhancements to ADAMSMNF Case

Control Command (Ch. 5).

Optimization

MD Nastran has had very powerful optimization routines since it was released in 2006. The functionality

in that release included shape, sizing, and basic topology optimization. MD Nastran R2 introduced

5CHAPTER 1


manufacturing and symmetry constraints for topology optimization. MD Nastran R3 extends this

functionality in the areas of topography and topometry optimization.

In topography optimization, the nodes on a surface mesh are moved normal to the surface during the

optimization loop to arrive at an optimal shape. In contrast, topometry optimization considers each

element in a design region to have a unique property and it will be modified to achieve an optimal design.

Additional optimization enhancements include:

• Design optimization solution permanent glued contact for design optimization studies,

• Automatic randomization of input variables rapid stochastic analysis set-up,

• Random element elimination for sensitivity studies of spot welds and connectors,

• A pre-release of a nonlinear response optimization routine based on equivalent static loads.

More information on these optimization enhancements can be found in Optimization (Ch. 8).

Aeroelasticity

MD Nastran R2.1 introduced an external spline evaluation capability. This capability has been enhanced

in R3 to support storage of the spline matrix in sparse format. This change allows larger models to fit

into memory.

MD Nastran R3 also introduces new capabilities for aeroelasticity analyses. There is a new aerodynamic

interpolation method that interpolates each term in the generalized aerodynamic matrix individually.

Examples for using this new interpolation method are given in Aeroelasticity and Rotor Dynamic

Improvements (Ch. 9).

SCA User Defined Services

As a result of the new MD Nastran architecture, MD Nastran R3 introduces the ability to include user

defined services as part of the MD Nastran analyses. For this release of MD Nastran, nonlinear force

elements are equipped with an external implementation allowing you to define a nonlinear squeeze film

damper. This element type is critical in the rotordynamic analysis of aircraft engines.

More detailed information on the SCA User Defined Services can be found in SCA User Services

(Ch. 10).

Symbolic Subsitution

Using the new Symbolic Substitution feature, you can run multiple analyses on an input file, while

modifying fields automatically. Using Symbolic Substitution you specify a special symbol in the input

file that identifies the location where changes are to be made. When you run your job, you specify a

replacement symbol value that replaces the special symbol in your input file, but only for that job. You

can then make several runs, each with a different value, without having to make any additional

modifications to the input file.


Overview6

For more information, please see Symbolic Substitution (App. A) in the MD Nastran Installation and

Operations Guide.

List of Errors Resolved

The list of errors resolved in this release can be found at:

http://www.mscsoftware.com/support/prod_support/nastran/errorlist/files/error2008.lst

List of Example Problems for the MD Nastran R3 Release

The table below is a list of the example problems in this release guide and the associated file name that

can be found in the test problem library, or in the documentation directory in your MD Nastran R3

installation.

Example Problems File Name

2D composite heat transfer element page 79 2d_comp.dat

3D composite heat transfer element page 80 3d_pcomp.dat

Quartz lamp model page 82 quartz_lamp_hemi.dat

2D Transient Thermal Analysis page 86 vtest8_pc.dat

Chaining page 93 hs_chain1.dat

Transient analysis in 2-D contact page 95 nlc021a.dat

Rotating Fan-Blade Model page 102 nlrot103.dat

Brake Squeal Model page 104 nlbsql01.dat

Beam-to-Solid page 143 nlcmc01.dat

Shell-toSolid page 144 nlcmc02c.dat

Four Co-plane Shell Bodies Edge-to-Edge page 148 nlc025a.dat

Five Irregular Shell Bodies Edge-to-Edge page 148 nlc026a.dat

Five Irregular Shell Bodies Edge-toEdge Glue plus the 6th Shell Body as a

“Footplate” page 150

nlc026c.dat

Crossed Beams page 153 nlc027a.dat

Coiled Beams page 154 nlc027b.dat

Shell Free Edge Contact page 155 nlc028a.dat

Thin-Wall Square Boxed Free Edges Contact page 156 nlc028b.dat

Imperfect Spherical Shell page 185 nla011b.dat

Three-bar Truss page 263 tomex1.dat

A Square page 273 togex1.dat

7CHAPTER 1


List of MD Nastran Documents Released with MD Nastran R3

Along with this Release Guide, the following documents are updated for the MD Nastran R3 release:

• MD Nastran Installation and Operations Guide

• MD Nastran Quick Reference Guide

• MD Nastran User’s Guide - Application Examples

• MD Nastran User’s Guide - Explicit Nonlinear (SOL 700)

• MD Nastran User’s Guide - SCA Service Guide

• MD Nastran User’s Guide - Topology Optimization

• MD Nastran User’s Guide - User Defined Services Guide

A Solid Beam page 275 topoug5.dat

Exterior Acoustic as Design Constraints page 288 d200exac.dat

Fluid Modes as Design Constraints page 288 d200fmd1.dat

10 Bar Truss page 302 deslo.dat

Example Problems File Name


Overview8

Chapter 2: Adaptive MeshingMD Nastran R3 Release Guide

2 Adaptive Meshing

� Local Adaptive Mesh Refinement


Local Adaptive Mesh Refinement

10


Introduction

MD Nastran R3 introduces a new Local Adaptive Mesh Refinement capability to the linear structural

solution sequences in both SOL 101 and SOL 400, possibly in situations involving contact and/or

superelements.

Adaptive mesh refinement is an automatic mechanism for altering and controlling locally the size of the

finite element mesh. Beginning with an initial mesh provided by the user, a sequence of new meshes is

automatically generated. Each new mesh of this sequence is an offspring of the previous, coarser mesh

and is obtained by refining (by subdivision) a subset of their elements.

The following figures illustrate this mechanism in three examples: the compression of an 2D L-shaped

elastic panel (Figure 2-1), 2D elastic analysis of a Mode-I fracture specimen (Figure 2-2) and an 3D

elastic analysis of a pinched cylindrical body (Figure 2-3 ) and (Figure 2-4).

Figure 2-1 Adaptive analysis of an L-shaped elastic panel subjected to compression

11CHAPTER 2

Adaptive Meshing

Figure 2-2 2D Elastic analysis of a mode-I fracture specimen



12

Figure 2-3 3D Elastic analysis of a pinched cylindrical body

13CHAPTER 2

Adaptive Meshing

Figure 2-4 3D Elastic analysis of a pinched cylindrical body

Adaptive mesh refinement can be applied to meshes that combine elements of different types (triangular

or quadrilateral surface elements, tetrahedral, pentahedral or hexahedral volume elements), different

interpolation orders (linear or quadratic), different dimensionality (line, surface or volume elements), or

models substructured into different superelements.

The following elements are supported:

• Line elements: CBEAM, CBEAM3 (with no offsets or warping), CBEND, CBAR (with no

offsets), CONROD, CROD, CTUBE, CVISC.

• Surface elements: CTRIA3, CTRIAR, CTRIA6, CQUAD4, CQUADR, CQUAD8

• Volume elements: CTETRA, CPENTA, CHEXA.

This new adaptive mesh refinement capability shouldn’t be confused with the existing p-adaptive

analysis or p-version adaptivity capability available in linear static (SOL 101) and normal modes

(SOL 103) analysis (see the MD Nastran Reference Manual). While p-adaptivity is an automatic

mechanism to altering the polynomial degree of the underlying finite element interpolating functions

defined over a fixed size mesh, adaptive mesh refinement (or h-adaptivity) attempts to change the



14

element size while keeping interpolation order unaltered. For the current release both types of adaptive

analysis cannot be combined.

The Adaptive Mesh Refinement Loop

During the adaptive mesh refinement process, a sequence of analysis supported over a sequence of

different finite element meshes is sequentially performed within an automatic loop (Figure 2-5).

Figure 2-5 The adaptive mesh refinement loop

This adaptive mesh refinement loop can be summarized as follows:

1. The user inputs an initial, preferably coarse, finite element mesh.

2. An analysis is run and a finite element solution (supported on the current mesh) is computed.

3. Some elements of the previous mesh are scheduled or marked for refinement. These elements are

chosen according to a user specified adaptivity criterion and implicit refinement propagation

rules.

4. The elements scheduled for refinement are refined and a new finite element mesh with new

elements and grid points are thus created.

5. Element properties, boundary conditions, constraints and loads are transferred or mapped from

the previous mesh to the new mesh.

6. Steps 2 to 5 are repeated until a termination criterion is met.

Table 2-1 schematically illustrates the first two iterations of the adaptive mesh refinement loop. Elements

scheduled for refinement due to the user specified adaptivity criterion are depicted in green. Notice that

there are neighboring elements that are also refined during the process (yellow elements). Implicit rules

15CHAPTER 2

Adaptive Meshing

to propagate the refinement from elements meeting the user specified criterion to their neighbors are

explained in Propagation of Refinement, 37.

Refinement by Regular Subdivision

Mesh refinement in MD Nastran R3 is accomplished by the so-called regular or isotropic subdivision of

a subset of parent elements into offspring or children sub-elements. Figure 2-6 illustrates the subdivision

rules for individual elements of the different types:

Table 2-1 First two iterations of the adaptive mesh refinement loop

First Iteration Second Iteration

1. Initial Mesh

2. Analysis ... ...

3. Mark for refinement

4. Refine

5. Transfer ...



16

Figure 2-6 Regular (isotropic) subdivision rules for individual elements of different types

Line Elements

CTRIA*

CQUAD*

CHEXA

CTETRA

CPENTA

17CHAPTER 2

Adaptive Meshing

These subdivision rules are called regular or isotropic because all edges in the boundary of a refined

element are subdivided into the same number of segments (two) as opposed to, for example, the

subdivision of a quadrilateral or a triangular element by bisection (Figure 2-7).

Figure 2-7 Isotropic vs. Anisotropic subdivision of a quadrilateral and a triangular element

For a tetrahedron, there are three possible regular subdivision schemes into eight children tetrahedra.

These three schemes are obtained as follows: first, each edge is bisected. This defines four corner

tetrahedra and an internal octahedron. Then, the latter might be subdivided into four additional tetrahedra

in three different ways, according to each of its three diagonals.

In MD Nastran, the diagonal selected to subdivide the internal octahedron is the one connecting node 7

(mid-node of the edge 1-3) to node 9 (mid-node of edge 2-4) as depicted in Figure 2-8. Furthermore,

corner nodes of the children tetrahedra are numbered according to the special rule illustrated in

Figure 2-8. This special labeling convention of nodes along with the selection of the diagonal connecting

nodes 7 to 9 to subdivide the inner octahedron ensures minimization of element distortion with

successive refinements.

Figure 2-8 Labeling convention for corner nodes of children tetrahedra



18

During subdivision, the following properties are preserved:

1. Preservation of element type: Quadrilateral elements are subdivided into quadrilateral elements,

triangular elements into triangular elements, etc., as opposed to, for example, subdivision of a

quadrilateral into triangles or subdivision of a triangle into quadrilaterals (Figure 2-9).

Figure 2-9 Preservation of element type during subdivision

2. Preservation of element orientation (Figure 2-10): The outlining nodes of children elements will

be listed in clockwise (respectively counterclockwise) order when the father element have been

defined in clockwise (respectively counterclockwise) order.

Figure 2-10 Preservation of orientation during subdivision

3. Preservation of interpolation order: Linear (4-noded) quadrilateral elements (CQUAD4,

CQUADR) will be subdivided into four 4-noded quadrilateral elements whereas quadratic (8-

noded) quadrilateral elements (CQUAD8) will be subdivided into four quadratic (8-noded)

quadrilateral elements (Figure 2-11). The linear case requires the creation of 5 new grid points

whereas the quadratic case demands the creation of 13, two on each edge, two on each internal

edge and one in the centroid of the element.

Figure 2-11 Preservation of interpolation order in quadrilateral elements during subdivisions

19CHAPTER 2

Adaptive Meshing

Similarly, linear (3-noded) triangular elements (CTRIA3, CTRIAR) will be subdivided into four

linear (3-noded) triangular elements whereas quadratic (6-noded) triangular elements will be

subdivided into four quadratic triangular elements (Figure 2-12). The linear case requires the

creation of 3 new grid points whereas the quadratic case involves the creation of 9 new grid

points, two on each edge and one on each internal edge.

Figure 2-12 Preservation of interpolation order in triangular elements during subdivision

The same rule applies to 3D elements (CTETRA, CPENTA, CTRIA), i.e., a linear tetrahedron

(4-noded), pentahedron (6-noded) or hexahedron (8-noded) will be respectively subdivided into

eight linear tetrahedra, pentahedra or hexahedra requiring respectively the creation of 6, 12 and

19 new grid points (Figure 2-13).

Figure 2-13 Preservation of interpolation order in 3D linear elements during subdivision



20

Equivalently, a fully quadratic tetrahedral (10 nodes), pentahedral (15 nodes) and hexahedral (20

nodes) element will be subdivided into eight fully quadratic tetrahedra, pentahedra or hexahedra.

This requires the creation of two new grid points per external and internal edge, five new grid

points per quadrilateral face and one new grid point in the bulk of the hexahedral element, a total

of 38 new grid points for CTETRA, 48 new grid points for CPENTA and 55 new grid points for

CHEXA.

For incomplete quadratic 3D elements, i.e., 3D elements created with a number of grid points

greater than 4 and less than 10 for CTETRA, greater than 6 and less than 15 for CPENTA and

greater than 8 and less than 20 for CHEXA, only a minimum number of new grid points will be

created during subdivision to avoid the generation of redundant degrees of freedom. For example,

an hexahedron defined with 10 grid points (two quadratic edges and 6 linear edges) will be

subdivided into eight quadratic hexahedra with only a few quadratic edges and new grid points

(Figure 2-14).

Figure 2-14 A variable number of new grid points is created during subdivision of incomplete

quadratic 3D elements

Location of New Grid Points

In linear elements, new edge nodes are placed at the mid-side of the (straight) edge. Similarly, new face

nodes of linear quadrilateral surface elements (CQUAD4, CQUADR) or quadrilateral faces of linear

pentahedral and hexahedral elements (6-noded CPENTA or 8-noded CHEXA) or new internal nodes of

linear tetrahedral or hexahedral elements (4-noded CTETRA or 8-noded CHEXA) are placed at the

baricenter of the surface element, face or 3D element, i.e., at the position obtained by averaging the

position of the corner nodes (Figure 2-15).

Figure 2-15 Location of new mid-edge and mid-face nodes in a linear element. Mid-edge

nodes are placed at the mid-side of the straight edge, mid-face nodes at the

baricenter of the face and internal nodes at the baricenter of the element.

21CHAPTER 2

Adaptive Meshing

In quadratic elements new nodes are positioned by making use of the isoparametric mapping. The

parametric space of the element is uniformly bisected and mid-edge and mid-face nodes are mapped back

to the physical space using the element (isoparametric) shape functions (Figure 2-16).

Figure 2-16 Uniform subdivision of the parametric domain and resulting subdivision in

physical space

No special provisions are taken during refinement of very distorted quadratic elements. In this case, the

user should expect distorted children elements (Figure 2-17).

Figure 2-17 Subdivision of a distorted quadratic (quadrilateral) element

The default method of placement of mid-edge nodes on mid-side edges might render inaccurate solutions

when the initial mesh provided by the user is very coarse and the boundary of the domain of analysis is

therefore poorly approximated.



22

For example, consider the analysis of a circular planar shell subjected to compression and initially

discretized with very few elements as illustrated in Figure 2-18. If mid-edge nodes are placed on the mid-

side of edges, inaccurate results are obtained because the circular domain remains poorly approximated

during all mesh refinement cycles.

Figure 2-18 Compression of a circular planar shell. Default location for mid-edge nodes is

on the mid-side of edges

To address this inaccuracy, the user can request to place mid-edge nodes on a smooth approximation of

the analysis domain boundary interpolated from the initial mesh.

Given the initial mesh, a smooth curve is interpolated using the nodes located on the mesh boundary to

approximate the analysis domain boundary. Then, mid-edge nodes are projected onto this smooth

approximation. Figure 2-19 depicts this alternative for the case of the compressed circular shell example

shown in Figure 2-18.

23CHAPTER 2

Adaptive Meshing

Figure 2-19 Compression of a circular planar shell. Projection of mid-edge nodes onto a

smooth approximation of the geometric boundary interpolated from the initial

mesh

It’s important to note that the smooth approximation of the boundary is computed using the boundary

nodes of the initial mesh provided by the user and that the accuracy of this approximation is determined

by the coarseness of this initial mesh.

The success and accuracy of this smooth boundary approximation depends also on appropriate detection

of corners and edges. In order to identify corners and edges, the initial mesh is preprocessed using an

automatic Geometric Feature Detection Algorithm, see Detection of Geometric Features and Material

and Superelement Interfaces, 49.

The alternative method of projecting edge-nodes onto a smooth approximation of the mesh boundary is

available only for edge nodes belonging to edge-boundaries of 2D and 3D geometries. However, no

repositioning for edge and face nodes belonging to 3D surfaces and face-boundaries of 3D geometries

is supported for the current release.

Hanging Nodes and Multipoint Constraints on Hanging Nodes

When an element is refined (subdivided) but its adjacent elements are not refined a non conforming mesh

is generated. Nodes created on the boundary between a refined and a non refined element are referred to

as hanging-nodes (Figure 2-20).



24

Figure 2-20 Hanging node

Displacement on hanging nodes need to be constrained or tied to the displacement of corner nodes to

avoid a discontinuity in the displacement field, as illustrated in Figure 2-21:

Figure 2-21 Displacement field over an incompatible mesh created due to the presence of

an unconstrained hanging node

In MD Nastran R3, all degrees of freedom (1 to 6) associated to a hanging node are automatically

constrained using internal Multipoint Constraint (MPC) equations derived from the isoparametric

mapping.

Figure 2-22 and Figure 2-23 depicts the MPC equation for hanging nodes laying respectively on a linear

and a quadratic edge. Notice that in the linear case, the MPC equation ties each component of the hanging

node displacement with those corresponding to the corner nodes 1 and 2 whereas in the quadratic

case each components of the hanging node displacements needs to be tied to the corresponding

displacements of both the corner nodes 1, 2 and the mid-edge node 3.

Figure 2-22 Constraint equations for hanging nodes laying on a linear edge

UM

UM

25CHAPTER 2

Adaptive Meshing

Figure 2-23 Constraint equations for hanging nodes laying on a quadratic edge

Figure 2-24 and Figure 2-25 show the MPC equations for hanging nodes laying respectively on a linear

and a quadratic face. In the linear case, the MPC equation ties each component of the hanging node

displacement with those corresponding to the corner nodes 1, 2, 3 and 4 whereas in the quadratic case,

each component of the hanging node displacements needs to be tied to the corresponding displacements

of both the corner nodes 1, 2, 3, 4 and the mid-edge nodes 5, 6, 7 and 8.

Figure 2-24 Constraint equation for hanging nodes laying on a linear face

Figure 2-25 Constraint equation for hanging nodes laying on a quadratic face

An example illustrating the need of enforcing constraints on hanging nodes is depicted in Figure 2-26,

Figure 2-27, and Figure 2-28 concerning the deformation of a cylindrical shell subjected to a central



26

concentrated load. Figure 2-26 shows the finite element mesh after the third iteration in the adaptive mesh

refinement loop along with the hanging nodes involved in MPC equations. Figure 2-27 and Figure 2-28

compare the deformed configuration and von Mises stresses obtained when the hanging node constraints

are enforced (left) or not enforced (right). Notice when the hanging node constraints are not enforced, an

incompatible configuration is obtained.

Figure 2-26 Multipoint constraints on hanging nodes

Figure 2-27 Compatible (left) and incompatible (right) deformations obtained when

multipoint constraints are enforced (left) or not (right)

27CHAPTER 2

Adaptive Meshing

Figure 2-28 Compatible (left) and incompatible (right) von Mises stresses obtained when

multipoint constraints are enforced (left) or not (right)

Selection of Elements to Refine

Elements that will be refined during a given iteration in the adaptive loop are selected in two steps; first,

all elements meeting the user specified adaptivity criterion are searched for and scheduled for

refinement. Second, some of the elements adjacent to the latter are also scheduled for refinement

according to a set of implicit propagation rules. If no elements meeting the user specified criterion are

found, the adaptivity loop is terminated.

MD Nastran R3 currently supports four refinement criteria (see Refinement Criteria, 28):

1. Error indicator based criterion

2. Nodes within a spherical spatial region criteria

3. Nodes within an orthogonal spatial region criteria

4. Nodes in contact criteria

The set of implicit refinement propagation rules are the following (see Propagation of Refinement, 37):

1. Horizontal propagation (2-to-1 rule)

2. Horizontal propagation from inner to outer children in triangular and tetrahedral elements

3. Vertical propagation

4. Propagation across superelement boundaries.



28

Refinement Criteria

The mesh refinement criteria available in MD Nastran R3 are the following:

Error Indicator Based Criterion

In this case an error indicator is computed over each element ‘e’ in the finite element mesh. Then, an

element is refined if

where f is a scalar factor such that and chosen by the user (as part of the Bulk Data entry

HADACRI) and is the quadratic mean of the error indicator defined as:

with N the total number of elements in the element set where element ‘e’ belongs, Thus, an element is

refined if its estimated error is larger than a fixed percentage of the quadratic mean.

Figure 2-29 schematically depicts a mesh with its corresponding elemental error indicator (blue) and

quadratic mean (red). Only those elements with error indicator above a fixed percentage of the quadratic

mean will be refined.

Figure 2-29 Error indicator distribution over a 1-D mesh (blue) with N elements and

corresponding quadratic mean (red). Only those elements for which is

above a fixed percentage of will be refined.

The factor f is specified by the user in the F1 field of the HADACRI Bulk Data entry (see User Interface,

55 or the Bulk Data entry HADACRI (p. 1733) in the MD Nastran Quick Reference Guide).

The error indicator is a scalar, elemental magnitude that provides a relative measure of the

discretization error, i.e., the error between the finite element solution and the analytical solution of the

underlying differential equations of the problem under analysis. It is computed using the grid point

stresses and element stress discontinuity following the procedure utilized by the ELSDCON Case Control

Ee

Ee

2fE

2≥

0 f 1≤ ≤

E

E2 1

NJJJJ Ee

2

e 1Z

N

∑Z

Ee

Ee

29CHAPTER 2

Adaptive Meshing

command and described in the MD Nastran Reference Manual, Section 8.3. This procedure can be

summarized as follows:

• Let be the weighted average over all elements ‘e’ concurrent to a given node

‘a’ of each component ‘ij’ of the grid point stresses where is a weighting factor assigned

to element ‘e’ and Na is the number of elements connected to the given node ‘a’.

• An estimate of the error in a particular component of stress ‘ij’ at a grid point ‘a’ is then be

computed as

Averaging the latter over the different stress components, ‘ij’, over the different shell fibers (for shell

elements) and over the different grid points ‘a’ connected by a given element ‘e’ the elemental, scalar

error indicator is obtained.

Figure 2-30 shows an example using the error indicator based adaptivity criterion involving the analysis

of a 2D mode-I fracture specimen. Notice that this criterion tends to cluster the refinement near areas of

stress concentration. This is due to the fact that stress gradients (and therefore element stress

discontinuities and error indicators) are considerably higher in those zones than in the rest of the mesh.

Figure 2-30 Analysis of a 2D mode-I fracture specimen

This refinement criterion is available for any of the surface or volume elements, namely CTRIA3,

CTRIAR, CTRIA6, CQUAD4, CQUADR, CQUAD8, CTETRA, CPENTA, CHEXA. It is not available

σaij Wa

eσaij

e

e 1Z

Na

∑Z

σaije

We

Eaij

2Wa σaij

eσaijÓ( )

2

e 1Z

N

∑Z

Ee



30

however for the family of line elements. The latter might be subdivided either by using any other criteria

of the remaining refinement criterion, or because they are connected to the boundary of a surface or

volume element (see Vertical Propagation, 40).

Elements Within a Spatial Spherical Region Criterion

In this criteria, the user defines a spherical region in space by specifying its center in basic coordinate

system and its radius R. Then, all elements with at least one node with basic coordinates

within the spherical region (i.e., such that || will be refined.

Figure 2-31 shows the mesh obtained in an example involving a 3D cylindrical body using this criterion.

Figure 2-32 shows a detail of the mesh obtained after the fourth refinement cycle along with the spatial

spherical region selected for refinement.

X0Y0Z0

, ,( )

X Y Z, ,( ) X Y Z, ,( ) X0Y0Z0

, ,( )Ó R<( )

31CHAPTER 2

Adaptive Meshing

Figure 2-31 Sequence of meshes obtained on a 3D cylindrical body using the “elements

within a spherical region” adaptivity criterion



32

Figure 2-32 Mesh obtained after the third refinement cycle of 3D cylindrical body using the

“elements within a spherical region” adaptivity criterion. Only the bottom half of

the cylinder is shown in the right picture.

Elements Within a Spatial Orthogonal Region Criterion

In this refinement criterion, the user defines an hexahedral region in space or box aligned with the basic

coordinates system by specifying the basic coordinates of opposite corners and of

the box. Then, all elements with at least one node with basic coordinates within the specified

hexahedral region (i.e., such that , and ) will be refined.

Figure 2-33 shows the mesh obtained in the same 3D cylindrical body used in Figure 2-31 but with the

nodes within a box refinement criterion. A detail of the mesh obtained after the third refinement along

with the orthogonal refinement region is shown in Figure 2-34.

X0Y0Z0

, ,( ) X1Y1Z1

, ,( )

X Y Z, ,( )X0

X X1

≤ ≤ Y0

Y Y1

≤ ≤ Z0

Z Z1

≤ ≤

33CHAPTER 2

Adaptive Meshing

Figure 2-33 Sequence of meshes obtained on a 3D cylindrical body using the “elements

within an orthogonal region” adaptivity criterion



34

Figure 2-34 Mesh obtained after the third refinement cycle of 3D cylindrical body using the

“elements within an orthogonal (box) region” adaptivity criterion. Only the

bottom half of the cylinder is shown in the right picture.

Elements in Contact Criterion

In this criterion, all touching elements with at least one node involved in contact and touched elements

with at least one face in contact will be refined. MD Nastran R3 supports glued contact, rigid-to-

deformable body contact, and deformable-to-deformable body contact situations.

Figure 2-35 shows the initial mesh of two 3D deformable bodies composed exclusively of linear

hexahedral elements and brought into contact after a vertical displacement is applied on the top body.

Figure 2-35 Two 3D deformable bodies in contact

Figure 2-36 shows the sequence of meshes obtained during the mesh refinement process.

35CHAPTER 2

Adaptive Meshing

Figure 2-36 Sequence of meshes during adaptive mesh refinement process using the

“Nodes in Contact” criterion on two 3D deformable bodies in contact

Figure 2-37 and Figure 2-38 depict the sequence of meshes obtained during mesh refinement using the

“Nodes in Contact” refinement criterion in a situation involving 3D rigid-to-deformable contact with 8-

noded CHEXA elements and 3D glue contact between two deformable bodies with 10-noded CTETRA

elements respectively.



36


“Nodes in Contact” criterion on a Rigid-to-Deformable body contact setting

37CHAPTER 2

Adaptive Meshing


“Nodes in Contact” criterion on a glue contact problem

Propagation of Refinement

Once elements meeting the refinement criteria are scheduled for refinement, the refinement is

propagated to some of their adjacent elements according to a set of implicit propagation rules. These

rules are the following:

Horizontal Propagation (2 to 1 rule)

The first refinement propagation rule is the 2-to-1 rule. The 2-to-1 rule restricts the number of hanging

nodes on each edge to one, see Hanging Nodes and Multipoint Constraints on Hanging Nodes, 23. To this

end, all the edge-neighbors of elements scheduled for refinement are selected for refinement as well. This

is illustrated in Figure 2-39. When one element scheduled for refinement (green element) is refined, two

hanging nodes are created on its adjacent edges. To restrict the number of hanging nodes to one the

refinement is propagated to its edge-neighbors (yellow elements).



38

Figure 2-39 The green element has been scheduled for refinement due to the user specified

refinement criteria. The refinement must be propagated to the edge neighbors

(yellow elements) to avoid the creation of more than one hanging node per

edge.

Notice that in 3D meshes, there might be more than one edge-neighbor per edge as illustrated in

Figure 2-40.

39CHAPTER 2

Adaptive Meshing

Figure 2-40 Propagation of refinement from an element meeting the user’s specified

refinement criterion (green element) to its edge-neighbors (yellow elements) to

enforce the 2-to-1 propagation rule. In 3D, there might be more than one

neighbor per edge.



40

Horizontal Propagation in Triangles and Tetrahedra

Consider a refined triangular or tetrahedral element. If the internal triangle or internal tetrahedra are

scheduled for a second refinement, then the external triangle or tetrahedral are automatically selected for

refinement as well. This is to avoid the creation of redundant degrees of freedom on internal edges or

faces that would otherwise be constrained with no net gain of mesh resolution (Figure 2-41).

Figure 2-41 If the internal (green) triangle of a refined triangular element is further refined,

no net addition of degrees-of-freedom is obtained (top row). To avoid this

redundancy, the refinement is automatically propagated to all external (yellow)

triangles of the refined triangular element (bottom row).

Vertical Propagation

Consider a line element (CBEAM, CBEAM3, CBEND, CBAR, CONROD, CROD, CTUBE, CVISC)

attached to an edge of a surface element (CQUAD4, CQUADR, CQUAD8, CTRIA3, CTRIAR,

CTRIA6) of a surface element attached to the face of a 3D element (CTETRA, CPENTA, CHEXA).

Then, if the element of higher dimensionality is scheduled for refinement, then the element of lower

dimensionality attached to its face is automatically selected for refinement as well (Figure 2-42).

41CHAPTER 2

Adaptive Meshing

Figure 2-42 The refinement is automatically propagated from elements of higher

dimensionality selected for refinement (green) to elements of lower

dimensionality attached to their boundary (yellow).

The same rule applies in the opposite direction: if an element of lower dimensionality attached to the

boundary of another element of higher dimensionality is scheduled for refinement, then the latter is

automatically selected for refinement (Figure 2-43).

Figure 2-43 The refinement is automatically propagated from elements of lower

dimensionality selected for refinement (green) and attached to elements of

higher dimensionality (yellow) to the latter.



42

Propagation of Refinement Across Partitioned Superelement Boundaries

Hanging nodes cannot occur at partitioned superelement boundaries because their corresponding degrees

of freedom cannot belong simultaneously to two different Degree-of-Freedom Sets (see Degree-of-

Freedom Set Definitions (Ch. 7) in the MD Nastran Quick Reference Guide). In order to prevent this

condition, the refinement is automatically propagated across superelement boundaries. In this way,

hanging nodes are moved from the boundary to the interior of the affected superelements (Figure 2-44).

Figure 2-44 When elements on a given superelement are scheduled for refinement (green

elements), the refinement is propagated into the neighboring superelement

(yellow elements) to avoid the creation of hanging nodes on the superelement

boundaries.

Transference of Analysis Data Between Unrefined and Refined Meshes

Once a refined mesh is obtained by subdividing selected elements from the previous mesh, analysis data

must be communicated or transferred from the old mesh to the new mesh in order set up the next analysis

on the new mesh. Analysis data to transfer includes element properties, shell thicknesses, material

orientations, pressure loads and permanent and single point constraints (displacement boundary

conditions). The rules to transfer this data are the following:

Transference of Element Properties

Children elements created after refinement inherit their parent’s property ID.

In surface elements (CQUAD4, CQUADR, CQUAD8, CTRIA3, CTRIAR, CTRIA6) with nonuniform

shell thicknesses, the thickness for corner nodes in the children elements are linearly interpolated from

the corner nodes of the parent element (Figure 2-45).

43CHAPTER 2

Adaptive Meshing

Figure 2-45 Transference of non-uniform shell thickness data from the parent to the children

elements

Furthermore, children elements inherit the material orientation angle (see THETA field on the CQUAD4,

CQUADR, CQUAD8, CTRIA3, CTRIAR, CTRIA6 entries). The orientation angle THETA for children

element is computed using the equations given in Figure 2-46. This takes into account that THETA is

defined as the angle between the edge joining nodes 1 and 2 of the element and the material direction

and, therefore, might not be uniform within children elements. Notice that uniform material orientation

does not imply uniform angle THETA.



44

Figure 2-46 Transference of material orientation angle from the parent of the children

elements. The blue arrow points in the direction of the material orientation which

is conserved during refinement. Notice that this does not imply the conservation

of the THETA angle.

Transference of Distributed Loads and Concentrated Forces

Pressure loads (PLOAD, PLOAD2, PLOAD4) distributed over parent elements are automatically

redistributed over children elements.

Thus, a uniform pressure load distributed over a quadrilateral surface element (PLOAD, PLOAD2) is

copied over children elements and redistributed with same magnitude and direction over their smaller

area.

45CHAPTER 2

Adaptive Meshing

Similarly, the magnitude of non-uniform pressure loads distributed over surface elements faces of 3D

elements or faces of surface elements (PLOAD4) are not just copied over but interpolated linearly from

corner pressures (Figure 2-47) and applied to children elements with the same direction.

Figure 2-47 Transference of PLOAD4 applied to the face of a 3D (CHEXA) element. Mid-

edge and mid-face pressures are linearly interpolated from corner values

No special provisions are taken regarding transference of concentrated forces or moments. Thus, no

concentrated loads will be created or new grids created for refinement but just carried over existing grid

points in the old mesh to the same grid points in the new mesh.

Transference of Displacement Coordinate System, Displacement Boundary Conditions and Constraints

Displacement coordinate systems, permanent single point constraints, single point constraints and

multipoint constraints on the new grid point c created during refinement are internally enforced

according to the following rules:

• If the coordinates systems defined on corner grid points (specified on the CD field in the GRID

Bulk Data entry) are identical, then the same displacement coordinate system is assigned for a

new mid-edge or mid-face node created during refinement. Furthermore, for edges of surface or

volume elements, each degree of freedom associated to the new mid-node created on the edge is

either permanently constrained (assigned to degree-of-freedom set SG), or explicitly constrained

via an internal Single point constrain SPC (assigned to the degree-of-freedom set SB) or

constrained to corner nodes via an internal Multipoint Constraints M (see Degree-of-Freedom

Set Definitions (Ch. 7) in the MD Nastran Quick Reference Guide) depending upon the degree-

of-freedom set where the corner nodes.

For faces of volume elements, each degree-of-freedom of a new mid-face node created during

refinement is also either permanently constrained, or explicitly constrained (via internal SPC) or

tied to corner nodes (via internal MPC) according to the permanent constraints, enforced

displacement or multipoint constraints defined on the corner nodes.



46

The specific constraints to be enforced internally for mid-edge or mid-face nodes are:

• If permanent constraints have been defined on a degree of freedom i at both corner nodes, then

a permanent constraint is also assigned to the degree of freedom i at the mid-edge of mid-face

node. For example (Figure 2-48), if both corner nodes a and b on an edge have been

permanently constrained in all degrees-of-freedom (by defining and

on the PS field in the GRID Bulk Data entry), then node c will be also

constrained permanently in all degrees-of-freedom (by defining internally).

Figure 2-48 Coordinate systems ( and ) defined on corner node a and b (using the

field in the Grid Bulk Data entry) must match in order for constraints to be

enforced on mid-edge node c. Permanent constraints (PS field on the GRID

Bulk Data entry) on each degree-of-freedom are then carried over the mid-edge

node.

• If single point constraints have been defined on a degree of freedom i for all corner nodes, then

the degree of freedom i on the mid-edge or mid-face node will be tied internally to the corner

nodes according to the same multipoint constraint equations used for hanging nodes on

straight edges (see Hanging Nodes and Multipoint Constraints on Hanging Nodes, 23,

Figure 2-22 and Figure 2-24). Notice that this is equivalent to imposing an SPC on the mid-

edge node, degree-of-freedom i, with a value for enforced displacement averaged from the

value at corner nodes. For example, if a displacement with value along direction 1 is

enforced on node a (by defining an SPC on node a, direction 1) and a displacement in the same

direction with value is enforced on node b (by defining another SPC on node b, direction

1), then a multipoint constrain for node c (direction 1) is internally defined such that

(Figure 2-49).

PSa 123456Z

PSb 123456Z

PSc 123456Z

CDa CDb

CD

Ua

Ub

Uc 1 2⁄ Ua UbH( )Z

47CHAPTER 2

Adaptive Meshing

Figure 2-49 If displacement is enforced on a given degree-of-freedom on corner nodes a

and b (using SPC or SPC1 entries), then a multipoint constraint that ties the

mid-edge node c with both corner nodes is internally enforced, provided that

displacement coordinate systems for all corner nodes coincide (CD field in the

GRID entry).

• The same multipoint constraint equation is applied on the mid-edge node c (in a given

direction i) if one of the corner nodes has been constrained permanently and the other corner

node has been constrained via a Single Point Constraint (SPC) on the same direction i. For

example, if a displacement with value along direction 1 is enforced on node a (by defining

an SPC on node a, direction 1) and a permanent constraint in the same direction has been

enforced for corner node b (by defining on the PS field in its GRID Bulk Data entry),

then a multipoint constraint for node c (direction 1) is internally defined such that

(Figure 2-50).

Figure 2-50 If a displacement is enforced on a given degree-of-freedom on corner node a

(using SPC or SPC1 entries) and a permanent constraint is enforced on the

same degree-of-freedom on corner node b (PS=1 on its GRID Bulk Data entry),

then a multipoint constraint that ties the mid-edge node c with both corner

nodes is internally enforced, provided that displacement coordinate systems for

all corner nodes coincide (CD field in GRID entry).

Ua

PSb 1Z

Uc 1 2⁄ Ua UbH( ) 1 2⁄ Ua 0H( ) 1 2⁄ UaZ Z Z



48

• Similarly, the same multipoint constraint is applied on the mid-edge or mid-face nodes (in a

given degree-of-freedom i) if some of the corner nodes are involved in a permanent constraint

(PS field in the GRID Bulk Data entry) or single point constraint (SPC or SPC1 Bulk Data

entry) and the others corner nodes are involved in a multipoint constraint (MPC Bulk Data

entry) on the same degree of freedom i.

• If the corner nodes are involved in contact, either as touching nodes or touched element faces

or edges, then the mid-edge nodes are regarded as nodes potentially in contact. Therefore,

constraints on any of the degrees-of-freedom associated to the latter are determined by the

contact detection algorithm.

The set of relations just outlined is summarized in the following table:

• If the displacement coordinate system defined on corner nodes on an edge or face are different,

then the displacement coordinate system for the mid-node on the edge or face is set to the basic

coordinate system. Furthermore, no constraints are enforced on any of its associated degrees-of-

freedom independently of the constraints that might have been imposed on corner nodes

(Figure 2-51).

Figure 2-51 If coordinate systems ( and ) defined on corner nodes a and b (using

the CD field in the GRID Bulk Data entry) are different then the mid-edge node

c is left free and its displacement coordinate system is set to the basic.

corner node a corner node b mid-node c

SG SG SG

SB SB M

SG

SB

SB

SG

M

SG or SB

M

M

SG or SB

M

Node in contact Node in contact Node potentially in contact

CDa CDb

49CHAPTER 2

Adaptive Meshing

Detection of Geometric Features and Material and Superelement Interfaces

Prior to the initiation of the adaptive mesh refinement loop, the initial mesh provided by the user is

preprocessed using an automatic Geometric Feature and Material interface Detection Algorithm aimed

to identify:

• Geometric features such as:

• Sharp corners and edges

• Non-manifold edges and vertices, i.e., edges joining more than two surfaces (in 3D) or

vertices joining more than two curves in 2D or 3D.

• Other interfaces such as:

• Interfaces between mesh regions with different property IDs.

• Interfaces between superelements.

Detection of Geometric Features

The Geometric Feature Detection Algorithm identifies edges and corners by comparing the angle

between each pair of adjacent elements with the “Feature Angle” VARPHI. The feature angle is a scalar

parameter specified by the user (PARAM,VARPHI) that defines how sharp a mesh edge or vertex should

be in order to be considered as a geometric feature.

More precisely, face outward normal vectors of each pair of adjacent mesh faces and the edge

oriented tangents of each pair of adjacent mesh edges are computed (Figure 2-52) by the geometric

feature detection algorithm. If the angle between and for mesh faces, or between and for

mesh edges is larger than the feature angle VARPHI then the common edge or vertex will be considered

a splitting edge or vertex where surfaces or lines are broken and a geometric feature is thus defined.

Figure 2-52

Mesh faces and elements are preprocessed to ensure consistent orientation and that the appropriate sign

of face normal vectors and edge tangents will be accounted for during the computation of their mutual

angle.

N1N2

,

T1T2

,

N1

N2

T1

T2



50

Figure 2-53, Figure 2-54, Figure 2-55, and Figure 2-56 show the edges identified by the Geometric

Feature detection algorithm on a surface mesh (Figure 2-53) and three 3D volume meshes (Figure 2-53,

Figure 2-54, Figure 2-55).

Figure 2-53 Edges detected by the geometric feature detection algorithm in a surface mesh

of triangular elements of a mechanical part with a non-manifold edge

Figure 2-54 Edges detected by the geometric feature detection algorithm in a 3D hexahedral

mesh of a cylindrical body

51CHAPTER 2

Adaptive Meshing

Figure 2-55 Edges detected by the geometric feature detection algorithm in a 3D

hexahedral mesh of an engine cup

Figure 2-56 Edges detected by the geometric feature detection algorithm in a 3D

hexahedral mesh of an engine cylinder head

Adequate identification of geometric features (by appropriately adjusting the feature angle VARPHI) is

essential to ensure the convergence of the mesh refinement process to expected results.

Thus, if the error indicator based refinement criterion is selected and sharp edges are not properly

identified by the geometric feature detection algorithm, the refinement might cluster indefinitely in the

neighborhood of the undetected sharp edges (Figure 2-53). This anomaly occurs mainly on sharp

intersections between shells due to the fact that the error indicator indirectly measures membrane stress

jumps between adjacent elements and the latter might be very high due to the abrupt change in shell

normal directions at sharp intersections.

Figure 2-57 and Figure 2-58 depict two orthogonal planar shells joined on a common edge and subjected

to a vertical displacement on the top. The feature angle must be chosen smaller than in order for

the joining edge to be detected and the error estimator to ignore (or filter) the large membrane stress

discontinuity across this edge (Figure 2-57). If the feature angle is not appropriately chosen, then the

π 2⁄



52

geometric feature algorithm will fail to identify the joining edge and the mesh refinement will cluster in

its neighborhood (Figure 2-58).

Figure 2-57 An adequate value of the VARPHI parameter ( in this case) will ensure that

the sharp edge shared by both planar shells is detected by the geometric

feature detection algorithm and the big membrane stress jumps occurring at the

edge are filtered out.

Figure 2-58 The geometric feature detection algorithm fails to detect the sharp edge shared

by both planar shells because the VARPHI parameter is too large. As a

consequence, the big membrane stress jumps occurring at the edge are not

filtered out and the refinement clusters in the neighborhood of the sharp edge.

The adequate identification of corners is also required to improve the smooth approximation of the

analysis domain boundary constructed by interpolating the mesh boundary nodes and used as a method

to place new mid-edge nodes during refinement (see Location of New Grid Points, 20) alternative to the

default location at the mid-side of the edge.

π 4⁄

53CHAPTER 2

Adaptive Meshing

Figure 2-59 and Figure 2-60 compare the two edge-node placement methods (mid-side placement and

projection of mid-edge nodes onto a smooth approximation of the boundary) in an example involving a

2D treble shaped planar shell subjected to compression. The boundary of this mesh exhibits three sharp

corners located at the intersection of each pair of circular leaves. The mesh is refined everywhere

(uniform refinement). This is accomplished by selecting the “nodes within a spatial sphere” refinement

criteria (see Refinement Criteria, 28) with a spherical refinement region big enough to contain the whole

mesh.

Figure 2-59 Mid-edge nodes are placed in the mid-side of edges



54

Figure 2-60 Projection of mid-edge nodes onto a smooth approximation of the geometric

boundary interpolated from the initial mesh

Notice that the three sharp corners are appropriately detected by the Geometric Feature Detection

Algorithm and kept as hard points during the mesh refinement process. By contrast, sharp corners might

become smeared out if the geometric feature detection algorithm is not successful due to an inadequate

selection of the feature angle (parameter VARPHI) (Figure 2-61).

Figure 2-61 Corners might be smeared out if they are not appropriately detected by the

automatic geometry feature detection algorithm. Corner detection can be

controlled by the user adjusting the VARPHI parameter.

55CHAPTER 2

Adaptive Meshing

Detection of Material and Superelement Interfaces

Interfaces between mesh regions with different properties IDs or superelement IDs are also automatically

detected during the preprocessing phase prior to the beginning of the adaptive mesh refinement loop.

Different properties or superelement may reference different materials or different shell thicknesses.

Therefore, stress of different order of magnitude are expected in areas with different properties or

superelements. This type of discontinuities must be filtered out by the error indicator (which averages

stress jumps across interelement boundaries) in order to be able to capture the discontinuities introduced

by the finite element discretization exclusively.

User Interface

Local adaptive mesh refinement is activated by the new Case Control command HADAPT and

controlled by the two new Bulk Data entries HADAPTL and HADACRI along with the optional feature

angle parameter VARPHI (Figure 2-62).

• The Case Control command HADAPT must reference the Bulk Data entry HADAPTL.

• The Bulk Data entry HADAPTL provides an interface to control the number of iterations in the

adaptive mesh refinement loop (REPEAT field), the refinement criteria (CRITID field), (see

Refinement Criteria, 28) which must reference a Bulk Data entry HADACRI, the refinement

region where the latter will be applied (WHEREMETHOD and WHEREID fields), the

placement method for new mid-edge nodes (SNAPMETHOD field), (see Location of New Grid

Points, 20), and the maximum levels of refinements permitted to any individual element in the

mesh (MAXLEVEL field).

• The Bulk Data entry HADACRI provides an interface for the specification of the refinement

criterion along with criteria specific parameters (see Refinement Criteria, 28).

• The parameter VARPHI, (feature angle) can be optionally adjusted when corners and edges are

not satisfactory detected to control how sharp a mesh edge or vertex should be in order to be

consider a split edge or vertex between two otherwise continuous curves or surfaces (see

Detection of Geometric Features and Material and Superelement Interfaces, 49).

• Different mesh refinement criteria might be applied to different refinement regions by

combining two pairs of Bulk Data entries HADAPTL and HADACRI. Furthermore, mesh

refinement can be driven by a combined error indicator based on stresses arising from multiple

load cases.



56

Figure 2-62 User interface to activate and control the new adaptive mesh refinement

capability

Selection of Refinement Region

Adaptive mesh refinement can be either requested for all elements in the mesh or for a subset of elements.

Two different mesh refinement subsets are supported:

• elements sharing a given property ID

• elements belonging to a given superelement.

The refinement region can be specified by the user via the pair of fields (WHEREMET,WHEREID) in

the HADAPTL Bulk Data entry as follows:

• If mesh refinement must be restricted to all elements sharing a given property identified with

property ID “PID”, then the WHEREMET field must be set to the keyword “PROP” and

WHEREID field must be set to the integer PID:

N 2 3 4 5 6 7 8 9 10

HADAPTL 1 101 PROP PID

57CHAPTER 2

Adaptive Meshing

• If mesh refinement must be restricted to a particular superelement identified with superelement

ID “SEID”, then the WHEREMET field must be set to the keyword “SUPER” and the

WHEREID field must be set to the integer SEID:

• Finally, if mesh refinement is requested for all elements in the mesh, then the field

WHEREMET must be set to the keyword “ALL” and the WHEREID field is ignored.

Consider by way of example a cylindrical shell subjected to a concentrated force as depicted in

(Figure 2-63). Two different properties (labeled with IDs 1 and 2) have been assigned to the top

and bottom halves of the shell. The concentrated force is applied on the center node of the shell

(located at the interface between both regions) and in the direction normal to the shell.

Figure 2-63 Pinched cylindrical shell. Different properties have been assigned to elements

in the top and bottom halves of the shell.

N 2 3 4 5 6 7 8 9 10

HADAPTL 1 101 SUPER SEID

N 2 3 4 5 6 7 8 9 10

HADAPTL 1 101 ALL



58

Mesh refinement using the error indicator based criterion have been requested for the bottom

half (property 2):

Figure 2-64 shows the sequence of meshes and deformed configuration obtained during the

adaptive mesh refinement process. Notice that even though the refinement is mainly confined to

the bottom half, it also propagates a few layers into the top half due to the 2-to-1 rule (see

Propagation of Refinement, 37).

Figure 2-64 Pinched cylindrical shell. Sequence of meshes and deformed configuration

obtained during the mesh refinement process.

Selection of Refinement Criterion

The refinement criterion that will be applied to the refinement region is selected by specifying a

refinement criteria ID on the CRITID field in the HADAPTL Bulk Data entry:

N 2 3 4 5 6 7 8 9 10

HADAPTL 1 101 PROP 2

HADACRI 101 1 0.9

N 2 3 4 5 6 7 8 9 10

HADAPTL 1 CRITID ALL

59CHAPTER 2

Adaptive Meshing

along with a corresponding HADACRI Bulk Data entry,

The particular refinement criteria is specified using the TYPE field in the HADACRI Bulk Data entry.

Four different refinement criteria (see Refinement Criteria, 28), can be selected, namely:

The fields F1 to F6 are parameters required to control each specific refinement criterion as follows:

• For the error indicator refinement criteria (see Error Indicator Based Criterion, 28), an element is

refined if the elemental error indicator is smaller than a fixed percentage f (with ) of

the quadratic mean of the error indicator, namely . In this case the field F1 is the factor f.

Fields F2 to F6 are ignored.

• For the nodes within a spherical spatial region criteria (see Elements Within a Spatial Spherical

Region Criterion, 30), an element is refined if any of its connected nodes lay within a spatial

spherical region with center (in basic coordinate system) and radius R. In this case

the fields (F1,F2,F3) specify the sphere center and the field F4 specifies the radius

R. Fields F5 and F6 are ignored.

N 2 3 4 5 6 7 8 9 10

HADACRI CRITID TYPE F1 F2 F3 F4 F5 F6

TYPE Name of Mesh Refinement Criterion

1 Error indicator based criterion

2 Element within a spatial spherical region criterion

3 Elements within a spatial cubic region criterion

4 Elements in contact criterion.

N 2 3 4 5 6 7 8 9 10

HADAPTL CRITID TYPE F1 F2 F3 F4 F5 F6

Error Indicator based criteria 1 f

Nodes within a sphere criteria

2 R

Nodes within a box criteria 3

Nodes in contact criteria 4

X0

Y0

Z0

X1

Y1

Z1

X2

Y2

Z2

Ee 0 f 1≤ ≤

Ee2

fE2

≥

X0Y0Z0

, ,( )

X0Y0Z0

, ,( )



60

• For the nodes within a spatial orthogonal region criteria (see Elements Within a Spatial

Orthogonal Region Criterion, 32), an element is refined if any of its connected nodes lay within a

spatial orthogonal region or box with diagonally opposed corners and (in

basic coordinate system). In this case the fields (F1, F2, F3) specify the box corner

and the fields (F4, F5, F6) specify the opposite corner . The coordinates

and must be chosen such that , and .

• For the nodes in contact criteria (see Elements in Contact Criterion, 34), elements connected to

nodes involved in contact are refined. In this case all fields F1 to F6 are ignored.

Different Criteria in Different Regions

Different refinement criteria might be applied to different refinement regions. This can be accomplished

by superposing two different HADAPTL entries with the same ID (and referenced from a unique Case

Control command HADAPT) and pointing to two different HADACRI entries on two different

refinement regions.

Consider by way of example a cylindrical body subjected to a concentrated forces as depicted in

(Figure 2-65). Two different properties (labeled with IDs 1 and 2) have been designated for the top and

bottom halves of the body. The nodes-within a spherical region criterion (TYPE=2) is requested for the

top half and the Nodes-within an orthogonal region criterion (TYPE=3) is demanded for the bottom half.

Figure 2-65 Two different refinement criteria are applied to two different refinement regions.

The top region is refinement criterion type 2 (nodes within a sphere) while the

bottom region is subjected to refinement criterion type 3 (nodes within a box).

The refinement regions are defined using different property IDs.

X1Y1Z1

, ,( ) X2Y2Z2

, ,( )

X1Y1Z1

, ,( )

X2Y2Z2

, ,( ) X1Y1Z1

, ,( )

X1Y1Z1

, ,( ) X1

X2

< Y1

Y2

< Z1

Z2

<

61CHAPTER 2

Adaptive Meshing

Two different HADAPTL entries (with the same ID) referencing two different HADACRI entries with

two different refinement regions (defined by two different pairs of values in the fields

(WHEREMET,WHEREID)) are thus required:

Each HADACRI requests different refinement criteria (TYPE=2 and TYPE=3) with different criteria

specific parameters.

Figure 2-66 shows the sequence of meshes obtained during the adaptive mesh refinement process. Notice

that even though the refinement is mainly confined to the specified refinement regions, some elements

away from these regions might also be refined due to the 2-to-1 rule (see Propagation of Refinement, 37).

SUBCASE 1

...

HADAPT = 1

BEGIN BULK

...

HADAPTL 1 4 111 PROP 1

HADAPTL 1 222 PROP 2

HADACRI 111 2 R

HADACRI 222 3

...

ENDDATA

X0

Y0

Z0

X1

Y1

Z1

X2

Y2

Z2



62

Figure 2-66 Sequence of meshes obtained with two different refinement criteria are applied

to two different refinement regions. The top region is subjected to refinement

criterion type 2 (nodes within a sphere) while the bottom region is subjected to

refinement criterion type 3 (nodes within a box).

63CHAPTER 2

Adaptive Meshing

Different Criteria in the Same Region

Different refinement criteria can be applied also to the same refinement region. As in the previous case,

two different pairs of HADAPTL and HADACRI entries are required. In this case both HADAPTL

entries should request refinement within the same refinement region (using identical specifications for

the fields WHEREMET and WHEREID). Both HADAPTL entries should be identified with the same

label (ID) and referenced from a unique case control entry HADAPT.

Consider for example the case of a cylindrical shell subjected to a concentrated force (Figure 11-5). Mesh

refinement is requested everywhere in the mesh (WHEREMET=ALL) using two different refinement

criteria: the error indicator based criterion (TYPE=1) and the nodes-within an orthogonal region criterion

(TYPE=3).

Two different HADAPTL entries (with the same ID) referencing two different HADACRI entries with

the same refinement regions are thus required:

Each HADACRI requests different refinement criteria (TYPE=1 and TYPE=3) with different criteria

specific parameters.

Figure 2-67 shows the sequence of meshes obtained during the adaptive mesh refinement process. Notice

that both refinement criteria are combined to produce one single refined mesh.

SUBCASE 1

...

HADAPT = 1

BEGIN BULK

...

HADAPTL 1 111 ALL

HADAPTL 1 222 ALL

HADACRI 111 1 f

HADACRI 222 3

...

ENDDATA

X1

Y1

Z1

X2

Y2

Z2



64

Figure 2-67 Different refinement criteria applied to the same refinement region

Combination of Subcases (SOL 101) or Static Steps (SOL 400) with Error Indicator Based Criterion

The error indicator is computed using the finite element stresses and measures indirectly the stress

discontinuity across interelement boundaries. When multiple load cases are defined, multiple finite

element stress solutions are obtained (one for each load case) and therefore, multiple instances of the

error indicator are computed.

In this case, the user can select any individual instance of the computed error indicator or any

combination of instances to create a refined mesh. To this end, multiple Case Control commands

HADAPT (one for each load case) referencing a single HADAPTL Bulk Data entry with its

corresponding HADACRI Bulk Data entry are required.

Consider by way of example the analysis of a cylindrical shell under the action of two different load

cases, each consisting of a concentrated force applied at different heights (Figure 2-68, Figure 2-69,

Figure 2-70). The error indicator might be computed using either the first load case only (Figure 2-68),

the second load case only (Figure 2-69), or the combination of both load cases (Figure 2-70).

65CHAPTER 2

Adaptive Meshing

Every load case that should be considered for the computation of the error indicator must include an

HADAPT Case Control command referencing a unique HADAPTL Bulk Data entry:

One single pair of Bulk Data entries HADPTL and HADACRI are required. The unique HADAPTL

entry must be referenced either by an HADAPT Case Control command included as part of the first load

case (Figure 2-68), or included as part of the second load case (Figure 2-69), or included at both load

cases (Figure 2-70).

Figure 2-68, Figure 2-69 and Figure 2-70 show the sequence of meshes obtained during the adaptive

mesh refinement process on the cylindrical shell subjected to two independent load cases on each one of

these three possibilities.

Error Indicator Based on Load Case 1 (Figure 2-68)

Error Indicator Based on Load Case 2 (Figure 2-69)

Error Indicator Based on the Combination of Load Case 1 and Load Case 2 (Figure 2-70)

SUBCASE 1

…

HADAPT = 1

SUBCASE 2

…

SUBCASE 1

…

SUBCASE 2

…

HADAPT = 1

SUBCASE 1

…

HADAPT = 1

SUBCASE 2

…

HADAPT = 1

BEGIN BULK

...

HADAPTL 1 111 ALL

HADAPTL 1 222 ALL

ENDDATA



66

Figure 2-68 Sequence of meshes and deformed configuration obtained using the error

indicator based criterion applied to the first load case

67CHAPTER 2

Adaptive Meshing


indicator based criterion applied to the second load case



68


indicator based criterion applied to both the first and second load cases

Output

User Information Messages (.f06 File)

The output requests for displacements, stresses, forces, etc., are automatically honored for each and all

the iterations of the adaptive mesh refinement loop (Figure 2-71). Thus, for example, if

DISPLACEMENT=ALL is specified in the case control section of the input file, then the grid point

displacements will be written to the .f06 file not only for the initial mesh, but for all the subsequent

meshes created during the mesh refinement process.

At the end of each refinement cycle in the adaptive mesh refinement loop (Figure 2-71) the following user

information message is printed to the .f06 file to signal the end of the analysis supported on the current

mesh and beginning of a new analysis supported on the refined mesh obtained from the previous:

------------------------------------------------------

* * * E N D O F A N A L Y S I S #: 2 * * *

------------------------------------------------------

69CHAPTER 2

Adaptive Meshing

The total number of elements meeting the user’s specified criterion and the total number of elements

actually refined is reported to the .f06 at the end of each successful refinement instance (step 3 and 4 in

Figure 2-71) and prior to the transference of analysis data between unrefined and refined meshes (step 5

in Figure 2-71).

Figure 2-71 User information messages reporting the progress of the adaptive mesh

refinement loop

Notice that the number of elements actually refined will be in general different from the number of

elements meeting the refinement criterion because the refinement is propagated from the latter to the

neighbors according to the set of implicit propagation rules described in Propagation of Refinement, 37.

When the error indicator based criterion is selected, a user message is printed to the .f06 file informing

the total number of elements scanned for the computation of the error indicator, the mean square average

over the whole mesh of the local error indicator and the relative change of this magnitude with respect

to the previous iteration in the adaptive mesh refinement loop:

It bears emphasis that the error indicator is not an error estimator in the sense that its numerical value

does not measure the actual (absolute) error but gives rather a relative assessment of where the mesh

should be refined.

------------------------------------------------------

GLOBAL NUMBER OF ELEMENTS: 64

AVERAGE ERROR INDICATOR: 3.522044E+04

CHANGE IN AVERAGE ERROR INDICATOR: 1.389418E+01 %

------------------------------------------------------



70

If no elements meet the user specified criterion or no elements are actually refined, the adaptive mesh

refinement loop is terminated and corresponding messages are printed to the F06 file.

Output Files for Postprocessing in MD Patran or SimX

A request for the creation of post processing files (“.xdb” using PARAM,POST,0 or “.op2” using

PARAM,POST,-2) is automatically honored for each and all analysis instances in the adaptive mesh

refinement loop. Different postprocessing files are automatically created in the same directory and with

the same name as the input file and with the extension “i.xdb” or “i.op2” where i is the iteration

counter in the adaptive mesh refinement loop. Thus, for example, if the input file is fender.dat,

then, PARAM,POST,0 will create the sequence of files

fender.xdbfender.1.xdbfender.2.xdbfender.3.xdb…fender.i.xdb…

while the sequence of files created via PARAM,POST,-2 will be called.

fender.op2fender.1.op2fender.2.op2fender.3.op2…fender.i.op2…

The first file in the sequence will contain postprocessing data corresponding to the initial mesh and

analysis results and subsequent files will contain postprocessing information for each refined mesh

created during the adaptive mesh refinement process.

All files are assigned to the same logical FORTRAN units which are internally closed at the end of each

mesh refinement cycle and renamed with the appended extensions “i.xdb” or “i.op2” prior to the

beginning of the subsequent cycle.

When using PARAM,POST,0, the user can specify a non default logical FORTRAN unit number to write

postprocessing data (using the parameter GEOMU) and assign a non default physical file name to this

user specified logical FORTRAN unit (using the ASSIGN statement in the File Management Section).

Similarly, when using PARAM,POST,-2, the user can request the use of a non-default logical FORTRAN

unit number to write postprocessing data (using the parameter OUNIT2) and assign a non default

physical file name to this users specified logical FORTRAN unit. In these cases, the user’s specified

logical FORTRAN unit and physical file name will be used (with the appended extension “i.xdb” or

“i.op2”) in the creation of the sequence of postprocessing files.

71CHAPTER 2

Adaptive Meshing

Bulk Data File Images of the Sequence of Refined Meshes

During the adaptive mesh refinement process, new elements, new grid points, new boundary conditions,

new multipoint constraints and new pressure loads are created automatically. Furthermore, contact

bodies are internally redefined to subtract refined elements and replace them by their children elements.

Bulk data file images containing the new mesh and analysis data created after each refinement cycle is

automatically generated prior to the beginning of each analysis cycle.

Each bulk data file image is created in the same directory and with the same name as the input file and

with the extension “.seid.i.bdf” where seid is the superelement ID (0 for models with no

superelements) and i is the iteration counter in the adaptive mesh refinement loop. Thus, for example,

if the input file is fender.dat and contains no upstream superelements (only the residual structure,

i.e. SEID=0), then the sequence of bulk data files created automatically will be named:

fender.0.1.bdffender.0.2.bdffender.0.3.bdf…fender.0.i.bdf…

If, for example, an input file engine.dat contains three upstream superelements labeled with SEID 7

and 24 (in addition to the residual structure with SEID=0) then the following sequence of bulk data file

images will be created:

engine.0.1.bdf engine.7.1.bdf engine.24.1.bdfengine.0.2.bdf engine.7.2.bdf engine.24.2.bdfengine.0.3.bdf engine.7.3.bdf engine.24.3.bdf…engine.0.i.bdf engine.7.i.bdf engine.24.i.bdf…

These bulk data file images might be used as the starting point for the creation of a new analysis input

files supported on any of the refined mesh obtained during the adaptive mesh refinement cycle.

Guidelines and Limitations

Modeling Guidelines

• The number of elements created during refinement grows exponentially. If on each refinement

iteration , a fraction of the total number of elements is refined by subdividing each

element of this fraction into children elements (with for line elements, for

surface elements and for volume elements), then, the total number of element at

iteration will be:

i fi Ni

M M 2Z M 4Z

M 8Z

i 1H

Ni 1HNiZ fiNiÓ fiNiH M⋅ Ni 1 fi M 1Ó( )H( )Z



72

Therefore, if the fraction remains approximately constant during the mesh refinement process,

i.e., if with a constant independent of , then the number of elements at iteration will be

given by the estimate

where is the number of elements in the initial mesh (the mesh provided by the user). For

example, in a surface mesh and if approximately 1/3 of the elements are refined on each

refinement iteration , then the number of elements at iteration will be roughly

. Thus an initial structure with thousands of shell elements will be refined

into millions of shell elements in about 10 iterations. In a 3D mesh , and

if approximately 1/3 of the elements are refined on each iteration, the total number of elements

expected at iteration i will be approximately . Thus, a mesh with thousands of 3D

elements will be refined into millions of 3D elements in about 6 iterations.

• Exponential growth of the number of elements implies that adaptive mesh refinement is memory

intensive. As a rough estimate, each refinement iteration requires on the order of

integer words of memory where is the number of elements of the mesh created during

refinement iteration .

• Instead of the traditional modeling practice, the user should start the process with an initial mesh

preferably coarse which will be refined automatically and selectively according to the

refinement criterion.

• The effectiveness of the refinement process depends on an appropriate detection of geometric

corners, creases and edges and interfaces between elements of different properties. Detection of

geometric features requires the selection of a proper value for the Geometric Feature parameter

(PARAM,VARPHI), (see Location of New Grid Points, 20 and Detection of Geometric Features

and Material and Superelement Interfaces, 49).

• When the initial mesh is very coarse and the boundary of the structure under analysis is poorly

approximated, it is recommended to activate the automatic projection of mid-edge nodes onto a

smooth approximation of the mesh boundary using SNAPMETH=1 (see Detection of Geometric

Features and Material and Superelement Interfaces, 49). Convergence of the mesh refinement

process might be dramatically improved using this method.

• The user should avoid the use of MPC sets 90000000 to 99999999 which are reserved for

hanging nodes constraints generated during the adaptive mesh refinement process (Hanging

Nodes and Multipoint Constraints on Hanging Nodes, 23)

• When mesh refinement is restricted to a specific mesh refinement region (by selecting

WHEREMET=PROP or WHEREMET=SUPER in the HADAPTL Bulk Data entry), the user

should expect refinement also in a few layers away from the refinement region due to the

enforced implicit propagation ruleMs (see Propagation of Refinement, 37).

• In partitioned superelements, the HADAPT entry must be specified in the main bulk data

section. Entries specified in the Bulk Data Section corresponding to individual parts (sections

beginning with BEGIN SUPER) will be ignored.

fi

fi f≅ f i i

Ni N0

1 f M 1Ó( )H( )i

Z

N0

M 4Z( )f 1 3⁄Z( ) i

Ni N02i

Z N0

O 103

( )Z( )

N0

O 106

( )Z( ) M 8Z( )

Ni N0

10 3⁄( )i

Z

i 100 Ni⋅

Ni

i

73CHAPTER 2

Adaptive Meshing

• When using regular superelements, the Bulk Data Section must begin with BEGIN SUPER as

opposed to BEGIN BULK in order to the refinement to be appropriately propagated across

superelement boundaries. If BEGIN BULK is used, grid points on the superelement boundaries

will be duplicated and not shared by the joining superelements.

• In SOL 400 (ANALYSIS=STATICS), multiple load cases should be listed in different STEP

entries and within one single SUBCASE entry. By contrast, in SOL 101, multiple load cases

should be listed under multiple SUBCASE entries.

Limitations

• The error indicator based refinement criterion can be used with surface or volume elements, but

not with line elements. The latter can be subdivided with any other of the refinement criteria, or

when they are attached to the boundary of a surface or volume elements

• Refinement of CBEAM, CBEAM3 with offsets or warping are not supported. Refinement of

CBAR with offsets is not supported.

• Temperature loads are not supported. Similarly, the HEATSTAT=YES option in SOL 101 that

runs a preliminary thermal analysis to compute thermal loads for a subsequent structural

analysis is not supported.

• For the current release, a mesh can be refined but not unrefined.

• Adaptive Mesh refinement cannot be combined with p-adaptivity.

• Adaptive Mesh refinement can be used either in structural linear analysis in SOL 101 or linear

structural analysis in SOL 400 (ANALYSIS=STATICS). It cannot be used in any other analysis

type in SOL 400.

• In SOL 400, an adaptive linear analysis cannot be chained with any other analysis and should be

run as an independent and unique SUBCASE, possibly with multiple STEPS to enforce different

load cases. All STEPS must be preceded by ANALYSIS=STATIC.



74

Chapter 3: Advanced Integrated Nonlinear and Contact MD Nastran R3 Release Guide

3 Advanced Integrated Nonlinear

and Contact

� SOL 400 Performance Enhancements

� SOL 400 Advanced Heat Transfer

� BCONTACT=ALLBODY

� Linear Perturbation and Brake Squeal Analyses in SOL 400

� SOL 400 Materials and Elements

� Enhancements to Connector Elements

� Adaptive Time Stepping Scheme Enhancements for Quasi-Static

Analysis

� Contact and Adaptive Time Stepping Enhancements for Transient

Dynamic Analysis

� Progressive Failure Analysis with a Micromechanical Module

� 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-

Surface and Edge-to-Edge

� Explicit Nonlinear - SOL 700

� Arc-Length Methods (Pre-release)

� Analysis Chaining

MD Nastran R3 Release Guide SOL 400 Performance Enhancements

76

SOL 400 Performance Enhancements

Dramatic performance improvements have been made to SOL 400 for the MD Nastran R3 release. For

specific details on these improvements, please see Linear and Nonlinear Contact Analysis (Ch. 6).

77CHAPTER 3

Advanced Integrated Nonlinear and Contact

SOL 400 Advanced Heat Transfer

Outline of New SOL 400 Heat Transfer Capabilities• Added new nonlinear elements such as composite thermal elements 3D. Composite thermal 2D

using PCOMP or PCOMPG.

• The performance for the hemi-cube view factor increases proportionally as the model size

increases. A speed up of 33 times has been observed in the test case.

• New output added for multiple layers of output for composite thermal element.

• Transient thermal analysis using SPCD and SPC1

• Chaining analysis is now available from the thermal analysis step into the structure analysis step

in a single run.

• Minimal Input test file change from previous existing test file in SOL 153 or SOL 159 into

SOL 400

SOL 400 is the most comprehensive thermal solver that exists in the MSC product line. It has integrated

the existing nonlinear steady state thermal SOL 153 and nonlinear transient thermal SOL 159 and all its

functionalities. In addition, 21 new finite heat transfer elements that included rod, planar 2D, membrane

2D element., Shell 3D element, and solid elements have been implemented. Also we have the 2D

composite heat transfer elements with multiple layers using either PCOMP or PCOMG that referenced

the MAT4 and MAT5 entries. The advantage of using 2D composite heat transfer is that the user can have

3D thermal analysis simulated on the 2D structure.

Nastran Type Req Nodes Type Code INT Code NL_PROP

ROD 2 ROD L PRODN1

Shell(3D)

CQUAD4 4 DCT L PSHLN1

CQUAD8 8 DCT Q PSHLN1

CTRIA3 3 DCT L PSHLN1

Planar(2D)

CQUAD4 4 PLST L PSHLN2

CTRIA3 3 PLST L PSHLN2

CQUAD8 8 PLST Q PSHLN2

CTRIA6 6 PLST Q PSHLN2

Planar Composite

CQUAD4 4 COMP L PLCOMP

CQUAD8 8 COMP Q PLCOMP

MD Nastran R3 Release Guide SOL 400 Advanced Heat Transfer

78

Let us say you want to use the SHELL 3D element.

CQUAD4,101,1,9,10,12,11PSHELL,1,5,0.1PSHLN1,1,5,,,IH,C4,,,DCT,LMAT4,5,20.0

Here is an example using the nonlinear extension for the CHEXA element.

psldn1,1,1,,,ihPSOLID 1 1 0CHEXA 5958 1 391 3742 3743 422 7355 7358 7357 7356

Membrane element

CQUAD4 4 MB L PSHLN1

CTRIA3 3 MB L PSHLN1

CQUAD8 8 MB Q PSHLN1

CTRIA6 6 MB Q PSHLN1

Solid Element

CHEXA 8 SOLI L PSLDN1

CHEXA 20 SOLI Q PSLDN1

CTETRA 4 SOLI L PSLDN1

CTETRA 10 SOLI Q PSLDN1

CPENTA 6 SOLI L PSLDN1

Solid Composite elements

CHEXA 8 SLCO L PLCOMP

CHEXA 20 SLCO Q PLCOMP

Nastran Type Req Nodes Type Code INT Code NL_PROP

N 2 3 4 5 6 7 8 9 10

PSHLN1 PID MID1 ANALY

C3 BEH3H INT3H

C4 BEH4H INT4H

C6 BEH6H INT6H

C8 BEH8H INT8H

79CHAPTER 3


The following is an example using a 2D composite heat transfer element:

MD Nastran test file: 2d_comp.dat

Boundary conditions:

1. Heat flux of 50 Btu/hr/inch2 impose on the top surface

2. Edge is held at 20 degree F

The PID of the CQUAD4 points to the PCOMP Bulk Data entry, and a PSHLN1 with ID 1 and PCOMP

specify number of layers, material ID and ply angles.

In this case we have a total of three layers with -45, 90,0 degree ply angles with call out to MAT5 ID of

1,2,1 respectively.

pshln1,1,1,,,ihPCOMP,1,1,0.1,-45.0,,2,0.1,90.0,2,0.1,0.0$CQUAD4 1 1 1 4 5 2CQUAD4 2 1 2 5 6 3CQUAD4 3 1 4 7 8 5CQUAD4 4 1 5 8 9 6MAT5 1 .2 .5 .6MAT5 2 1. 2. 3.

N 2 3 4 5 6 7 8 9 10

PSLDN1 PID MID1 ANALY

C4 BEH4H INT4H

C6 BEH6H INT6H

C8 BEH8H INT8H

C10 BEH10H INT10H

C20 BEH20H INT20H


80

NLSTRESS=all will give you the following new output.

Using the 3D composite heat transfer element:

MD Nastran test file: 3d_pcomp.datpcompls,1,-1,,,ih,c20,,,slco,q

0 SUBCASE 1 STEP 1 LOAD STEP = 1.00000E+00

G R A D I E N T S A N D F L U X E S F O R L A Y E R E D C O M P O S I T E E L E M E N T S

ELEMENT INTEG. -------G R A D I E N T S----------------F L U X E S----------------T E M P- ID PLY ID POINT ID T-X T-Y T-Z F-X F-Y F-Z T 1 1 1 -5.877E-01 1.142E+02 0.000E+00 -1.692E+01 -3.988E+01 0.000E+00 3.206E+01 2 -5.877E-01 1.126E+02 0.000E+00 -1.668E+01 -3.931E+01 0.000E+00 3.189E+01 3 -2.193E+00 1.142E+02 0.000E+00 -1.636E+01 -3.963E+01 0.000E+00 6.503E+01 4 -2.193E+00 1.126E+02 0.000E+00 -1.612E+01 -3.907E+01 0.000E+00 6.439E+01 2 1 -5.877E-01 1.142E+02 0.000E+00 1.175E+00 -1.142E+02 0.000E+00 3.206E+01 2 -5.877E-01 1.126E+02 0.000E+00 1.175E+00 -1.126E+02 0.000E+00 3.189E+01 3 -2.193E+00 1.142E+02 0.000E+00 4.387E+00 -1.142E+02 0.000E+00 6.503E+01 4 -2.193E+00 1.126E+02 0.000E+00 4.387E+00 -1.126E+02 0.000E+00 6.439E+01 3 1 -5.877E-01 1.142E+02 0.000E+00 5.877E-01 -2.284E+02 0.000E+00 3.206E+01 2 -5.877E-01 1.126E+02 0.000E+00 5.877E-01 -2.252E+02 0.000E+00 3.189E+01 3 -2.193E+00 1.142E+02 0.000E+00 2.193E+00 -2.284E+02 0.000E+00 6.503E+01 4 -2.193E+00 1.126E+02 0.000E+00 2.193E+00 -2.252E+02 0.000E+00 6.439E+01

TOTAL -1.646E+00 -5.061E+01 0.000E+00 AVERAGE -1.391E+00 1.134E+02 0.000E+00 -4.116E+00 -1.265E+02 0.000E+00 4.834E+01

81CHAPTER 3


,101,1,0.001,102,1,0.001CHEXA 1 1 23 21 1 3 773 766 768 771 22 14 2 15 774 767 769 772 777 770 776 775

composite group number 1 number of layers 12 solid composite layer direction -1 allowable interlaminar bond shear stress 0.0000 actual layer thickness is given below layer layer id mat id thickness ply angle 1 112 1 1.000E-03 0.000E+00 2 111 1 1.000E-03 0.000E+00 3 110 1 1.000E-03 0.000E+00 4 109 1 1.000E-03 0.000E+00 5 108 1 1.000E-03 0.000E+00 6 107 1 1.000E-03 0.000E+00 7 106 1 1.000E-03 0.000E+00 8 105 1 1.000E-03 0.000E+00 9 104 1 1.000E-03 0.000E+00 10 103 1 1.000E-03 0.000E+00 11 102 1 1.000E-03 0.000E+00 12 101 1 1.000E-03 0.000E+00


82

The following is a quartz lamp model.

Boundary Conditions:

• The volumetric heating for the center lamp is 50 watt/cubic cm.

• There is view factor calculation for the complete enclosure including the third-body shading of

the inner Quartz lamp

• Free convection to air at 20 degrees C occurs on the outer surface with h=5 watt/cm**2*C

MD Nastran test file: quartz_lamp_hemi.dat

83CHAPTER 3


Hemicube: 321.3 cpu sec

Gaussian (VIEW3D): 10751.9 cpu sec

A speed up of 33 times.


84

We can see that the performance is 4 times faster for this medium size model.

The HEMICUBE method is selected by this NLMOPTS,HEMI,1

SOL 400CENDANALYSIS = HSTATTITLE = MSC/NASTRAN job created on 29-Oct-98 at 16:46:24ECHO = NONEMAXLINES = 999999999TEMPERATURE(INITIAL) = 1$ Direct Text Input for Global Case Control DataSUBCASE 1$ Subcase name : Default SUBTITLE=Default NLPARM = 5 SPC = 1 LOAD = 2 THERMAL(SORT1,PRINT)=ALL FLUX(SORT1,PRINT)=ALL$ Direct Text Input for this SubcaseBEGIN BULKnlmopts,hemi,1PARAM POST 0PARAM AUTOSPC YESPARAM TABS 273.149PARAM* SIGMA 5.6699-12

How Do We Convert an Existing Heat Transfer Test File from SOL 153 into SOL 400?SOL 153$ Direct Text Input for Executive ControlCENDANALYSIS = HEATTITLE = workshop 1ECHO = NONETEMPERATURE(INITIAL) = 1DataSUBCASE 1SUBTITLE=Default NLPARM = 1 SPC = 1 LOAD = 2 THERMAL(SORT1,PRINT)=ALL FLUX(SORT1,PRINT)=ALL OLOAD(SORT1,PRINT)=ALL SPCFORCES(SORT1,PRINT)=ALL$ Direct Text Input for this SubcaseBEGIN BULK

Number of CHBDYG Elements Hemicube Gaussian I

1440 48.3 sec 182.6 sec

19594 321.3 sec 10751.9 sec

76243 4851.9 sec 259251 sec

85CHAPTER 3


SOL 400$ Direct Text Input for Executive ControlCENDANALYSIS = HSTATTITLE = workshop 1ECHO = NONETEMPERATURE(INITIAL) = 1SUBCASE 1$ Subcase name : Default SUBTITLE=Default NLPARM = 1 SPC = 1 LOAD = 2 THERMAL(SORT1,PRINT)=ALL FLUX(SORT1,PRINT)=ALL OLOAD(SORT1,PRINT)=ALL SPCFORCES(SORT1,PRINT)=ALLBEGIN BULK

How Do We Convert SOL 159 into SOL 400?ID MSC-NASTRAN V68SOL 159 TIME 10CENDTITLE = EXAMPLE 7B ANALYSIS = HEATTHERMAL = ALLFLUX = ALLSPCF = ALLOLOAD = ALLIC = 20TSTEPNL = 100DLOAD = 200BEGIN BULKTSTEPNL,100,7500,1.0,1,ADAPT,,,U ID MSC-NASTRAN V68SOL 400TIME 10CENDTITLE = EXAMPLE 7B ANALYSIS = HTRANTHERMAL = ALLFLUX = ALLSPCF = ALLOLOAD = ALLIC = 20TSTEPNL = 100DLOAD = 200BEGIN BULKTSTEPNL,100,7500,1.0,1,ADAPT,,,U

The only exception to this conversion in transient thermal analysis is when you have enforced

temperature as a function of time, or having convection coefficient as a function of time, or radiation

view factor as a function of time.

In SOL 400, MD Nastran uses SPCD and SPC1 to impose enforced temperature boundary conditions

instead of large stiffness method where u=P/K. Therefore if the test file has Bulk Data entry TEMPBC,

then you need to replace it with SPCD and SPC1.


86

To Convert SOL 159 Models to SOL 400 Models

1. Executive Control Section - change SOL 159 to SOL 400.

2. Case Control Section - replace ANALYSIS=HEAT by ANALYSIS=HTRAN, also add SPC if all

temperature boundary conditions are transient (the following Case 3b).

3. Bulk Data Section - replace the “TRAN” type TEMPBC by SPC1 and SPCD. The details are

explained below.

a. If all temperature boundary conditions are constant, no changes are required.

b. If all temperature boundary conditions are transient, replace TEMPBC by SPC1 and SPCD

and modify TLOAD1.

For example, replace the following entries of SOL 159 model:

TLOAD1,40,400,,,4000

TEMPBC,400,TRAN,300.0,99

by

SPC = 111 (Case CC)

:

TLOAD1,40,400,,1,4000

SPCD,400,99,,300.0

SPC1,111,,99

c. If a model has both constant and transient temperature boundary conditions, all boundary

conditions must be converted into SPC1 and SPCD.

For example, replace the following entries of SOL 159 model:

DLOAD,222,1.0,1,0,30,1.0,40

TLOAD1,40,400,,,4000

TEMPBC,400,TRAN,300.0,99

SPC,111,98,,20.0

by

DLOAD,222,1.0,1,0,30,1.0,40, 1.0,50

TLOAD1,40,400,,1,4000

SPCD,400,99,,300.0

SPC1,111,,99

TLOAD1,50,500,,1,5000

SPCD,500,98,,20.0

SPC1,111,,98

TABLED1,5000,,,,,,,,

,0.0,1.0,1000.0,1.0,ENDT

2D Transient Thermal Analysis

Reference: NAFEM Thermal benchmark problems.

1. Adiabatic at the left end

2. Qvol(temp)= 1.0e7*(1+0.005*T)

87CHAPTER 3


3. Initially the temperature is at zero degree everywhere

4. The model is 0.01 m by 0.01 m

The analytical solution is at:

X=0.005 m, time=2 sec, Temp=3.81 CK=52 w/m.C, Cp=460 J/Kg.C, Density=7850 Kg/m3NASTRAN test deck: vtest8_pc.dat

This point corresponds to grid 6 for the model.

Figure 3-1 Finite element model


88

Figure 3-2 Grid 6 at time equal to 2 is 3.80258

89CHAPTER 3


$ANALYTICAL FOR GRID 6 AT X=0.005 AT TIME=2 SEC IS 3.81SOL 400$ Direct Text Input for Executive ControlCENDANALYSIS = HTRANTITLE = MSC.Nastran job created on 20-Mar-03 at 10:11:51ECHO = NONESPC = 1IC = 1$ Direct Text Input for Global Case Control DataSUBCASE 1$ Subcase name : tran SUBTITLE=tran TSTEPNL = 1 DLOAD = 2 THERMAL(SORT2,PRINT)=ALL FLUX(SORT2,PRINT)=ALL OLOAD(SORT2,PRINT)=ALL SPCFORCES(SORT2,PRINT)=ALL$ Direct Text Input for this SubcaseBEGIN BULKPARAM POST 0PARAM PRGPST NOTSTEPNL,1,100,.025,10,.001,,0$ Direct Text Input for Bulk Data$ Elements and Element Properties for region : platePSHELL 1 1 1.$ Pset: "plate" will be imported as: "pshell.1"CQUAD4 1 1 1 2 13 12AND ETCCQUAD4 10 1 10 11 22 21$ Referenced Material Records$ Material Record : mat4$ Description of Material : Date: 20-Mar-03 Time: 10:08:36MAT4,1,52.,460.0,7850.,,,1.0MATT4,1,,,,,,123TABLEM2,123,0.0,1.0E7,3.0,1.015E7,6.0,1.03E7,10.0,1.05E7,,20.0,1.10E7,50.0,1.25E7,100.0,1.5E7,200.0,2.0E7,ENDT$ Nodes of the Entire ModelGRID 1 0. 0. 0.GRID 2 .001 0. 0.AND ETCGRID 22 .01 .01 0.$ Loads for Load Case : tranTLOAD1 4 3 1DLOAD 2 1. 1. 4$ Fixed Temperatures of Load Set : rightSPC 1 11 1 0. 22 1 0.$ Volumetric Heat Generation of Load Set : qvol

Time step = 0.025 sec Temp (CQUAD4) Temp(DCT)

Analytical =3.81 3.802579 3.80284


90

QVOL,3,1.0,,1,THRU,10$ Referenced Dynamic Load Tables$ Constant Load TableTABLED1 1 0. 1. 1000. 1. ENDT$ Initial Temperatures from Temperature Load SetsTEMP 1 11 0. 22 0.$ Default Initial TemperatureTEMPD 1 0.$ Referenced Coordinate FramesENDDATA 88c8f88b

In transient thermal analysis you can have time adaptive scheme. The advantage of using adaptive

scheme is that you can get to the end time with fewer steps. In SOL 400 the adaptive scheme is turn ON

by setting the NO field (5) on the TSTEPNL Bulk Data entry to a minus 1.

TSTEPNL,5,100,5.0,-1,adapt,,,u

The No field is time step interval for output.

For a large transient thermal problem using the adaptive time step can be much more efficient.

The adaptive method is the recommend method for SOL 400 transient thermal analysis.

The analysis chaining is now available from heat transfer analysis into the structure analysis.

Previously in MD Nastran you could run a linear thermal analysis followed by the linear static analysis

in a single execution by using PARAM,HEATSTAT,YES.

For example:

SOL 101CEND ECHO = sortSUBCASE 1 THERMAL(PRINT) = ALL SPCFORCE(PRINT) = ALLFLUX(PRINT) = ALL SPC = 1load=101SUBCASE 2temp(load)=1disp=allstress=allspc=8BEGIN BULKparam,heatstat,yes

However, the restriction using the SOL 101 is that the thermal analysis must be linear, that is there is no

radiation or thermal conductivity or convection coefficient as a function of temp.

Now in SOL 400 the user can run an analysis chaining, with a nonlinear thermal analysis, followed by

nonlinear structural analysis.

91CHAPTER 3


Figure 3-3 Thermal boundary conditions

1. Apply a 30 btu/hr/in2 on one face

2. Radiation to space at 70 F with view factor=1

3. The thermal conductivity is at 0.3 btu/hr/in.F

4. Sigma is equal to 1.1903e-11


92

Figure 3-4 Temperature contour

Figure 3-5 Structure boundary (conditions fixed on one end)

93CHAPTER 3


Figure 3-6 Thermal displacement

MD NASTRAN test file: hs_chain1.dat

SOL 400

CEND

TITLE = MD Nastran job created on 08-Feb-08 at 10:24:41

ECHO = NONE

TEMPERATURE(INITIAL) = 1

$ Direct Text Input for Global Case Control Data

SUBCASE 1

STEP 1

analysis=hstat

SUBTITLE=Default

NLPARM = 1

SPC = 1

LOAD = 2

THERMAL(SORT1,PRINT)=ALL

FLUX(SORT1,PRINT)=ALL

tstru=9

STEP 2

analysis=nlstat

temp(load)=9

NLPARM= 1


94

SPC=2

disp=all

stress=all

BEGIN BULK

param,lgdisp,1

In this SOL 400 analysis chaining we have two steps. The first step is the nonlinear thermal analysis

indicated by analysis=hstat, and the second step is the nonlinear static analysis using the final temperature

from step 1 as the temperature load for step 2.

If one does not specify the TSTRU option in the first step, then the default TEMP(LOAD) =1.

If you want to change the TEMP(LOAD) ID, you can use the TSTRU option which allows you to change

the ID number for the TEMP(LOAD)=n.

95CHAPTER 3


BCONTACT=ALLBODY

Introduction

The Case Control command BCONTACT is used to request 3-D contact analysis in SOLs 101 and 400.

The format BCONTACT = n, where n is the ID number of all corresponding BCTABLE (required),

BCMOVE (optional), and BCHANGE (optional) Bulk Data entries, is supported in MD Nastran R2. In

this release, a new format of the BCONTACT=ALLBODY Case Control command is added to support

3-D Contact. The BCONTACT=ALLBODY functionality was a pre-release capability in the MD

Nastran R2.1 release. For MD Nastran R3 this is now a production capability.

Benefits

The use of BCONTACT=ALLBODY can save considerable time in preparing the contact input (see the

following example).

Input

Unlike BCONTACT = n, which selects the contactable bodies on the BCTABLE Bulk Data entry when

BCONTACT=ALLBODY is specified in the Case Control Section, all BCBODYs listed in the file are

selected as contactable bodies to each other. Also, since there is no BCTABLE referenced, default values

are used in the BCTABLE fields.

To specify BCMOVE or BCHANGE Bulk Data entries when BCONTACT=ALLBODY, two new Case

Control commands, BCMOVE = n and BCHANGE = n, are introduced in this release. These new

commands can also be used to overwrite the SID = n from the BCONTACT = n case.

Output

There is no new output for BCONTACT=ALLBODY.

Limitation

Although potentially convenient, it is strongly recommended to use BCONTACT=ALLBODY carefully.

It is appropriate for simple models, or for checking out runs, to use BCONTACT=ALLBODY. Setting

BCONTACT=ALLBODY without careful study may produce unacceptable results and poor

convergence.

Example

The test problem nlc021a.dat can be used as an example to show the advantage of

BCONTACT=ALLBODY. This example is a transient analysis in 2-D contact that uses four deformable

contact bodies and one rigid contact body. Each of these bodies is contactable, which yields ten possible

MD Nastran R3 Release Guide BCONTACT=ALLBODY

96

combinations of contact. With four self-contacts of the deformable bodies, excluding the rigid body, there

are a total of fourteen possible combinations.

1. Bodies 6 and 13 contact.










11. Body 13 self-contacts.




When BCONTACT=1 is specified, the following BCTABLE Bulk Data entry is required, which must

include fourteen slave and master pairs.

BCTABLE 1 14 SLAVE 16 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 16 SLAVE 17 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 16 SLAVE 17 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 17 SLAVE 16 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 14 SLAVE 17 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 14 SLAVE 14 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 14 SLAVE 16 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 13 SLAVE 17 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0.

97CHAPTER 3


MASTERS 13 SLAVE 14 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 13 SLAVE 13 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 13 SLAVE 16 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 6 SLAVE 17 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 6 SLAVE 14 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 6 SLAVE 13 0. 0. 0. 0. 0 0 0 0 FBSH 1.+20 0. 0. MASTERS 6

Note that this long BCTABLE Bulk Data entry can be eliminated by setting BCONTACT=ALLBODY.

MD Nastran R3 Release Guide Linear Perturbation and Brake Squeal Analyses in SOL 400

98

Linear Perturbation and Brake Squeal Analyses in SOL 400

Introduction

Linear perturbation analyses, such as Normal Modes, Direct and Modal Complex Eigenvalues, have been

implemented in SOL 400. The linear analysis is performed on top of a user-specified linearly or

nonlinearly deformed structure configuration. Case Control command, NLIC, is utilized to select a static

solution, which is either linear or nonlinear, from the solutions of loading history. The brake squeal

analysis which is a combination of general contact with unsymmetrical friction force stiffness matrix and

complex eigenvalue extraction is also implemented as a special application of linear perturbation

analyses under the framework of the so-called analysis chaining in SOL 400.

The system matrices of the linear perturbation analysis include the tangent stiffness matrix, which

contains the effects of both linear and nonlinear elements. Damping effect are also included. The tangent

stiffness matrix includes both geometrical and material nonlinearities, as well as the follower force

stiffness.

Contact constraints, either from a general contact or a permanent glued contact, are incorporated in the

linear perturbation analyses.

Benefits

Bringing the linear perturbation analyses into SOL 400 helps expand its analysis capacities beyond the

existing nonlinear static and transient domain. With its flexible control structure of analysis chaining,

users are allowed to reference the nonlinear solutions, where the linear perturbation analyses are based

upon, at various load increments from different loading steps, without running multiple individual jobs

or dealing with the restart.

The general contact capability implemented in SOL 400 is available in the ensuing linear perturbation

analysis.

A major benefit of implementations is the brake squeal analysis, which embraces the full capacity of

nonlinear analyses with contact offered by SOL 400.

Input

A linear perturbation analysis is introduced by Case Control command, ANALYSIS, with a given value,

such as MODES, DCEIG or MCEIG, for a specific analysis discipline. At least one STEP of a nonlinear

(or linear) static analysis must precede the STEP of a linear perturbation analysis. Case Control

command, NLIC, is used to point to a nonlinear solution, which is previously calculated and saved.

For the brake squeal analysis, a new Case Control command, BSQUEAL, as well as a Bulk Data entry

of the same name has been introduced. There are two Case Control approaches: One is the same as the

general linear perturbation analysis where the brake squeal analysis is performed as a separate STEP

99CHAPTER 3


from the STEP of a nonlinear static analysis. The other is the single-STEP approach in that both a

nonlinear and the brake squeal analyses are executed in a single STEP. In a single-STEP approach, the

user can choose either to run a complete loading step with the brake squeal analysis at either the pre-load

or a given load increment, or alternatively to run only the brake squeal analysis at the specified load

increment and exit the nonlinear iteration immediately afterward.

Case Control Commands

• ANALYSIS=MODES

This is for Normal Modes analysis. A Case Control command, METHOD, must be present in

the same STEP.

• ANALYSIS=DCEIG

This is for Direct Complex Eigenvalue analysis. A Case Control command, CMETHOD, must

be present in the same STEP.

• ANALYSIS=MCEIG

This is for Modal Complex Eigenvalue analysis. Both Case Control commands, METHOD and

CMETHOD, must be present in the same STEP.

• BSQUEAL

This command activates the brake squeal analysis. It points to a Bulk Data entry, BSQUEAL,

with the same set identification. BSQUEAL is SUBCASE-STEP selectable.

In the single-STEP approach where ANALYSIS=NLSTATIC, the approach of the eigenvalues

extraction for the brake squeal analysis is determined by how the Case Controls, CMETHOD

and METHOD, are present. For instance, if BSQUEAL coexists with both CMETHOD and

METHOD, then the modal approach is performed. Otherwise, if only CMETHOD is present,

then the direct approach is executed.

Bulk Data Entry

• BSQUEAL

This Bulk Data entry referenced by a Case Control command, BSQUEAL.

Output1. The output of linear perturbation analyses shares the same data formats and data-blocks as their

corresponding linear solution sequences, such as SOL 103, SOL 107 and SOL 110.

2. The solutions, such as stresses and strains, from a linear perturbation analysis are not

superimposed on top of the nonlinear static solutions.

3. Data recovery of a linear perturbation analysis is performed in its current SUBCASE-STEP,

while the solutions of the nonlinear analysis are output after all iterations are completed, except

for the nonlinear PHASE II output.


100

Guidelines and Limitations1. It is advised that the user put together all steps of linear perturbation analyses and place the group

after the step(s) of nonlinear static analysis, for a better organization of the solution sequences. It

is not recommended that the steps of nonlinear analyses are intertwined with the steps of linear

perturbations.

2. Case Control command, NLIC, must be explicitly specified if the STEP of a linear perturbation

analysis does not immediately follow the STEP of a nonlinear static analysis.

3. The linear perturbation analysis must be in the same SUBCASE as the nonlinear static analysis

which it references. In other words, NLIC is not allowed to point to a nonlinear solution from a

SUBCASE other than the current one.

4. Both super-elements and parts super-elements are not supported in the linear perturbation and

brake squeal analyses.

5. Stresses, strains, and forces are not computed for those advanced nonlinear materials and

elements (as introduced in the MD Nastran R2 Release Guide under section “SOL 400 Material

and Elements”, as well as Nastran nonlinear elements, such as hyperelastic elements).

6. For the brake squeal analysis, there are two approaches. One is the so-called single-STEP

approach which combines Case control commands, ANALYSIS=NLSTATIC, BSQUEAL,

CMETHOD and/or METHOD in a single STEP. The other is the regular chaining approach with

either explicitly or implicitly specified NLIC, along with ANALYSIS=DCEIG/MCEIG and

BSQUEAL. In the latter approach, LOADFAC in NLIC overrides OMETH in Bulk Data entry,

BSQUEAL.

7. In a brake squeal analysis, the rotating body, such as a brake disk or rotor, may not be completely

constrained and acts like a floating body. To achieve a reliable convergent nonlinear static

solution, it is helpful to add some insignificant spring element to the brake disk or rotor to

constrain the floating movement. Floating bodies in an FE model are sometimes detrimental to

the convergence of nonlinear iterations in SOL 400. However if the brake squeal analysis is

performed in the pre-load state and BSONLY=YES in Bulk Data entry, BSQUEAL then the

floating body is not a concern.

8. AVSTIF from Bulk Data entry, BSQUEAL, and the friction coefficients of contact bodies are

primary sources to compute matrices of friction force and normal contact constraint stiffness.

Friction-induced heat and thermo-mechanical coupling are not included.

Examples - Examples of Case Control Approaches

Example 1: General Case Control Structure of Linear Perturbation Analyses

The following is an example of Case Control paradigm used in linear perturbation analyses. The

nonlinear static analyses are performed in the first three loading steps. The linear perturbations are then

carried out in the following steps, with NLIC referencing the selected load factors from different steps.

SUBCASE 1STEP 1

ANALYSIS=NLST

101CHAPTER 3


…...STEP 2

ANALYSIS=NLST…...

STEP 3ANALYSIS=NLST…...

STEP 4ANALYSIS=MODESNLIC STEP 1, LOADFAC, 0.2METHOD=1…...

STEP 5ANALYSIS=DCEIGNLIC STEP 2, LOADFAC, 0.5CMETHOD=1......

Example 2: Case Control Structure of Single-STEP for Brake Squeal Analysis

This is an example of the so-called single-STEP approach. The nonlinear static analysis is performed

while a brake squeal analysis is requested. In this approach, the user can choose either to continue the

nonlinear iterations after the brake squeal analysis is done until the whole nonlinear solution process is

completed, or to exit the nonlinear iterations right after the brake squeal analysis is completed. Case

Control commands, CMETHOD and METHOD, are placed to determine what eigenvalue extraction

approach is used.

Example 3: Case Control Structure of Brake Squeal Analysis, Separate STEP

This example shows that a brake squeal analysis is performed in a separate STEP from a regular

nonlinear STEP. Case Control command, BSQUEAL, is the trigger of the brake squeal analysis.

LOADFAC of NLIC overrides OMETH from the referenced Bulk Data entry, BSQUEAL.

SUBCASE 1STEP 1

ANALYSIS=NLSTATIC

SUBCASE 1

STEP 1

ANALYSIS=NLST

NLPARM=201

BCONTACT=1

LOAD=2

BSQUEAL=101

CMETHOD=1

METHOD=1

…...

Direct approach: CMETHOD only

Modal approach: CMETHOD+ METHOD


102

NLPARM=1BCONTACT=1......

STEP 2ANALYSIS=MCEIGNLIC STEP 1, LOADFAC, 0.2BSQUEAL=101CMETHOD=1METHOD=1......

Examples of Linear Perturbation and Brake Squeal Analyses

Example 4: Rotating Fan-Blade Model (nlrot103.dat), NLSTATIC+MODES

This example is converted from a SOL 106 file, as shown in Figure 3-7. The finite element model consists

of CQUAD4 elements. The applied loads include both pressure (PLOAD) and rotational force

(RFORCE). Both loads are of follower force loads in nature. The geometrical nonlinearity and the

follower force stiffness are taken into consideration in the analysis. The eigensolutions match very well

with the ones from SOL 106. Figure 3-8 shows the nonlinear static deformation and linear perturbation

mode shapes. The mode shapes are not plotted on the deformed shape. Instead, they are plotted on the

pre-deformed structure configuration.

Input FileID, MSC NLROT103 $SOL 400CENDTITLE =EDB ROTATING BLADE, SOL400, NORMAL MODESSUBCASE 101 STEP 1 SUBTI =Nonlinear Static SPC = 200 LOAD = 300 NLPARM= 400 NLSTR = NONE DISPL = ALL STEP 2 SUBTI =Normal Modes ANALYSIS=MODES SPC = 200 METHOD= 500 DISPL = ALL AUTOSPC= YES RESVEC = NOBEGIN BULKGRID 1 5. -2.427 -1.763GRID 2 6.25 -2.48835-1.7562GRID 3 7.5 -2.5497 -1.7494...GRID 126 30. 3.654 1.627CQUAD4 1 100 1 2 23 22CQUAD4 2 100 2 3 24 23...

103CHAPTER 3


CQUAD4 100 100 104 105 126 125PSHELL 100 100 .1 100MAT1 100 16.+6 .275 2.-4SPC1 200 123456 1 22 43 64 85 106LOAD 300 1. 1. 301 1. 302RFORCE 301 40. 1. 2PLOAD 302 .01665 2 3 24 23PLOAD 302 .05435 69 70 91 90...PLOAD 302 .04905 40 41 62 61$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------NLPARM 400 10 FNT PW ++ 1.E-6 1.E-6 1.E-6$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------EIGRL 500 3PARAM COUPMASS+1PARAM K6ROT 100.PARAM LGDISP 1ENDDATA

Figure 3-7 FE Model of Rotating Fan Blade

Eigenvalues

0 SUBCASE 101 STEP 2

R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS 1 1 6.779929E+04 2.603830E+02 4.144123E+01 1.000000E+00 6.779929E+04 2 2 3.178284E+05 5.637627E+02 8.972562E+01 1.000000E+00 3.178284E+05 3 3 5.492646E+05 7.411239E+02 1.179535E+02 1.000000E+00 5.492646E+05


104

Figure 3-8 Nonlinear Static Deformation and Perturbed Mode Shapes

Example 5: Brake Squeal Model (nlbsql01.dat)

Figure 3-9 shows a finite element model of a simplified brake assembly. The brake system consists of a

disk, two brake pads and pistons. The pistons are glued to the pads through a general flexible body-to-

body contact. The modal brake squeal analysis is performed in the pre-load state and the job is terminated

immediately after the brake squeal analysis. Figure 3-10 shows the first unstable mode of brake

squealing.

1. Nonlinear Static Deformation 2. First Mode Shape (41.44 Hz)

3. Second Mode Shape (89.73 Hz) 4. Third Mode Shape (117.95 Hz)

105CHAPTER 3


Figure 3-9 FE Model of a Simplified Brake Assembly

Input FileID MSC, NLBSQL01 $SOL 400CENDECHO=SORT( EXCEPT GRID, CHEXA )BCONTACT = 0SUBCASE 1 SUBTITLE=CASE1 STEP 1 LABEL=Nonlinear Static Step, Loading + Contact NLPARM = 1 BCONTACT = 1 BOUTPUT=ALL BSQUEAL = 988 SPC = 2 LOAD = 2 CMETHOD=1 METHOD =2 $ Modal Approach DISP(PLOT)=ALL AUTOSPC(NOPRINT)=YES RESVEC=NOBEGIN BULKBCPARA 0 NLGLUE 1PARAM LGDISP 1NLPARM 1 FNT PV NO$-------2-------3-------4-------5-------6-------7-------8-------9-------0----BCTABLE 1 4 SLAVE 9 0. 0. 1. 0. 0 0.

Disk is in contact with pads

Pads are glued to piston but are in contact with disk

Pistons are glued to pads


106

1 2 0 MASTERS 8 SLAVE 10 0. 0. 1. 0. 0 0. 1 2 0 MASTERS 8 SLAVE 11 0. 0. 0. 0. 1 0. 1 2 0 MASTERS 9 SLAVE 12 0. 0. 0. 0. 1 0. 1 2 0 MASTERS 10EIGC 1 CLAN 20EIGRL 2 15$-------2-------3-------4-------5-------6-------7-------8-------9-------0----$ ID OMETH AVSTIF GLUE ICORD BSONLYBSQUEAL 988 0.0 1.e+4 YES 0.0 0.0 1.0 0.0 0.0 0.0PSOLID 1 1 0$ Pset: "disk" will be imported as: "psolid.1"CHEXA 1 1 1 2 9 8 1001 1002 1009 1008CHEXA 2 1 2 3 10 9 1002 1003 1010 1009CHEXA 3 1 3 4 11 10 1003 1004 1011 1010...$ Elements and Element Properties for region : pad1PSOLID 2 2 0$ Pset: "pad1" will be imported as: "psolid.2"CHEXA 1004 2 2004 2005 2012 2011 3004 3005 3012 3011CHEXA 1005 2 2005 2006 2013 2012 3005 3006 3013 3012...CHEXA 1030 2 2034 2035 2042 2041 3034 3035 3042 3041$ Elements and Element Properties for region : pad2PSOLID 3 2 0$ Pset: "pad2" will be imported as: "psolid.3"CHEXA 1031 3 4000 4001 4005 4004 4024 4025 4029 4028CHEXA 1032 3 4001 4002 4006 4005 4025 4026 4030 4029...CHEXA 1045 3 4018 4019 4023 4022 4042 4043 4047 4046$ Elements and Element Properties for region : pistonPSOLID 4 2 0$ Pset: "piston" will be imported as: "psolid.4"CHEXA 1046 4 5007 5008 5002 5005 5012 5009 5010 5011CHEXA 1047 4 5004 5001 5008 5007 5014 5013 5009 5012

107CHAPTER 3


.

.

.CHEXA 1053 4 10007 10008 10006 10004 10016 10013 10012 10018MAT1 1 21000. 8076.92 .3 7.8-6MAT1 2 2000. 769.231 .3 2.3-6$ Nodes of the Entire ModelGRID 1 40. 0. 0. 1GRID 2 50. 0. 0. 1GRID 3 60. 0. 0. 1...GRID 10018 89.08 31.9591 -10.$ Loads for Load Case : case1SPCADD 2 1 3 4LOAD 2 1. 1. 1LOAD 4 1.0-8 1. 1$ Contraints in Cylindrical Coord. 1$ On one edge$ SID C G1 G2 .......SPC1 1 13 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 120 127 134 141 148 155 162 169 176 183 190 197 204 211 218 225 232 239 246$ Displacement Constraints of Load Set : pad_fixedSPC1 3 12 3004 3005 3006 3007 3039 3040 3041 3042$ Displacement Constraints of Load Set : pad_fixed2SPC1 4 12 4000 THRU 4023$ Deform Body Contact LBC set: diskBCBODY 8 3D DEFORM 8 0BSURF 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23.. . 208 209 210 211 212 213 214 215 216$ Deform Body Contact LBC set: pad1BCBODY 9 3D DEFORM 9 0BSURF 9 1004 1005 1006 1010 1011 1012 1016 1017 1018 1022 1023 1024 1028 1029 1030$ Deform Body Contact LBC set: pad2BCBODY 10 3D DEFORM 10 0BSURF 10 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045$ Deform Body Contact LBC set: pistonBCBODY 11 3D DEFORM 11 0BSURF 11 1046 1047 1048 1049 BCBODY 12 3D DEFORM 12 0BSURF 12 1050 1051 1052 1053$ Pressure Loads of Load Set : pressurePLOAD4 1 1046 50. 5009 5011PLOAD4 1 1047 50. 5013 5012PLOAD4 1 1048 50. 5014 5015PLOAD4 1 1049 50. 5012 5017


108

PLOAD4 1 1050 50. 50. 50. 50. 10008 10003PLOAD4 1 1051 50. 50. 50. 50. 10005 10009PLOAD4 1 1052 50. 50. 50. 50. 10001 10008PLOAD4 1 1053 50. 50. 50. 50. 10007 10006$ Referenced Coordinate FramesCORD2C 1 0. 0. 0. 0. 0. 1. 1. 0. 0.ENDDATA $

Figure 3-10 First Instable Mode Shape (Frequency=31.1 Hz)

C O M P L E X E I G E N V A L U E S U M M A R Y ROOT EXTRACTION EIGENVALUE FREQUENCY DAMPING NO. ORDER (REAL) (IMAG) (CYCLES) COEFFICIENT 1 1 0.0 0.0 0.0 0.0 2 2 0.0 5.267539E+01 8.383549E+00 0.0 3 3 0.0 5.758587E+01 9.165074E+00 0.0 4 4 0.0 8.833070E+01 1.405827E+01 0.0 5 5 0.0 1.052037E+02 1.674369E+01 0.0 6 6 0.0 1.070820E+02 1.704263E+01 0.0 7 8 -1.901260E+00 1.953634E+02 3.109305E+01 1.946383E-02 8 7 1.901260E+00 1.953634E+02 3.109305E+01 -1.946383E-02 9 10 -1.548788E+00 3.172325E+02 5.048912E+01 9.764370E-03 10 9 1.548788E+00 3.172325E+02 5.048912E+01 -9.764370E-03 11 15 0.0 3.943055E+02 6.275567E+01 0.0 12 14 0.0 4.006665E+02 6.376806E+01 0.0 13 13 0.0 4.113044E+02 6.546112E+01 0.0 14 12 0.0 4.669658E+02 7.431991E+01 0.0 15 11 0.0 4.695969E+02 7.473867E+01 0.0

109CHAPTER 3


SOL 400 Materials and Elements

Introduction

MD Nastran R3 introduces into SOL 400 extensive enhancements for nonlinear large strain and material

behavior. In addition to the materials introduced in MD Nastran R2, the following have been added or

enhanced:

• Orthotropic material properties for 3-dimensional and plane strain behavior via the MATORT

Bulk Data entry,

• Nonlinear gasket material properties for compression behavior via the MATG Bulk Data entry,

• Elastoplastic material properties for use in large deformation analysis via the MATEP Bulk Data

entry,

• Also, several new materials have been introduced in MD Nastran R3.

Substantial enhancements to element technology in MD Nastran R3 include introduction of several new

full and reduced integration continuum and shell elements. The continuum elements include:

• Lower and higher order plane stress,

• Plane strain,

• Axisymmetric elements for two dimensional analysis

• Tetrahedral, hexahedral and pentahedral elements for three dimensional analysis.

Other plane stress elements for structural elements include lower order thin and thick shells using full

and reduced integration schemes as well as membrane elements. In addition, several truss and beam

elements have also been added.

The MD Nastran R3 material modeling enhancements include:

• A new modeling procedure for large strain incompressible materials using a multiplicative

decomposition of deformation gradient and is activated using the NLMOPTS Bulk Data entry,

• Anisotropic plasticity (Hill and Barlat models),

• Pressure dependent plasticity (linear and parabolic Mohr-Coulomb),

• Viscoplasticity,

• Cyclic plasticity and viscoplasticity (Chaboche model),

• Nonlinear stress-strain law for isotropic and orthotropic materials using the advanced nonlinear

elements,

• Viscoelasticity with or without temperature dependent behaviors (power law, WLF and

Narayanaswamy models),

• Creep (Maxwell and Kelvin models),

• Elastomers (Mooney, Ogden, Arruda-Boyce and Gent models)

MD Nastran R3 Release Guide SOL 400 Materials and Elements

110

• Shape memory alloy materials (Aruchhio for mechanical and Asaro-Sayeedvafa for thermo-

mechanical models).

To take advantage of these material descriptions the new PSHLN1, PSHLN2, and PSLDN1 Bulk Data

entries must be used.

Two new procedures for progressive failure analysis of composite materials have been added. Micro-

mechanical module and damage capability have been incorporated and are available through the MATM

Bulk Data entry. The MATM option allows the definition of composite properties by giving the properties

of the constituent materials. See the separate section for a more detailed description of this option.

Secondly, the existing failure criteria in the MATF option have been enhanced to support progressive

failure. The available failure criteria include the Puck criterion and variants of the Hashin criterion.

Special formulations for tape and fabric type of composites are available. These new procedures are only

available together with the PSHLN1, PSHLN2, and PSLDN1 Bulk Data entries.

In addition, support for multi-dimensional tables: TABLE3D0, TABL3D1, TABL3D2 has been extended

for the advanced nonlinear elements. Initial stress and initial plastic strain can also be input to the analysis

for these elements in MD Nastran R3.

For the advanced nonlinear elements, the composite shell capabilities in MD Nastran are invoked through

use of the PCOMP or PCOMPG Bulk Data entries with PSHELL being extended by PSHLN1 Bulk Data

entry. For continuum elements, PLCOMP (for plane strain and axisymmetric elements) and PCOMPLS

(for three-dimensional solids) Bulk Data entries must be used.

The onset of delamination is simulated using a new class of hexahedral, pentahedral, quadrilateral, and

axisymmetric quadrilateral interface elements. This capability is invoked via the CIFPENT, CIFHEX,

CIFQUAD, and CIFQDX Bulk Data entries and their associated property entry defined by PCOHE. The

elements use cohesive material modeled using the MCOHE Bulk Data entry. Mixed mode delamination

is incorporated by converting the normal and shear components of relative displacement into an

equivalent relative displacement using the shear-normal weighting factor.

Fracture mechanics modeling is now possible using the Virtual Crack Closure Technique via the VCCT

Bulk Data entry for evaluating energy release rates. Multiple cracks can be defined and results will be

obtained for each crack separately. Each crack consists of a crack tip grid for shells and a crack front for

solids. A crack is also allowed to grow. This can occur if the crack is in a glued contact interface. You

can enter a crack growth resistance (fracture toughness) for the crack. If the calculated energy release rate

is larger than this value the crack will grow. This is done by automatically releasing the glued contact

interface segment by segment.

Benefits

With these material enhancements, MD Nastran SOL 400 is in a better position to support model products

and processes requiring advanced nonlinear analysis in several products and industries e.g.

manufacturing processes requiring large deformation plasticity and contact, rubber seals and boots

requiring elastomers, stents in bio-medical applications requiring use of shape memory materials, creep

and viscoplasticity in analysis of high temperature material behavior for aerospace materials and

composite materials design requiring an accurate modeling of failure and delamination.

111CHAPTER 3


Advanced Integrated Nonlinear Analysis

Input

To take advantage of the new large strain, new material, and fracture mechanics enhancements the

following Bulk Data entries are needed:

New Element Input

1. CIFPENT, CIFHEX, CIFQUAD, and CIFQDX Bulk Data entries: These are new MD Nastran

interface elements (currently valid only in SOL 400) used to simulate the onset or progress of

delamination.

2. CQUAD, CQUADX, and CTRIAX Bulk Data entries: These three existing entries have had a

(THETA/MCID) field added to their description. This new field is only applicable if the

PLPLANE entry has an associated PSHLN2 entry. If the element only has a PLPLANE property,

the field is ignored.

New Property Input

1. PSHLN1 Bulk Data entry: This entry extends the large strain and new material capabilities to the

general shells defined by CQUAD4, CQUADR, CQUAD8, CTRIA3, or CTRIAR elements. This

entry MUST have the same property ID as the PSHELL, PCOMP, or PCOMPG associated with

the element. If any GRID of a shell element is listed on the new VCCT (Virtual Crack Closure

Technique) Bulk Data entry, that shell element MUST have a PSHLN1 entry associated with it.

2. PSHLN2 Bulk Data entry: This entry extends the large strain and new material capabilities to the

two-dimensional solid plane strain, plane stress, or axisymmetric elements defined by the

CQUAD4, CQUAD8, CTRIA6, CQUAD and CQUADX with either four or eight grids, or

CTRIAX with six grids. This entry MUST have the same property ID as the PLPLANE

associated with the element. These element MUST lie in the basic X-Y plane. If any GRID of a

two-dimensional solid element is listed on the new VCCT Virtual Crack Closure Technique Bulk

Data entry, that 2-dimensional solid element must have a PSHLN2 entry associated with it.

3. PSLDN1 Bulk Data entry: This entry extends the large strain and new material capabilities to the

three-dimensional solid elements defined by the CHEXA and CTETRA. This entry MUST have

the same property ID as the PSOLID associated with the element. If any GRID of a 3-dimensional

solid element is listed on the new VCCT (Virtual Crack Closure Technique) Bulk Data entry, that

three-dimensional solid element MUST have a PSLDN1 entry associated with it.

4. PLCOMP Bulk Data entry: This entry extends composites to the 2-dimensional solid plane strain,

plane stress, or axisymmetric elements defined by CQUAD4, CQUAD8, CQUAD and CQUADX

with either four or eight grids.

5. PCOMPLS Bulk Data entry: This entry extends composites to the three-dimensional solid

element defined by CHEXA. A solid shell formulation is available with this entry.

6. PCOHE Bulk Data entry: The property interface or the CIFPENT, CIFHEX, CIFQUAD, and

CIFQDX elements.


112

7. PSHEARN Bulk Data entry: This entry extends large membrane rotation to the CSHEAR

element. Stringer effectiveness is ignored. The Bulk Data entry MDLPRM,SHRTOQ4,1 cannot

be used with this entry.

8. PCOMPF Bulk Data entry: This entry allows the use of fast integration for composite shells

leading to a computationally efficient solution. This is available for elastic materials, which may

use progressive failure, and can include thermal strains. No other material nonlinearity than

progressive failure is allowed.

9. PBEMN1 and PBARN1 Bulk Data entry: This entry allows the use of thin elastic as well as open

and closed section beams for large deformation nonlinear analysis.

10. PRODN1 Bulk Data entry: This entry allows the use of truss elements for line elements in three-

dimensional analysis.

New Material Input

1. MCOHE Bulk Data entry: This entry specifies material cohesive properties used to simulate the

onset or progress of delamination.

2. MATORT and MATG Bulk Data entries: These existing primary material entries have been

extended for use with SOL 400. Their associated MATTORT and MATTG entries are also valid

for specifying temperature dependent materials.

3. MATEP and MATF Bulk Data entries: These existing associated material entries have been

extended for use with SOL 400 for isotropic and anisotropic plasticity, pressure dependent

plasticity (linear and parabolic Mohr-Coulomb) as well as cyclic plasticity and viscoplasticity

(Chaboche model). The associated MATTEP entry is also valid for specifying temperature

dependent materials.

4. MAT3 Bulk Data entry: This existing entry may also be used in conjunction with PSHLN2 and

PLCOMP axisymmetric elements. The associated MATT3 entry is also valid for specifying

temperature dependent materials.

5. MATS1, MATS3 and MATSORT Bulk Data entries: To model nonlinear stress-strain laws using

the advanced nonlinear elements for isotropic and orthotropic materials.

6. MATHE Bulk Data entry: To model elastomers using the generalized Mooney, Ogden as well as

Arruda-Boyce and Gent Models. The associated MATTHE entry is also valid for temperature

dependent materials.

7. MATVP Bulk Data entry: To allow the use of creep material models using Kelvin and Maxwell

models.

8. MATVE Bulk Data entry: To allow the modeling of time dependent behavior of isotropic,

elastomeric, foam and glass materials. The associated MATTVE entry is valid for temperature

dependent materials represented by the power, WLF (William-Landel-Ferry) and

Narayanaswamy models.

9. MATSMA Bulk Data entry: To allow the use of mechanical (Aruchhio) and thermo-mechanical

(Asaro-Sayeedvafa) models for analysis of shape memory alloy models.

10. IPSTRAIN and IPSTRESS Bulk Data entry: To allow the use of initial stress and initial plastic

strain at the start of analysis from previous analyses.

113CHAPTER 3


11. MATM Bulk Data entry: To flag the use of the micro-mechanical failure and damage capability

for constituent material modeling and progressive failure. MATTM is available for specifying

temperature dependent failure data.

New Analysis Options Input

NLMOPTS Bulk Data entry: This entry controls parameters associated with PSHLN1, PSHLN2,

PLCOMP, PCOMPLS, and PCOHE. This allows the use of creep material behavior (using CREEP) as

well as new finite strain plasticity procedure using the multiplicative decomposition of deformation

gradient (using LRGSTRAIN). If, in the analysis with solid composite elements, a second order shear

correction is required (e.g. for compatibility with shells) then it can be triggered through the use of

TSHEAR parameter. This transverse shear option is only available for elastic materials and the elements

must not be stacked.

New Analysis Procedure Input:

1. VCCT Case Control command: By specifying VCCT=n, this command selects the VCCT Bulk

Data entry to be used in a given STEP.

2. VCCT Bulk Data entry: This entry specifies the Virtual Crack Closure Technique entry for

evaluating energy release rates.

Extensions to Table Input

The multi-dimensional table options have also been supported in the MD Nastran R3 release. They are

TABL3D0, TABL3D1 and TABL3D2. These table options allow you to define a table or formula with

up to 4 independent variables and can only be used with Marc elements or materials. These are especially

helpful when the material properties are a function of temperature, history variables like plastic strains

etc. or time (e.g. rate sensitive materials).

Output

The element output is obtained via standard MD Nastran STRESS=n and NLSTRESS=n commands.

Both linear formatted nonlinear stress and nonlinear stress/strain output is available. The Virtual Crack

Closure Technique output data is automatically placed on file OFVCCT. VCCT is utilized in the run it

is automatically output to the .f06 file.

Guidelines and Limitations1. For the beam and shell elements, the two-dimensional solid elements and three-dimensional solid

elements there are two types of property entries:

a. The primary property entries are the PROD, PBAR (or PBARL), PBEAM (or PBEAML),

PSHELL, PCOMP, PCOMPG, PLPLANE, PSOLID, PLCOMP, PCOMPLS, and PSHEAR.

b. An associated property such as a PRODN1, PBARN1, PBEMN1, PSHLN1, PSHLN2,

PSLDN1, PCOMPF and PSHEARN.

c. The associated property is matched to the primary property by having the same ID.


114

d. The PSHLN1 invokes the enhanced nonlinear capability for shell elements whose PID points

to a PSHELL, PCOMP, or PCOMPG. The PSHLN2 invokes the enhanced nonlinear

capability for two-dimensional solid elements whose PID points to a PLPLANE. The

PSLDN1 invokes the enhanced nonlinear capability for 3-dimensional solid elements whose

PID points to a PSOLID. The PBARN1 and PBEMN1 invoke the enhanced nonlinear

capability for one-dimensional structural with bending (i.e. beam elements) whose PID points

to a PBAR (or PBARL) and PBEAM (or PBEAML) respectively. The PRODN1 invokes the

enhanced nonlinear capability for one-dimensional membrane elements whose PID points to

a PRODN1.

2. In MD Nastran there are two types of material entries:

a. A primary material entry whose ID may appear on an appropriate PSHELL, PLPLANE,

PSOLID, PCOMP(G), PSHLN1, PSHLN2, PSLDN1, PLCOMP, PCOMPLS, PSHEAR etc.

(e.g. MCOHE, MATG, MATSMA)

b. An associated material entry whose ID must appropriately match one of the primary material

entry ID’s (e.g. MATEP, MATVP, MATVE)

c. The primary material entry MATORT ID may only appear on PSHLN2, PSLDN1, PLCOMP,

and PCOMPLS. If its ID appears on say a PSOLID in the MID field it will be ignored and the

run will fail with no material defined error. The primary material entry MATG ID may only

appear on PSHLN2 and or PSLDN1.

d. If the associated materials MATEP or MATF point to a primary material ID for shell elements

and there is no associated PSHLN1 pointing to a PSHELL, PCOMP, or PCOMPG the

associated material will not be used. If the associated materials MATEP or MATF point to a

primary material ID for two-dimensional solid elements that have a PLPLANE as their

primary property, and there is no associated PSHLN2 pointing to a PLPLANE, the associated

material will not be used. If the associated materials MATEP or MATF point to a primary

material ID for three-dimensional solid elements that have a PSOLID as their primary

property, and there is no associated PSLDN1 pointing to a PSOLID the associated material

will not be used.

3. Using the PSHLN1 entry you can change the material ID associated with the MID1 or MID2 or

both on the PSHELL. If these entries are left blank on the PSHLN1 then the MID1 and MID2

values on the PSHELL are used. The flow diagram below shows the PSHLN1’s relationship to

the shell elements.

LOAD STEP = 1.00000E+00V C C T C R A C K R E S U L T SCRACK TIP ------------- ENERGY RELEASE RATE ------------ ESTIMATED CRACK GROWTH DIRECTIONCRACK ID GRID ID TOTAL MODE I MODE II MODE III X Y Z100 1 4.5493E+01 4.5493E+01 7.6309E-16 0.0000E+00 1.0000E+00 1.3297E-16 0.0000E+00100 2 4.5484E+01 4.5484E+01 1.4533E-15 0.0000E+00 1.0000E+00 1.0262E-16 0.0000E+00100 3 4.5484E+01 4.5484E+01 4.3923E-17 0.0000E+00 1.0000E+00 1.6459E-16 0.0000E+00100 4 4.5493E+01 4.5493E+01 1.6856E-15 0.0000E+00 1.0000E+00 9.2419E-17 0.0000E+00

115CHAPTER 3


4. Using the PSHLN2 entry the user can change the material ID associated with the MID on the

PLPLANE. There is no default. The PLPLANE requires a MATHP and the user must override

with a MAT1, MAT2, MAT3, MAT8, MATORT, MATHE, or if appropriate a MATG, MCOHE

or MATSMA. The flow diagram below shows its relationship to the two-dimensional solid using

a PLPLANE entry as its primary property entry. On the PSHLN2 entry the BEHi codes are

sensitive to the required primary material used. MAT1 is applicable to all BEHi codes. MAT2

anisotropic and MAT8 orthotropic are applicable to BEHi=PSTRS codes only. MAT3

axisymmetric orthotropic is applicable to BEHi=AXSOLID code only. MATORT orthotropic are

applicable to BEHi=PLSTRN code only. MATG is applicable for BEH4=COMPS or AXCOMP

with INT4=L codes only. The BEH4=COMPS or AXCOMP with INT4=L should not be used

with MAT1, MAT2, MAT3, MAT8, or MATORT as they will suffer hour-glassing. In SOL 400,

if a PLPLANE entry has an associated PSNLN2 entry, it can directly refer to an appropriate

MAT1, MAT2, etc., material entry and not have a MATHP referral. However, in this case all

elements referring to the PLPLANE entry will fail in all other solution sequences.


116

5. The “key” word field entries on the PSHLN1, PSHLN2, PSLDN1, PLCOMP, and PCOMPLS

Bulk Data have default integration schemes and do not need to be defined in the property entry

again, if you are willing to use these defaults.

6. The MATG gasket material requires a special integration scheme. It is only available for elements

using a PSHLN2 or PSLDN1 Bulk Data entry. For the PSHLN2, the “C4” keyword entry with

BEH4=COMPS or AXCOMP and INT4=L would be required. For the solid BEH8=SLCOMP,

INT8=L would be required.

117CHAPTER 3


7. For composites, a solid shell element formulation is available. The DIRECT field entry must be

DIRECT=1 (the default). For the linear and quadratic formulations, no “key” word entry is

required. The sample below shows the solid shell element request.

8. Because these new material features often involve large deformation, it is recommended that a

full Newton iteration scheme be used. This has been facilitated on the NLPARM Bulk Data entry

by the addition to the KMETHOD field the key word “FNT” or “PFNT” and the TSTEPNL Bulk

Data entry by the addition to the METHOD field the key word “FNT” or “PFNT”. If the “FNT”

option is chosen, then a “V” is added to either one or more of the “U”, “P” or “W” type of

convergence criteria.

9. Any shell element that has non structural mass (NSM) that utilizes any PSHELN1 or PSHLN2

entry will lose the associated non structural mass.

MD Nastran R3 Release Guide Enhancements to Connector Elements

118

Enhancements to Connector Elements

Introduction

In MD Nastran R3 the connector elements CBUSH, CWELD and CFAST have been enhanced for usage

in a nonlinear SOL 400 analysis. In SOL 400 the elements fully support large displacement and large

rotation effects and can now be used in a geometrically-nonlinear analysis where these effects can no

longer be ignored. There is no additional modeling effort required for the connector elements when

preparing a nonlinear model that includes them, so the input Bulk Data entries CBUSH/PBUSH,

CWELD/PWELD and CFAST/PFAST remain unchanged. However, the elements are treated differently

internally in a nonlinear SOL 400 analysis than a linear analysis. This results in slightly different ways

of presenting the results in the .f06-file and in the op2- or .xdb files.

CBUSH Enhancements in SOL 400

CBUSH is a generalized spring-damper element representing a bushing connection. The element has

been enhanced to

• Support geometrically-nonlinear analysis involving large displacement and large rotation.

• Allow the materially-nonlinear force-deflection curve to support radial and spherical behavior.

• Allow the CBUSH to FUSE at various failure criteria.

For CBUSH to support large rotations, appropriate transformations are needed during element stiffness

and damping matrices generation as well as during internal force computations. In addition, differential

stiffness terms need to be computed. All CBUSH orientation configurations have been enhanced. These

include:

• Axial CBUSH.

• CBUSH defined using an orientation vector .

• CBUSH defined using a coordinate system CID.

During large rotation, an axial CBUSH will always be oriented from grid GA to grid GB. The user is

allowed the following options to control the behavior of a CBUSH defined using a coordinate system or

an orientation vector during large rotation:

• Allow the CBUSH to rotate with the rotational degrees of freedom of GA (default).

• Fix the CBUSH orientation to the initial orientation defined by CID or .

• Use a mid-increment method to rotate the CBUSH defined by

The large rotation options are controlled using the LRGR flag under the modified PBUSHT Bulk Data

entry. Enhancements to the materially-nonlinear force-deflection curve to support radial and spherical

behavior are controlled by the new flag FDC, under the modified PBUSHT Bulk Data entry. The CBUSH

ν

ν

ν

119CHAPTER 3


failure criteria introduced in this release include an ultimate load and a maximum relative displacement.

These are specified using the FUSE option also under the modified PBUSHT Bulk Data entry.

Inputs

The CBUSH element is modeled by the CBUSH and PBUSH Bulk Data entries and the modified

PBUSHT Bulk Date entry. The details of these entries are described in the MD Nastran Quick Reference

Guide.

Outputs

There are no new outputs associated with the CBUSH enhancements.

Example

The following example demonstrates the use of CBUSH in a geometrically-nonlinear SOL 400 analysis.

In this example, an axial CBUSH is undergoing an axial extension followed by a 90o rigid body rotation.

One end of the CBUSH is fixed while the other moves with prescribed displacements to simulate the

extension and rotation. The LGDISP flag is turned on. The input file follows:

SOL 400CENDDISP=ALLSPCF=ALLSTRESS=ALLSTRAIN=ALLNLSTRESS=ALLNLPARM=1STEP 1 SPC = 1 LOAD = 1STEP 2 SPC = 1 LOAD = 2BEGIN BULKPARAM LGDISP 1PARAM POST 0NLPARM 1 1GRID 1 0.0 0.0 0.0GRID 2 1.0 0.0 0.0GRID 3 2.0 0.0 0.0CBUSH 1 2 1 2PBUSH 2 K 1.0E5SPC1 1 123456 1SPC1 1 123456 2SPCD 1 2 1 1.0 2 2 0.0SPCD 2 2 1 -1.0 2 2 2.0ENDDATA


120

The results are as follows:

The nonlinear forces and stresses section of the output indicate that the element forces due to the axial

extension remain constant during the large rotation and are always along the element local x-direction.

The SPC forces indicate that the reactions at the grid points due to the prescribed displacements have

changed directions from the global x-direction to the global y-direction.

Nonlinear CWELD and CFAST Elements in SOL 400

In a nonlinear SOL 400 analysis each connector element is not assembled as one element, but is internally

mapped onto a group of elements, that when assembled together, simulate the behavior of the original

connector element. Each assembly consists of one deformable element and a group of rigid body

elements. In the case of a CWELD, this deformable element is a CBEAM element, and in the case of a

CFAST it is a CBUSH element. The rigid body elements insure that the deformable element gets

connected to the plate surfaces on either side of a connection in exactly the same way as the original

connector element and all connection types for CWELD (i.e. PARTPAT, ELPAT, ELEMID, GRIDID and

ALIGN) and for CFAST (i.e. PROP and ELEM) are supported. All rigid body elements involved in the

connections are RBE3 elements. The process of mapping the connector elements requires a number of

new elements and grids to be generated internally, that are not present in the original Bulk Data input.

LOAD STEP = 1.00000E+00 N O N L I N E A R F O R C E S A N D S T R E S S E S I N B U S H E L E M E N T S ( C B U S H ) F O R,C E S T R E S S S T R A I N ELEMENT ID. FORCE-X FORCE-Y FORCE-Z STRESS-TX STRESS-TY STRESS-TZ STRAIN-TX STRAIN-TY STRAIN-TZ MOMENT-X MOMENT-Y MOMENT-Z STRESS-RX STRESS-RY STRESS-RZ STRAIN-RX STRAIN-RY STRAIN-RZ 1 1.00000E+05 0.0 0.0 1.00000E+05 0.0 0.0 1.00000E+00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

LOAD STEP = 2.00000E+00 N O N L I N E A R F O R C E S A N D S T R E S S E S I N B U S H E L E M E N T S ( C B U S H ) F O R,C E S T R E S S S T R A I N ELEMENT ID. FORCE-X FORCE-Y FORCE-Z STRESS-TX STRESS-TY STRESS-TZ STRAIN-TX STRAIN-TY STRAIN-TZ MOMENT-X MOMENT-Y MOMENT-Z STRESS-RX STRESS-RY STRESS-RZ STRAIN-RX STRAIN-RY STRAIN-RZ 1 1.00000E+05 0.0 0.0 1.00000E+05 0.0 0.0 1.00000E+00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

LOAD STEP = 1.00000E+00 D I S P L A C E M E N T V E C T O R POINT ID. TYPE T1 T2 T3 R1 R2 R3 1 G 0.0 0.0 0.0 0.0 0.0 0.0 2 G 1.000000E+00 0.0 0.0 0.0 0.0 0.0 3 G 0.0 0.0 0.0 0.0 0.0 0.0

LOAD STEP = 2.00000E+00 D I S P L A C E M E N T V E C T O R POINT ID. TYPE T1 T2 T3 R1 R2 R3 1 G 0.0 0.0 0.0 0.0 0.0 0.0 2 G -1.000000E+00 2.000000E+00 0.0 0.0 0.0 0.0 3 G 0.0 0.0 0.0 0.0 0.0 0.0

LOAD STEP = 1.00000E+00 F O R C E S O F S I N G L E - P O I N T C O N S T R A I N T POINT ID. TYPE T1 T2 T3 R1 R2 R3 1 G -1.000000E+05 0.0 0.0 0.0 0.0 0.0 2 G 1.000000E+05 0.0 0.0 0.0 0.0 0.0

LOAD STEP = 2.00000E+00 F O R C E S O F S I N G L E - P O I N T C O N S T R A I N T POINT ID. TYPE T1 T2 T3 R1 R2 R3 1 G 0.0 -1.000000E+05 0.0 0.0 0.0 0.0 2 G 0.0 1.000020E+05 0.0 0.0 0.0 0.0

121CHAPTER 3


The deformable element in a connection inherits the ID of the original connector element, but the RBE3

elements obtain IDs that are automatically assigned by the program. The GA and GB grids of the

connector element define the two grids of the deformable CBEAM or CBUSH element and if they are

not entered on the CWELD or CFAST entries, their IDs are automatically assigned by the program. The

connection types ELPAT and PARTPAT for CWELD and ELEM and PROP for CFAST, define four

auxiliary points on each side of a connection. These points are mapped internally to grids that get their

IDs automatically assigned by the program. The grid IDs and element IDs assigned by the program have

large offsets with respect to the IDs in the model and these offsets may be changed with

PARAM,OSWPPT (by default 101,000,000) and PARAM,OSWELM (by default 100,001,001). The

material models supported for a CWELD are the ones that are supported for a CBEAM element. For a

CFAST the linear stiffness values are entered on the PFAST input. If the CFAST element has a mass, it

is mapped on two CONM2 elements connected to the GA and GB grids of the CBUSH element.

Inputs

The CWELD and CFAST Bulk Data entries are used to define a CWELD and CFAST element in the

same way as for a linear analysis. The properties are defined in the PWELD and PFAST Bulk Data

entries. No additional data is needed to prepare these inputs for a nonlinear analysis. MD Nastran

recognizes the analysis type and for a nonlinear SOL 400 analysis, it applies the mapping procedure as

outlined in the previous section. The MSET-field on the PWELD Bulk Data entry has no effect in a

nonlinear SOL 400 analysis. The details of these bulk data entries are described in the MD Nastran Quick

Reference Guide.

Outputs

The results of a CWELD element are output to the. f06 file in the format of the CBEAM element. The

CWELD output is separated from the CBEAM output if there are also CBEAM entries in the bulk data

input. The CBEAM output, if present, is always listed first, followed directly by the CWELD output. The

CWELD output can be recognized by the presence of the string “C W E L D” in the header lines of the

element output. There is no distinction between CWELD, CWELDC and CWELDP elements as there is

in the linear case.

Similarly the results of a CFAST element are output to the .f06 file in the format of the CBUSH element.

The CFAST output is separated from the CBUSH output if there are also CBUSH entries in the bulk data

input. The CBUSH output, if present, is always listed first, followed directly by the CFAST output. The

CFAST output can be recognized by the presence of the string “C F A S T” in the header lines of the

element output.

Details about the locations of the projection points, their associated grid IDs and the internally generated

RBE3 IDs are printed when the PRTSW-parameter on the SWLDPRM Bulk Data entry is activated.

For post-processing the results of connector elements are available as CBEAM or CBUSH results on the

.op2- or .xdb-file.


122

Supported Output Requests

The following element output requests are supported for the CWELD and CFAST elements: NLSTRESS,

STRESS/ELSTRESS, FORCE/ELFORCE, STRAIN and ESE.

The element summary (ELSUM) reflects the presence of CWELD or CFAST elements, they are not

lumped together with the CBEAM or CBUSH elements.

The GPFORCE output for the grids involved in a CWELD or CFAST element reflects the output for each

separate element that arises from the mapping procedure and not for the assembly of these elements into

one connector element, i.e. there is output for the GA- and GB-grids of the deformable element (WELD

or BUSH) and the grids of the rigid body elements (RBE3).

Details of these output requests are found in the The Case Control Section (Ch. 4) in the MD Nastran

Quick Reference Guide.

Limitations

When requesting .op2- or .xdb-output to be used for further processing in a separate post-processor, you

must include the geometry in these files and open the files in the post-processor reading both the model

and the results data. You cannot add the results data to the model data that may already be present in the

database of the pre-processor, since the mapping procedure alters the element type of the connector

elements and generates additional grids and rigid body elements not present in the original data base. The

connector elements are post processed as CBEAM or CBUSH elements and they are present as such in

the model and result parts of the .op2- or .xdb-file.

The DISP(CONN = …, …) output request for the displacements of grids of selected connector elements

is not yet supported.

Example

Figure 3-11 shows the connection of two square plates by one CWELD of type ELPAT. The relevant bulk

data input for this model is shown. Of special interest for this analysis are the SOL 400 Executive Control

statement, the NLPARM Case Control command, the “PARAM, LGDISP,1”, the NLPARM,

SWLDPRM, CWELD and PWELD Bulk Data entries. The diameter of the CWELD is 11.28379 mm,

resulting in a 10x10 mm auxiliary patch on each side. The two 25x25 mm plates are 5 mm apart, thus the

connector element length is 5.0 mm. The material behavior is linear elastic, but the PARAM,LGDISP,1

input allows for large displacement and large rotation effects.

123CHAPTER 3


Figure 3-11 Input data for a model with one CWELD of type ELPAT connecting two square

plates.

pli=QMM`bkaqfqib=Z=ja=k^pqo^k=`tbiaIbim̂ qIûfîpr_`^pb=N=pr_qfqibZabc^riq=kimôjZN=pm`ZQ=ilâZR=afpmi^`bjbkqEploqNIobîFZîi=pm`clo`bpEploqNIobîFZîi=jm`clo`bpEploqNIobîFZîi=kipqobppEploqNFZîi=pqobppEploqNIobîIslkjfpbpI_fifkFZîi=pqo^fkEploqNIobîIslkjfpbpI_fifkFZîi=biclo`bEploqNIobîIslkjfpbpI_fifkFZîi=bpbEqeobpeZMKMFZîi=dmclo`bZîi=biprjE_lqeFZîiAA=k^pqo^k=_rih=a^qÂ_bdfk=_rihptiamojImoqptINm̂ o^j====mlpq=====Mm̂ o^j====^rqlpm`=klm̂ o^j====idafpm==Nm̂ o^j===moqjûfj=vbpkim̂ oj==N=======NM==============^rql====R=======OR======rm======klclo`b===R=======TS==============MK======KRTTPR==KRTTPR==KRTTPRpm`âa==Q=======N=======O=======PAA=bibjbkqp=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZA`nrâQ==O=======N=======N=======NN======NO======S=======`nrâQ==P=======N=======S=======NO======NP======T=======KKK`nrâQ==RM======N=======SV======TQ======TR======TM======`nrâQ==RN======N=======TM======TR======QO======TN======AA=dofap=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZAdofaG===N==================================JNKORMMMMbHMN===JNKORMMMMbHMNG==========JOKRMMMMMbHMMM===============dofaG===O===================================NKORMMMMbHMN===JNKORMMMMbHMNG==========JOKRMMMMMbHMMM===============KKKdofaG===TR==================================NKORMMMMbHMN====TKRMMMMMbHMMG===========OKRMMMMMbHMMM===============dofaG===TS==================================MKMMMMMMbHMM====MKMMMMMMbHMMG===========MKMMMMMMbHMMM===============AA=j^qbofîp=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZAj^qNG===N===================OKMMMMMMbHMR====================PKMMMMMMbJMNG===========NKMMMMMMbHMM====MKMMMMMMbHMMAA=molmboqfbp=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZAmpebii=========N=======N=====OKM=======N===============Nmtbia==========O=======NNNKOUPTVIMKMO`tbia=======NMMM=======O======TS==bim̂ q=================================HH=============NQ======PVAA=_lrkaôv=`lkafqflkp=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZApm`G====N===============N==============================N====MKMMMMMMbHMMG=======pm`G====N===============N==============================O====MKMMMMMMbHMMG=======pm`G====O===============N==============================P====MKMMMMMMbHMMG=======KKKAA=pmà=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZApmàG===R===============N==============================P===JNKMMMMMMbHMMG=======KKKbkaa^q^


124

The elements and grids with their IDs are shown in Figure 3-12. The CWELD element ID is 1000,

therefore the CBEAM ID in the OP2- or XDB-results file is also 1000. A number of grids are generated

internally. The two grids of the CBEAM obtain IDs 101,000,001 and 101,000,002. Per CWELD eight

auxiliary grids are generated which obtain IDs 101,000,003 through 101,000,010.

Figure 3-12 FEM model with one CWELD of type ELPAT connecting two square plates.

Results for the connector element are as follows:

...

...

CWELD EID= 1000 WITH ELPAT OR PARTPAT AUXILIARY POINTS= (-5.0000E+00,-5.0000E+00,-2.5000E+00) ( 5.0000E+00,-5.0000E+00,-2.5000E+00) ( 5.0000E+00, 5.0000E+00,-2.5000E+00) (-5.0000E+00, 5.0000E+00,-2.5000E+00) (-5.0000E+00,-5.0000E+00, 2.5000E+00) ( 5.0000E+00,-5.0000E+00, 2.5000E+00) ( 5.0000E+00, 5.0000E+00, 2.5000E+00) (-5.0000E+00, 5.0000E+00, 2.5000E+00) AUXILIARY GRIDS GHA= 101000003 101000004 101000005 101000006 AUXILIARY GRIDS GHB= 101000007 101000008 101000009 101000010 RBE3 IDS FOR GHA1-4= 100001004 100001005 100001006 100001007 RBE3 IDS FOR GHB1-4= 100001008 100001009 100001010 100001011 NUMBER OF TIMES GS MOVES= 0 NUMBER OF TIMES DA IS REDUCED= 0 ANGLE BETWEEN TWO SHELL NORMALS= 0.00 GS=( 0.000E+00, 0.000E+00, 0.000E+00) GA=( 0.000E+00, 0.000E+00,-2.500E+00) GB=( 0.000E+00, 0.000E+00, 2.500E+00) T_BE MATRIX: 0.0000E+00 1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.0000E+00 1.0000E+00 0.0000E+00 0.0000E+00

125CHAPTER 3


d^=fa=====Z=NMNMMMMMN===d_=fa=====Z=NMNMMMMMORBE3 ID A = 100001002 RBE3 ID B = 100001003

PATCH A: EID= 8 GIDS= 12 18 19 13 0 0 0 0 EID= 18 GIDS= 24 30 31 25 0 0 0 0 EID= 20 GIDS= 26 32 33 27 0 0 0 0 EID= 10 GIDS= 14 20 21 15 0 0 0 0PATCH B: EID= 33 GIDS= 49 55 56 50 0 0 0 0 EID= 43 GIDS= 61 67 68 62 0 0 0 0 EID= 45 GIDS= 63 69 70 64 0 0 0 0 EID= 35 GIDS= 51 57 58 52 0 0 0 0...LOAD STEP = 1.00000E+00 N O N L I N E A R S T R E S S E S I N W E L D E L E M E N T S ( C W E L D )

ELEMENT GRID POINT STRESS EQUIVALENT TOTAL STRAIN EFF. STRAIN EFF. CREEP ID ID STRESS PLASTIC/NLELAST STRAIN 1000 101000001 C 1.290066E+02 1.290066E+02 6.450332E-04 0.0 0.0 D 1.290066E+02 1.290066E+02 6.450332E-04 0.0 0.0 E 1.290066E+02 1.290066E+02 6.450332E-04 0.0 0.0 F 1.290066E+02 1.290066E+02 6.450332E-04 0.0 0.0 101000002 C 1.290066E+02 1.290066E+02 6.450332E-04 0.0 0.0 D 1.290066E+02 1.290066E+02 6.450332E-04 0.0 0.0 E 1.290066E+02 1.290066E+02 6.450332E-04 0.0 0.0 F 1.290066E+02 1.290066E+02 6.450332E-04 0.0 0.0...LOAD STEP = 1.00000E+00 D I S P L A C E M E N T V E C T O R POINT ID. TYPE T1 T2 T3 R1 R2 R3 54 G -2.366882E-04 2.518907E-03 2.201321E-01 -4.363906E-02 2.793858E-02 -1.280631E-02 55 G -3.291661E-03 -1.991543E-03 -1.020590E-02 -4.370676E-02 2.255758E-02 -9.173469E-04... 75 G -7.230500E-03 -2.870318E-03 5.085921E-01 7.637381E-02 -6.415410E-02 3.673183E-02 76 G 0.0 0.0 0.0 0.0 0.0 0.0 101000001 G -4.453620E-15 -4.830421E-15 -1.612583E-03 -1.973814E-15 1.700749E-15 1.505883E-17 101000002 G 3.312258E-15 3.882926E-15 1.612583E-03 -2.339357E-15 2.159162E-15 -5.508353E-17 101000003 G -3.721987E-03 -3.721987E-03 -1.612583E-03 3.667419E-02 -3.667419E-02 -1.298351E-16 101000004 G 3.721987E-03 -3.721987E-03 -1.612583E-03 3.667419E-02 3.667419E-02 1.079322E-16 101000005 G 3.721987E-03 3.721987E-03 -1.612583E-03 -3.667419E-02 3.667419E-02 -2.717700E-17 101000006 G -3.721987E-03 3.721987E-03 -1.612583E-03 -3.667419E-02 -3.667419E-02 -1.795417E-16 101000007 G -3.721987E-03 -3.721987E-03 1.612583E-03 -3.667419E-02 3.667419E-02 1.043341E-16 101000008 G 3.721987E-03 -3.721987E-03 1.612583E-03 -3.667419E-02 -3.667419E-02 -6.137916E-17 101000009 G 3.721987E-03 3.721987E-03 1.612583E-03 3.667419E-02 -3.667419E-02 -2.464781E-17 101000010 G -3.721987E-03 3.721987E-03 1.612583E-03 3.667419E-02 3.667419E-02 1.751367E-16

...LOAD STEP = 1.00000E+00 F O R C E S I N W E L D E L E M E N T S ( C W E L D ) STAT DIST/ - BENDING MOMENTS - - WEB SHEARS - AXIAL TOTAL WARPINGELEMENT-ID GRID LENGTH PLANE 1 PLANE 2 PLANE 1 PLANE 2 FORCE TORQUE TORQUE 1000 101000001 0.000 0.0 -2.019484E-28 0.0 -4.038968E-29 1.290066E+04 0.0 0.0 101000002 1.000 0.0 0.0 0.0 -4.038968E-29 1.290066E+04 0.0 0.0...LOAD STEP = 1.00000E+00 S T R A I N S I N W E L D E L E M E N T S ( C W E L D ) STAT DIST/ELEMENT-ID GRID LENGTH SXC SXD SXE SXF S-MAX S-MIN M.S.-T M.S.-C 1000 101000001 0.000 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 101000002 1.000 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04


126

LOAD STEP = 1.00000E+00 F O R C E S O F M U L T I P O I N T C O N S T R A I N T

POINT ID. TYPE T1 T2 T3 R1 R2 R3 12 G 3.521063E-04 3.521062E-04 8.062816E+02 0.0 0.0 0.0 13 G -1.718600E-09 -1.697555E-09 8.062912E+02 0.0 0.0 0.0 14 G -1.636564E-09 1.511392E-09 8.062912E+02 0.0 0.0 0.0 15 G 3.521063E-04 -3.521064E-04 8.062816E+02 0.0 0.0 0.0 18 G -1.677591E-09 -1.656546E-09 8.062912E+02 0.0 0.0 0.0 19 G -3.521096E-04 -3.521096E-04 8.063008E+02 0.0 0.0 0.0 20 G -3.521096E-04 3.521095E-04 8.063008E+02 0.0 0.0 0.0 21 G -1.634595E-09 1.509423E-09 8.062912E+02 0.0 0.0 0.0 24 G 1.497272E-09 -1.671058E-09 8.062912E+02 0.0 0.0 0.0 25 G 3.521094E-04 -3.521096E-04 8.063008E+02 0.0 0.0 0.0 26 G 3.521095E-04 3.521094E-04 8.063008E+02 0.0 0.0 0.0 27 G 1.519796E-09 1.485394E-09 8.062912E+02 0.0 0.0 0.0 30 G -3.521064E-04 3.521063E-04 8.062816E+02 0.0 0.0 0.0 31 G 1.497269E-09 -1.671055E-09 8.062912E+02 0.0 0.0 0.0 32 G 1.521348E-09 1.486946E-09 8.062912E+02 0.0 0.0 0.0 33 G -3.521064E-04 -3.521065E-04 8.062816E+02 0.0 0.0 0.0 49 G 3.521064E-04 3.521065E-04 -8.062816E+02 0.0 0.0 0.0 50 G -1.457365E-09 -1.495689E-09 -8.062912E+02 0.0 0.0 0.0 51 G -1.521572E-09 1.645789E-09 -8.062912E+02 0.0 0.0 0.0 52 G 3.521064E-04 -3.521063E-04 -8.062816E+02 0.0 0.0 0.0 55 G -1.464358E-09 -1.502682E-09 -8.062912E+02 0.0 0.0 0.0 56 G -3.521094E-04 -3.521095E-04 -8.063008E+02 0.0 0.0 0.0 57 G -3.521095E-04 3.521096E-04 -8.063008E+02 0.0 0.0 0.0 58 G -1.521775E-09 1.645992E-09 -8.062912E+02 0.0 0.0 0.0 61 G 1.659815E-09 -1.486565E-09 -8.062912E+02 0.0 0.0 0.0 62 G 3.521096E-04 -3.521094E-04 -8.063008E+02 0.0 0.0 0.0 63 G 3.521096E-04 3.521096E-04 -8.063008E+02 0.0 0.0 0.0 64 G 1.635683E-09 1.671656E-09 -8.062912E+02 0.0 0.0 0.0 67 G -3.521063E-04 3.521065E-04 -8.062816E+02 0.0 0.0 0.0 68 G 1.659034E-09 -1.485783E-09 -8.062912E+02 0.0 0.0 0.0 69 G 1.634400E-09 1.670374E-09 -8.062912E+02 0.0 0.0 0.0 70 G -3.521063E-04 -3.521063E-04 -8.062816E+02 0.0 0.0 0.0 101000001 G 1.101021E-09 1.278798E-09 -1.290066E+04 2.306006E-09 -4.593276E-09 1.887649E-09 101000002 G -1.098538E-09 -1.280010E-09 1.290066E+04 -8.807850E-09 1.016273E-08 -1.933290E-09 101000003 G 6.469971E-09 6.435660E-09 1.113312E-08 -4.506068E-02 4.506068E-02 -3.828222E-10 101000004 G -6.311491E-09 6.317369E-09 1.294347E-08 -4.506068E-02 -4.506068E-02 6.001081E-14 101000005 G -6.310388E-09 -6.311536E-09 1.294302E-08 4.506068E-02 -4.506068E-02 -1.564326E-11 101000006 G 6.314220E-09 -6.314174E-09 1.294165E-08 4.506068E-02 4.506068E-02 1.954644E-11 101000007 G 6.166376E-09 6.268448E-09 -1.343187E-08 4.506069E-02 -4.506068E-02 7.144588E-10 101000008 G -6.314767E-09 6.312995E-09 -1.294438E-08 4.506068E-02 4.506068E-02 -7.594164E-12 101000009 G -6.313828E-09 -6.315761E-09 -1.294393E-08 -4.506068E-02 4.506068E-02 1.315762E-11 101000010 G 6.313032E-09 -6.311856E-09 -1.294347E-08 -4.506068E-02 -4.506068E-02 -1.921700E-12...LOAD STEP = 1.00000E+00 S T R E S S E S I N W E L D E L E M E N T S ( C W E L D ) STAT DIST/ELEMENT-ID GRID LENGTH SXC SXD SXE SXF S-MAX S-MIN M.S.-T M.S.-C 1000 101000001 0.000 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 101000002 1.000 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02...LOAD STEP = 1.00000E+00 E L E M E N T S T R A I N E N E R G I E S

ELEMENT-TYPE = WELD * TOTAL ENERGY OF ALL ELEMENTS IN PROBLEM = 1.118831E+04 SUBCASE 1 * TOTAL ENERGY OF ALL ELEMENTS IN SET -1 = 1.118831E+04

ELEMENT-ID STRAIN-ENERGY PERCENT OF TOTAL STRAIN-ENERGY-DENSITY 1000 2.080338E+01 0.1859 4.160678E-02

TYPE = WELD SUBTOTAL 2.080338E+01 0.1859

127CHAPTER 3


Table 3-1 Results for a model with one CWELD of type ELPAT connecting two square plates.

...LOAD STEP = 1.00000E+00 G R I D P O I N T F O R C E B A L A N C E POINT-ID ELEMENT-ID SOURCE T1 T2 T3 R1 R2 R3 1 F-OF-SPC -6.081972E+03 -6.081972E+03 -3.240928E+03 0.0 0.0 0.0 1 2 QUAD4 6.081972E+03 6.081972E+03 3.240928E+03 -5.258240E+00 5.258240E+00 1.925268E-11 1 *TOTALS* 0.0 0.0 0.0 -5.258240E+00 5.258240E+00 1.925268E-11 2 F-OF-SPC 6.081972E+03 -6.081972E+03 -3.240928E+03 0.0 0.0 0.0 2 22 QUAD4 -6.081972E+03 6.081972E+03 3.240928E+03 -5.258240E+00 -5.258240E+00 -2.108151E-11 2 *TOTALS* 0.0 0.0 0.0 -5.258240E+00 -5.258240E+00 -2.108151E-11......101000001 1000 WELD 2.002407E-11 2.246709E-11 1.290066E+04 2.019484E-28 0.0 0.0101000001 100001002 RBE3 1.101021E-09 1.278798E-09 -1.290066E+04 2.306006E-09 -4.593276E-09 1.887649E-09101000001 *TOTALS* 1.121045E-09 1.301265E-09 8.185452E-11 2.306006E-09 -4.593276E-09 1.887649E-09101000002 1000 WELD -2.002407E-11 -2.246709E-11 -1.290066E+04 0.0 0.0 0.0101000002 100001003 RBE3 -1.098538E-09 -1.280010E-09 1.290066E+04 -8.807850E-09 1.016273E-08 -1.933290E-09101000002 *TOTALS* -1.118563E-09 -1.302477E-09 -8.185452E-11 -8.807850E-09 1.016273E-08 -1.933290E-09101000003 100001002 RBE3 -3.224113E-10 -2.725434E-10 3.225165E+03 0.0 0.0 0.0101000003 100001004 RBE3 6.792382E-09 6.708203E-09 -3.225165E+03 -4.506068E-02 4.506068E-02 -3.828222E-10101000003 *TOTALS* 6.469971E-09 6.435660E-09 1.113312E-08 -4.506068E-02 4.506068E-02 -3.828222E-10... * * * END OF JOB * * *

MD Nastran R3 Release Guide Adaptive Time Stepping Scheme Enhancements for Quasi-Static Analysis

128

Adaptive Time Stepping Scheme Enhancements for Quasi-Static Analysis

An adaptive time stepping scheme was introduced in SOL 400 (MD Nastran R2) by using the NLAUTO

Bulk Data entry. The primary control scheme of the load step is based upon the number of recycles

needed to obtain convergence if full Newton Raphson method is used. For modified Newton Raphson

method, both the number of recycles and the number of new stiffness formations are taken into account.

In the current release (MD Nastran R3), several extensions have been made to improve robustness and

user-friendliness. To improve the overall convergence control, the artificial damping and auto-switch

features have been added. To analyze the creep material behavior, the adaptive time stepping for creep is

introduced. For convenience of use, the Bulk Data entry (NLAUTO) has been replaced by a new Bulk

Data entry NLADAPT. With NLADAPT (combined with NLPARM), you can set up the parameters for

SOL 400 to control the load step size of each increment.

NLADAPT Bulk Data Entry

NLADAPT is newly designed in MD Nastran R3 to replace the original NLAUTO Bulk Data entry used

in MD Nastran R2. With the NLADAPT Bulk Data entry, the time stepping control parameters defined

by NLAUTO are now defined with the optional word “STEP”. In addition, another optional word

“CREEP” is made available for the time step control of creep behavior in the current release.

Recycling Criterion

The default recycle based criterion works as follows: You specify a desired number of recycles. For most

problems, it is sufficient to provide a value in the range of three to five. For problems with severe

nonlinearities, or for problems with very small convergence tolerances, it may be necessary to increase

this number. This number is used as a target value for the load stepping scheme. If the number of recycles

required in the current increment is less than the desired number, the load step for the next increment is

increased. The time step increase is based on a factor, , that you can also specify. Typical values for

are in the range of 1.2 to 1.5. While the time step increase is obviously more aggressive with larger scale

factors, it should be noted that there may be excessive recycling and cutbacks if sudden nonlinearities are

encountered. In order to avoid this, the following logic is used for higher scale factors : If the actual

number of recycles in an increment is greater than 60% of the desired number of recycles (i.e., the current

increment did not converge easily), the increased scale factor for the next increment is limited to 1.25 for

scale factor values between 1.25 and 1.5625, and to 80% of the value for scale factors above 1.5625.

Time Step Cutback Scheme

The load step is never increased during an increment. If the number of recycles needed to obtain

convergence exceeds the desired number, the load step size is scaled back, the recycling cutback number

is incremented by 1 and the increment is performed again with the new load step. The scaleback factor

for the th cutback is taken as , where the factor is calculated from the expression

Su Su

Nr

Nr sNr s

129CHAPTER 3


where is the maximum number of recycling related cutbacks for the increment and is calculated from

is the time increment before any recycling related cutbacks occur for the increment and is the

minimum possible time step for the increment. is equal to the value set by the user ( by default)

if there is no quasi-static inertial damping and is equal to times the value set by the user ( by

default) if there is quasi-static inertial damping. The scale-back factor for any cutback is the smaller of

( , ). This scheme guarantees that no matter what the starting time step for an increment, the

minimum time step is reached in a reasonable number of cutbacks if the increment consistently fails to

converge.

Quasi-Static Damping Scheme

For mechanical static analysis, instability often occurs under the conditions with very strong

nonlinearities or very low stress of the whole analyzed model. In order to improve the stability under

such circumstances, the artificial damping scheme is made available to SOL 400 in the current MD

Nastran R3 release.

The optional default damping scheme is identified as scheme number 4 in the corresponding Marc

technology (and is the only one implemented in MD Nastran SOL 400).

With this feature a damping factor, , is introduced, which at the start of the loadcase, is set to 0. The

time step for the first increment is set equal to the user defined initial time step. During the assembly of

the stiffness matrix and the right-hand side vector , the contributions from damping are added to

both sides of the equation system as and , respectively.

With artificial damping option, the adaptive time stepping scheme is still used to control the time step

size, however, the adjustment will be made based on the damping energy of the system. For the first

increment of the loadcase, the calculation of and predicted energy is based on the estimated strain

energy and damping energy for the loadcase. For the subsequent increments of the loadcase, and the

time step size are modified according to the total strain energy and estimated strain energy.

Adaptive Time Stepping Control for Creep Analysis

Creep is a time-dependant inelastic behavior that can occur at any stress level, either below or above the

yield stress of a material. In many cases, creep is also accompanied by plasticity, which occurs above the

yield stress of the material. Along with the existing adaptive time stepping scheme, a new option is added

to activate the additional time stepping control due to creep behavior of materials. For the current release,

sTs

Tm

JJJJJJJ

2 Nrm

Nrm

1H( )( )⁄

Z

Nrm

Nrm log10

105

Ts⋅

Tm

JJJJJJJJJJJJJJJJJJJ

⎝ ⎠⎜ ⎟⎛ ⎞

Z

Ts Tm

Tm 105Ó

103Ó

108Ó

sNr

1 Su⁄

Fd

K F

Kdamp Fdamp

Fd

Fd


130

this option only applies to the advanced nonlinear elements, for other elements, the creep stepping control

still uses the existing scheme.

The NLADAPT Bulk Data entry has added the parameters for the creep time stepping control through

optional keyword “CREEP”. The time period of creep time can be specified and a suggested time

increment can be defined through NLPARM by fields 2 and 3 of the first line.

For a given step , a solution is obtained and SOL 400 finds the largest values of stress change per stress,

and creep strain change per elastic strain, . It compares these values to the tolerance

values, (stress change tolerance) and (strain change tolerance), for this period. The value is

calculated as the larger of and . If , the solution is continued. Upon the

completion of the existing time stepping, the time stepping will chosen for the next step as ,

where is a factor calculated according to the criteria for the creep analysis. The criteria are the

tolerances you entered through the optional word “CREEP” of NLADAPT entry.

When you enter the tolerances and controls, the following conventions apply:

• All stress and strain measures in tolerance checks are second invariants of the deviatoric state

(that is, equivalent von Mises uniaxial values).

• You can reset all the tolerances and control upon the completion of one load step (NLADAPT)

sequence.

Since the time increment is adjusted to satisfy the tolerances, it is impossible to predetermine the total

number of time increments for a given total creep time.

Auto-Switch

In several types of analyses, maximum reactions or displacements are extremely small (even close to the

round-off errors of computers). In such circumstances, not all types of relative convergence criteria may

work properly. For example, in a problem with stress-free motion, the convergence check based on

relative displacement increments works correctly but not the convergence check based on relative

residual or strain energy. In this situation, it is necessary to check the convergence with absolute values

of reactions or strain energy; otherwise, the analysis may terminate prematurely. Similarly, this kind of

situation may happen for problems with springback and free thermal expansion or constraint thermal

expansion. The details for the cases where convergence checking with relative values may encounter

difficulties are listed in the table below. The AUTO SWITCH option is designed to switch to the proper

convergence check scheme automatically if any of the situations mentioned above occur during the

analysis. This optional convergence check is activated by adding character “A” into field (1, 8) of the

NLAPRM entry. This AUTO SWITCH option allows automatic switching of the convergence check

scheme to check as required on either residuals or displacements if small reactions or displacements are

detected, or to use the absolute strain energy checking if necessary. If AUTO SWITCH is turned on, it:

1. Switches on the relative residual checking if the relative displacement criterion is used (which

fails when the maximum incremental displacement becomes very small

Max._incremental_displacement/Smallest_element size < 1.0e-6)

t

Δσ σ⁄ Δεcr

εel

⁄

Ts Te p

Δσ( ) σ⁄( ) Tσ

⁄ Δεcr

εel

⁄( ) Tε

⁄ p 1<

tnew toldZ α⋅

α

131CHAPTER 3


2. Switches on the relative displacement checking if the relative residual force (moment) criterion

is used (which fails when the maximum reaction force becomes very small <1.0e-8)

3. To switch on the absolute energy checking if the structure is free of stress and deformation (strain

energy density < 1.0e-15).

Note that if both residual and incremental displacement criteria are already chosen (like “UP”), AUTO

SWITCH feature will not be activated even if character “A” is specified. In this case, SOL 400 will

ignore it.

Exceptions

There are some exceptions to the basic scheme outlined above. If an increment is consistently converging

with the current load step and the number of recycles exceeds the desired number, the number of recycles

is allowed to go beyond the desired number until convergence is achieved or up to the user specified

maximum number. The time step is then decreased for the next increment by . An increment is

determined to be converging if the convergence ratio was decreasing in three previous recycles.

Special rules also apply in a contact analysis. During the recycles, the contact status can keep changing

(new nodes come in contact, nodes slide to new segments, separate etc.). Whenever the contact status

changes during an increment, a new set of contact constraints are incorporated into the equilibrium

equations and more recycles are necessary in order to find equilibrium. These extra recycles, due to

contact changes, are not counted when the recycle number is checked against the desired number for

determining if the load step needs to be decreased within the increment. Thus, only true Newton-

Raphson iterations are taken into account. For the load step of the next increment, the accumulated

number of recycles during the previous increment is used. This ensures that the time step is not increased

when there are many changes in contact during the previous increment.

Results Output

In many analyses it is convenient to obtain post file results at specified time intervals. This is naturally

obtained with a fixed load stepping scheme but not with an automatic scheme. Traditionally, the post

output frequency is given as every nth increment. Using the NLPARM option, you can request post

output to be obtained at equally spaced time intervals. In this case, the time step is temporarily modified

to exactly reach the time for output. The time step is then restored in the following increment.

Defaults

The defaults of the NLADAPT option are carefully chosen to be adequate in a wide variety of

applications. There are cases, however, when the settings may need to be modified. Assume that the

default settings are used, which means that the recycle based control is active with an initial load of one

per cent of the total. If the structure is weakly nonlinear, convergence is obtained in just a few recycles

and the time steps for successive increments get progressively larger. This can lead to problems if the

initially weakly nonlinear structure suddenly exhibits stronger nonlinearities; for instance, occurrence of

plasticity or parts coming into contact. Possible remedies to this problem include:

1. Decrease the time step scale factor to a smaller number so the step size does not grow so rapidly.

1 Su⁄


132

2. Use the maximum time step to limit large steps.

3. Decrease the desired and maximum number of recycles to decrease the load step if more recycles

are needed.

Another situation is if the structure is highly nonlinear and convergence is slow. In this case, it may be

necessary to increase the desired number and maximum number of recycles. In general, there is a close

connection between the convergence tolerances used and the desired number and maximum number of

recycles.

133CHAPTER 3


Contact and Adaptive Time Stepping Enhancements for Transient Dynamic Analysis

MD Nastran R3 contains significant enhancements for transient dynamics. This includes enhancements

for dynamic contact and dynamic time-stepping scheme.

Enhancements for Dynamic Contact

The purpose of the MD Nastran R3 enhancements is to enable a stable solution for dynamic contact /

impact problems. High frequency oscillations are excited during dynamic contact and they cause

unrealistic solutions unless eliminated/ damped out quickly. The following enhancements have been

implemented for dynamic contact:

1. The existing HHT scheme has been extended to a Generalized-Alpha scheme. The generalized-

alpha scheme is a two-parameter scheme that allows the spectral radius to vary between 0.0 and

1.0. The governing equations are given by

(3-1)

where is identified by NDAMP and can vary between -0.5 and 0.0, is identified by

NDAMPM and can vary between -0.5 and 1.0. By default, for contact/impact problems, MD

Nastran R3 automatically uses NDAMP = 0.0 and NDAMPM = 1.0. This corresponds to a

spectral radius of 0.0. For non-contact problems, MD Nastran R3 uses previous HHT defaults:

NDAMP = -0.05 and NDAMPM = 0.0. The values of NDAMP and NDAMPM can be explicitly

changed by the user by using PARAM,NDAMP,xxx and PARAM,NDAMPM,yyy in the input

file.

2. A dynamic penetration cutback scheme has been implemented. The default iterative penetration

scheme that is used for statics does not work well for dynamics since high-frequency oscillations

are excited by this process. Instead, a time step cutback is triggered when dynamic penetration is

detected. The increment is repeated with a smaller time step. This time step is defined by the

penetration algorithm as a factor of the original time step . The scheme is depicted in

Figure 3-13:

Muˇ̌ n 1 αm

H HCuˇ n 1 α

fH H

Fn 1 αf

H H

in tH H Fn 1 α

fH H

extZ

αf αm

Δ tc

Δ to

MD Nastran R3 Release Guide Contact and Adaptive Time Stepping Enhancements for Transient Dynamic Analysis

134

Figure 3-13 Cutback scheme implemented for Dynamic Penetration

Multiple penetrations are possible in a single increment. After the penetration cutbacks, time step

for the subsequent increment is restored to the pre-penetration time step. Note that the penetration

cutback is independent of the bisection algorithm, i.e., MAXBIS, DTBIS do not control the

penetration time steps. The penetration cutback is indicated in the .f06 file by

*** USER INFORMATION MESSAGE 4550 (nl3con)*** TIME-STEP REDUCTION IS ACTIVATED BY DYNAMIC PENETRATION.

3. Miscellaneous enhancements for dynamic contact include the following:

a. Nodal projection (pulling/pushing a node that falls within the distance tolerance onto the

surface) is avoided for dynamic contact. This again avoids high frequency oscillations being

excited by the nodal projection. The lack of nodal projection may be a result of a small gap

seen between the contacting node and the contacted surface at the end of the increment.

b. Cutbacks are also initiated when the maximum displacement increments violate internally

calculated contact super-box dimensions. This prevents run-away increments where the nodal

displacements become unbounded. As a result, a cutback, when there is no apparent

penetration, is likely triggered in the program by such a large displacement in the system.

4. The limitations of the dynamic contact enhancements are as follows:

a. The Generalized-Alpha scheme with zero spectral radius is a damped operator. The accuracy

of the operator is a function of the time steps used. Large time steps can cause frequency

ranges of interest also to be damped out. A general recommendation would be to use time steps

about 2 to 5% of the dominant period of the system.

b. There is no special code to deal with momentum / energy conservation for impact problems.

While the elimination of high-frequency content through the mechanisms described

previously and satisfaction of the dynamic equilibrium equations given in (1) generally

suffices for most contact / impact problems, it may not suffice for systems where large

amounts of energy conversion (kinetic energy to strain energy and vice versa) occur during

the contact process.

Δto

Δtc

135CHAPTER 3


A simple example of a ball falling under gravity and bouncing off a rigid surface is shown. All

the enhancements described above have been used in calculating the dynamic response of the

ball. The model is shown in Figure 3-14 and the displacement response for three successive

bounces is shown in Figure 3-15. It is seen that for this elastic problem, there is good conservation

of momentum although there is some energy dissipation with small reductions in successive

bounce heights.

Figure 3-14 Bouncing Ball Model Setup

MD Nastran R3 Release Guide Contact and Adaptive Time Stepping Enhancements for Transient Dynamic Analysis

136

Figure 3-15 Displacement response of Bouncing Ball

Enhancements for Dynamic Time-Stepping

The purpose of the MD Nastran R3 enhancements for dynamic time stepping is to address some short-

comings in the MD Nastran R2 time-stepping scheme.

1. The Initial Time Step Adjustment process is extended in MD Nastran R3 to advanced non-linear

elements. During this process, if the ADJUST setting (time-step adjustment flag on TSTEPNL)

is non-zero and TZEROMAX (specified through integer system cell 373) is non-zero, then after

completing a minimum of two converged time steps, the analysis restarts with an appropriate time

step size. Note that this time step can be the same as the user-prescribed value or can be smaller.

In MD Nastran R2, the TZEROMAX process was not available for advanced non-linear elements

identified through PSHLN1, PSHLN2, PSLDN1, PBEMN1. This limitation has been removed in

MD Nastran R3. Note that for contact problems, the TZEROMAX process is still not available in

MD Nastran R3.

2. If the time step interval, NO, on the TSTEPNL entry is > 1, then the time steps can exceed the

initial time step DT specified by the user. The time step bounds for each increment are given by

MINDT

MAXBISJJJJJJJJJJJJJJJJJJJJJJJ

DT

MAXRJJJJJJJJJJJJJJJJJ,⎝ ⎠

⎛ ⎞ Δt MIN MAXRˇ

DT NOˇ

DT,( )≤ ≤

137CHAPTER 3


Note that if NO = 1 (default value), then cannot exceed (this is similar to the functioning

of MD Nastran R2). However, for NO > 1, can exceed in MD Nastran R3. The

following factors are taken into account by the time stepping algorithm while deciding on the time

step for the next increment:

a. The time step cannot exceed the values prescribed by the frequency algorithm and by output

time step requirements.

b. Whenever feasible, the time step will adjust such that it is a perfect sub-multiple (1/2, 1/4,

etc.) of the output time step. The time step will also adjust to an optimal value to prevent

thrashing (where the frequency and output requirements alternately control the time step).

3. The time steps will adjust such that end-of-step time is reached exactly. This allows multiple steps

with tabular loading to function accurately.

4. The default MSTEP value has been set to 10 or 20 depending on the non-linearity of the problem.

This default allows better accuracy for nonlinear problems.

5. The frequency based algorithm is used for the time stepping only if ADJUST is not zero.

However, the output based algorithm is used for the time stepping even if ADJUST is zero. For

instance, if the time step is reduced to an arbitrary number due to a penetration cutback, then the

output algorithm will still ensure that the next required output time will be reached exactly.

Dt DT

Dt DT

MD Nastran R3 Release Guide Progressive Failure Analysis with a Micromechanical Module

138

Progressive Failure Analysis with a Micromechanical Module

Introduction

A module to facilitate the micromechanical analysis has been integrated with MD Nastran R3 using an

advanced composite technology that can be used for composite materials using shells, solid shells and

composite bricks in solution sequences 400 (SOL 400) and shells in solution sequence 700 (SOL 700).

It is only available for nonlinear elements, so for shells the PCOMP or PCOMPG must be used (in

addition with PSHLN1 for SOL 400) and for solids the PCOMPLS option must be used. The usage of

the micromechanical module is possible by the MATM option (See MATM (SOLs 400/700) (p. 2114) in

the MD Nastran Quick Reference Guide). The property options PCOMP, PCOMPG or PCOMPLS refer

to a material, and a MATM definition can be associated with this material. If any material in a composite

definition has an associated MATM, then the micromechanical module will be used for calculating the

material stiffness for this composite. The MATM Bulk Data entry may specify the use of properties from

other materials also.

The micromechanical module calculates the material stiffness for the composite. In addition, it calculates

material damage and degrades the material stiffness in case damage occurs.

Definition of a Composite

For SOL 400, there are currently five types of composite definitions available: total ply, fiber and matrix,

braided, triaxial and honeycomb. These are defined using the parameters of the MATM entry: PLY,

MATRIX, BRAID, TRIAX and HONEY. For SOL 700 only the following options are available: PLY,

MATRIX and HONEY.

Total Ply

The orthotropic properties of the ply are given directly. The material moduli are given through the

standard MAT8 (shells) or MATORT (solids) options. The PLY keyword to MATM is used, and it

identifies which MAT8/MATORT to use and provides the strength values for the ply.

Fiber and Matrix

The properties for the matrix and fiber materials are given separately. The matrix is isotropic so the

moduli are given through MAT1 and the fibers are orthotropic given by MAT8 or MATORT. The fiber

material and strength values are given with the PLY keyword and for the matrix the MATRIX keyword

is used. The presence of the MATRIX keywords signals to the program to interpret the data under PLY

as fiber properties. One also defines the fiber volume fraction and the void volume fraction. The program

internally calculates the total ply properties.

139CHAPTER 3


Braided (SOL 400 only)

The braided composite is a variant of a fiber and matrix definition. In addition to specifying the fiber and

matrix properties, the BRAID keyword of MATM is used for defining the braiding of the fibers. With

this option, multiple fiber definitions can be used in the same ply.

Triaxial (SOL 400 only)

Similar to braided, this option allows further specification of the fibers. The TRIAX keyword is used for

defining the fiber packing information.

Honeycomb

The honeycomb option defines a honeycomb material. The ply properties are defined with the PLY

keyword and the cell size of the honeycomb is defined with the HONEY keyword. The stress-strain

option and thermal loads are not supported with the honeycomb model and only shell elements are

supported.

Failure Analysis

There are currently 24 failure theories available. They are listed under FTi in the bulk data definition of

MATM. The strength values (maximum stresses etc.) are defined with the PLY and MATRIX keywords.

When failure occurs, the material stiffnesses are degraded. This can be done in two ways: critical and

non-critical failure. Associated with each these two failure types is a degradation factor, both of which

default to 0.01.

Critical Failure

For critical failure, all moduli are decreased to the critical degradation factor times the original modulus.

Non-Critical Failure

For non-critical failure, the modulus in the fiber direction is not affected. If total ply properties are used,

the modulus in the first material direction is not changed. If fiber and matrix properties are given, only

the matrix properties are degraded when failure occurs.

Crack Density Model (SOL 400 only)

A crack density model is available. It allows a gradual degradation of the stiffness upon failure. Only

failure in the transverse direction will occur. This model is activated by setting ITYPE=2 (first line of

the MATM option).

Nonlinear Stress-Strain Curve (SOL 400 only)

A simple model for a non-linear stress-strain behavior is available. It is quite similar to the existing

NLELAST option of MATS1, MATS3 or MATSORT. A curve giving the effective stress vs. the effective

strain is given through the TABL3D0 Bulk Data entry. It can be specified for the PLY or the MATRIX

MD Nastran R3 Release Guide Progressive Failure Analysis with a Micromechanical Module

140

keyword. If specified on the PLY it refers to the whole ply, and if given on MATRIX it only affects the

matrix properties. This option is not supported for the honeycomb model.

Temperature Effects (SOL 400 only)

There are two effects of temperatures available: temperature dependent material properties and thermal

strains.

Temperature Dependent Material Properties (SOL 400 only)

The material moduli can change with the temperature as in any SOL 400 analysis. The standard options

MATT8, MATT1 etc. are used. Temperature dependency of the strength values in MATM is given

through the MATTM option.

Thermal Strains (SOL 400 only)

Thermal strains due to prescribed temperatures are also supported for the micromechanical module. This

option is not supported for the honeycomb model.

Output

The failure status (1 for failed and 0 for non-failed), crack density and active failure modes are printed to

the f06 file. The output can look something like this

Results of failure status and crack density are also available in the DBALL file for post processing in

Patran and SimXpert.

Licensing

The PFA and advanced composites in MD Nastran R3 require separate licensing and can be obtained

from your local MSC offices.

A D V A N C E D P F A R E S U L T S F O R L A Y E R E D C O M P O S I T E E L E M E N T S

ELEMENT INTEG. FAILURE CRACK FAILURE ID PLY ID POINT ID STATUS DENSITY MODES 322 4 1 1 4.295E+00 in-plane shear + 2 1 4.290E+00 in-plane shear +

141CHAPTER 3


3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

Introduction

General 3D contact capability, along with 2D solid edge to edge contact, was implemented in MD

Nastran R2 that supports the Grid-to-Surface type of contact in all translational degree-of-freedoms. In

addition, the Permanent Glue and General Glue contact also were introduced at the same time.

In MD Nastran R3, the primary enhancements of the 3D contact are (1) Moment-Carrying-Glue contact

that includes the rotational degree-of-freedoms in glued-contact as well as the translational degree-of-

freedoms and (2) General Line contact capability that includes general Beam-to-Beam contact, Edge-to-

Surface and Edge-to-Edge contact for beam, plate and shell elements. (Note that “Edge” means the

perimeter of plate and shell elements.)

The new features listed below are discussed in the following sections:

1. Moment Carrying Glue

2. Improved Flexibility in Contact (for Shells only, in this release)

3. In-Plane Shell Edge-to-Edge Glue

4. General Line Contact

• Beam-to-Beam Contact

• General Shell Edge(-to-Edge and -to-Surface) Contact

5. Optimize Contact Constraints

6. GLUE Control

• UNGLUE – release specified grids from being glued.

• Breaking Glue

7. Miscellaneous Items

• Case Control Command BCONTACT=ALLBODY

• Case Control Commands BCMOVE and BCHANGE

• Support 3D Contact Restart

• MPC with Contact Logic Improvement

• Separation Logic Improvement

All 3D contact capabilities introduced in this release are supported in both SOL 400 and SOL 101

contact. At the same time, any type of the Permanent Glue contact is supported in the following solution

sequences: SOL 101, 103, 105, 107, 108, 109, 110, 111, 112, 200 and 400.

MD Nastran R3 Release Guide 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

142

Benefits1. Moment Carrying Glue makes the jointing of two dissimilar meshes more realistic and passes the

grounding check. Also potential spurious modes should no longer occur.

2. Improved Flexibility in Contact for Shells gives the user more options and controls to the plate

and shell in contact.

3. General Line Contact gives users more freedom in modeling. There are no Grid-to-Surface

contact limitations when working with beam, plate and shell type of elements.

4. Optimize Contact Constraints can help users determine the contact slave-and-master relation

automatically.

5. UNGLUE helps users to exclude Grids from glued-areas to make modeling easier.

6. Breaking Glue offers a new capability to separate the glued-areas under specified conditions.

7. MPC with Contact Logic Improvement remove the conflict between user specified MPCs',

including linear Rigid Elements, with the contact constraint equation.

8. BCONTACT=ALLBODY gives the user a choice to abandon the complicated BCTABLE inputs.

9. BCMOVE and BCHANGE Case Control Commands in conjunction with the BCONTACT=

ALLBODY allows the user control and change contact definition with

BCONTACT=ALLBODY.

10. 3D Contact is supported in chaining analysis.

Moment Carrying Glue

In MD Nastran R2, the contact constraint for glued contact with shells only involved the grids

translational degrees of freedom. In other words, the Moments were not carried across the contact

interface. In MD Nastran R3, full moment carrying glue is supported. It includes all the following types

of contact (1) Shell-to-Shell, (2) Shell-to-Solid, (3) Beam-to-Shell, and (4) Beam-to-Solid.

Input

Moment Carrying Glue can work with both General Glue and Permanent Glue. By using the existing

IGLUE entry on BCTABLE, the user can apply this capability to the model:

• IGLUE=3 on BCTABLE: full moment carrying glue with projection of the node

onto the surface

• IGLUE=4 on BCTABLE: full moment carrying glue without projection of the node onto the

surface

Limitations

Moment carrying glue is NOT supported for the following types of contact:

• Beam-to-Beam

143CHAPTER 3


• Shell Edge-to-Shell Edge (with BEAMB=1 on BCPARA)

Examples

Following are examples for the Moment Carrying Glue Contact. Since all of them have been included

in the QA Decks library, they are not listed in this guide. The referenced input files can be found in the

TPL directory in the MD Nastran R3 installation.

Example 1: Beam-to-Solid (nlcmc01.dat)

As an example of the Moment Carrying Glue contact in SOL 400, Figure 3-16 shows the undeformed

and deformed shape and location.

Figure 3-16 Moment Carrying Glue Contact (Beam-to-Solid)

Here is the basic description of this model

• 2 Contact bodies:

• Body 1: beam element

• Body 2: solid element

• Enforced rotation of end point of beam around x-axis


144

• Beam is in moment carrying glued contact with solid

• BCTABLE:

• IGLUE=3

• BCPARA:

• NLGLUE=1 (optional)

Note that if NLGLUE=1 is specified on BCPARA, this job run as Permanent Glue contact. Otherwise,

it runs as the General Glue contact.

Example 2: Shell-to-Solid (nlcmc02c.dat)

As an example of the Moment Carrying Glue contact in SOL 400, Figure 3-17 shows the undeformed and

deformed shape.

Figure 3-17 Moment Carrying Glue Contact (Shell-to-Solid)

Here is the basic description of this model

• 2 Contact bodies:

• Body 3: shell elements

• Body 5: solid elements

145CHAPTER 3


• Pressure load on shell elements

• Shells are in moment carrying glue contact with solids

• BCTABLE:

• IGLUE=4

• BCPARA:

• NLGLUE=1 (optional)

Note that if NLGLUE=1 is specified on BCPARA, this job run as Permanent Glue contact. Otherwise,

it runs as the General Glue contact.

Improved Flexibility in Contact (for Shell only in MD Nastran R3)

Currently, different types of elements are not allowed to be mixed in one contact body (defined on

BCBODY Bulk Data entry). For example, beam type of elements, plate or shell type of elements and

solid type of elements cannot be mixed in one BCBODY. New input flags COPT’s on BCBODY and

BCTABLE defining which contact is possible between two contact bodies are introduced for this

purpose. We currently only use the COPT's family for Shell elements in contact body. Since the COPT's

family is described below in general. Some of the relationships do not apply for the MD Nastran R3

release and are so marked.

The basic format of COPT is “COPT = A + 10 * B + 1000 * C”

• A: the outside of the solid elements in the body (can be ignored in MD Nastran R3)

• = 1: the outside will be in the contact description (DEFAULT)

• B (flexible bodies): the outside of the shell elements in the body

• = 1: both top and bottom faces will be in the contact description, thickness offset will be

included (DEFAULT)

• = 2:only bottom faces will be in the contact description, thickness offset will be included

• = 3:only bottom faces will be in the contact description, shell thickness will be ignored

• = 4: only top faces will be in the contact description, thickness offset will be included

• = 5: only top faces will be in the contact description, shell thickness will be ignored

• = 6: both top and bottom faces will be in the contact description, shell thickness will be

ignored

Note that if B = 6 for both bodies in a contact combination, then nodes that separate from a body,

cannot come in contact again in the current step or in subsequent steps unless a different flag is

chosen for one of the bodies.

• B (rigid bodies): the rigid surface (can be ignored in MD Nastran R3)

• = 1: the rigid surface should be in the contact description (DEFAULT)

• C (flexible bodies): the edges of the body


146

• = 1: only the beam/bar edges are included in the contact description (DEFAULT)

• = 10: only the free and hard shell edges are included in the contact description

• = 11: both the beam/bar edges and the free and hard shell edges are included in the contact

description C. It has no effect if beam-to-beam contact is OFF (BEAMB1 on BCPARA).

BCPARA BEAMB will be discussed under Beam-to-Beam Contact.

Free shell edge means the opened edge and all the other shell edges are hard shell edges.

Input

The new entries of COPT family on BCBODY and BCTABLE are listed here.

BCBODY

COPTB are the defaults for the contact body, may be overridden by COPTS/COPTM or

COPTS1/COPTM1 on BCTABLE:

BCTABLE

1 2 3 4 5 6 7 8 9 10

BCBODY BID DIM BEHAV BSID ISTYP FRIC IDSPL CONTROL

NLOAD ANGVEL DCOS1 DCOS2 DCOS3 VELRB1 VELRB2 VELRB3

“ADVANCE” SANGLE COPTB

“RIGID” CGID NENT --- Rigid Body Name ---

“GROW” GF1 GF2 GF3 TAB-GF1 TAB-GF2 TAB-GF3

“HEAT” CFILM TSINK CHEAT TBODY HCV HNC ITYPE

BNC EMISS HBL

“PATCH3D” NPATCH

1 2 3 4 5 6 7 8 9 10

BCTABLE ID IDSLAVE IDMAST NGROUP COPTS COPTM

“SLAVE” IDSLA1 ERROR FNTOL FRIC CINTERF IGLUE

ISEARCH ICOORD JGLUE TOLID DQNEAR DISTID

“FBSH” FRLIM BIAS SLIDE HARDS COPTS1 COPTM1

X “BKGL” BGST BGSN BGM BGN

“HHHB” HCT HCV HNC BNC EMISS HBL

FK EXP METHOD ADAPT THICK THICKOF PENV

FACT TSTART TEND MAXPAR PENCHK FSF VSF

EROSOP IADJ SOFT DEPTH BSORT FRCFRQ SNLOG

ISYM I2D3D IGNORE SPR MRP VDC SBOPT

SFS SFM SST MST SFST SFMT AUTO

LCID FCM US PSF FA ED INTTYPE

147CHAPTER 3


COPTS and COPTM are the defaults for the slave and master body combinations in this BCTABLE and

may be overridden for a particular body combination by COPTS1 and COPTM1.

Examples

In-Plane Shell Edge-to-Edge Glue

Only the mid-plane of shell elements are considered in this capability; therefore, shell thickness is

ignored. Both top and bottom faces of the shell are included in contact description. Separation is based

on the absolute value of the component of the contact force in the direction perpendicular to the touched

body.

Input

The basic requirements of input are

• COPTB=60 on BCBODY, or COPTS=COPTM=60 on BCTABLE

• IGLUE > 0 on BCTABLE

Since it is shell with glued contact, the Moment Carrying Glue option IGLUE=3 or 4 on BCTABLE are

recommended but not forced.

Limitations

In the In-Plane Shell Edge-to-Edge Glue Contact, when Grids separate from a body, cannot come in

contact again in the current STEP or in subsequent STEP’s unless a different COPT flag is chosen for

one of the bodies.

Examples

The following examples are for the In-Plane Shell Edge-to-Edge Glue Contact. Since all of them have

been included in the QA Decks library, they are not listed in this guide.

NFLS SFLS IGNOFF FSLIM PYS TDIC CDIST

NFLF SFLF NEN MES TBLCID TBLAB IGAP

X FTBID VC SMOOTH FLANGL PENMAX THKOPT SHLTHK

X SLDTHK SLDSTF

X DBID TIDRF TIDNF DBDTH DFSCL NUMINT

“MASTERS” IDMA1 IDMA2 IDMA3 IDMA4 IDMA5 IDMA6 IDMA7

IDMA8 IDMA9 ...

1 2 3 4 5 6 7 8 9 10


148

Example 3: Four Co-plane Shell Bodies Edge-to-Edge Glue (nlc025a.dat)

As an example of the In-plane Shell Edge-to-Edge Glue contact in SOL 400, Figure 3-18 shows the

undeformed and deformed shape. These four shells are co-plane in undeformed shape. Their thicknesses

are ignored in contact description.

Figure 3-18 Four Shell Bodies Edge-to-Edge Glue

• 4 Contact bodies (all shell elements, edges match)

• Pressure load on all shells

• Shells are in moment carrying glue contact with each other, shell thickness is ignored

• BCTABLE:

• COPTS1=COPTM1=60

• IGLUE=3

Please refer to the previous Improved Flexibility in Contact (for Shell only in MD Nastran R3), 145, for the

details of COPTS1=COPTM1=60.

Example 4: Five Irregular Shell Bodies Edge-to-Edge Glue (nlc026a.dat)


undeformed and deformed shape. These 5 shells are not co-plane in undeformed shape. Their thickness

are ignored in contact description.

149CHAPTER 3


Figure 3-19 Five Irregular Shell Bodies Edge-to-Edge Glue

• 5 Bodies (all shell elements)

• Pressure load on some shells

• Clamped at bottom (open size)

• Shells are in moment carrying glue contact with each other, shell thickness is ignored

• BCTABLE:


• IGLUE=3

• ISEARCH=0

• ICOORD=3

• BCBODY:

• IDSPL= -1

• ISTYP=2

Note that ISEARCH=0 and ISTYP=2 trigger on the Optimize Contact Constraint capability, which is to

be introduced below. The entry ICOORD=3 turn on Initial Stress Free and Delay Sliding Off

capabilities. At the same time IDSPL=-1 activate the Analytic (SPLINE) Analysis.


150

Example 5: Five Irregular Shell Bodies Edge-to-Edge Glue plus the 6th Shell Body as a "Footplate" (nlc026c.dat)


undeformed shape only. The 1st 5 Shell Bodies are the same as Example 4: Five Irregular Shell Bodies

Edge-to-Edge Glue (nlc026a.dat), 148. Their thicknesses are ignored in contact description. Contact

between the new added footplate structure and the other old Grid-to-Surface contact structure is

considered. Its thickness is not ignored.

Figure 3-20 Five Irregular Shell Bodies Edge-to-Edge Glue plus the 6th Shell Body as a

“Footplate"

• Clamped at edge of “footplate”

• Bodies 1-5 are in moment carrying glue contact with body 6

• Thickness of “footplate” is included

• BCTABLE:

• COPTB=60 (Bodies 1~5)

• COPTB=10 (Body 6)

• IGLUE=3

• ISEARCH=0

• ICOORD=3

151CHAPTER 3


• BCBODY:

• IDSPL= -1

• ISTYP=2

This model is almost the same as Example 4 except the Footplate, the 6th Body. Note that COPTB=10

for the 6th BCBODY tells that its thickness is not ignored in the contact analysis. In other word, the

contact relation between the 6th BODY and others is not the In-plane Shell Edge-to-Edge Glue.

Beam-to-Beam Contact

All beam types of elements have to associate cylindrically or conically shaped contact surface first before

they can do the general line contact. The radius of the contact surface (beam contact radius) is entered

via BCBMRAD Bulk Data entry on a per element basis. Note that the beam contact radii are averaged

at the nodes of the beams; therefore, the taper shape is possible to each beam Body.

Contact is established between the closest points of the contact surfaces associated with two beam

elements. A multi-point constraint is imposed on the closest points of beam elements in contact to

suppress relative displacement in the direction of the normal to the contact surfaces.

Since beam elements do not have cross-sectional stresses, beam-to-beam contact separation is always

based on nodal forces. Only the bilinear Coulomb friction model (FTYPE=6) is supported.

Input

When running Beam-to-Beam contact, the following two inputs are required.

• BCPARA: BEAMB=1

• BCBMRAD

Limitations

1 2 3 4 5 6 7 8 9 10

BCBMRAD RADIUS TYPE ID1 ID2 THRU ID3 BY N

ID4 THRU ID5 ID6 ID7 ID8 ID9

Field Contents

RADIUS Equivalent radius to be used for beam-beam contact problems. (Real, no Default)

TYPE The attribute of all following ID’s. (Character, Default = “EID”)

EID Defines all the following entries are the IDs of beam-type elements.

BODY Defines all the following entries are the IDs of BCBODYs.

ALL Defines the default RADIUS for all beam-type elements.

IDi ID of a beam-type element, CROD, CBAR, CBEAM and CBEAM3, or a BCBODY

with the specified radius. (Integer, no Default)


152

1. Only 2-noded beam, bar and rod elements are supported by beam-to-beam contact. CBEAM3

elements are not supported

2. If a beam element is touching another beam element, then the direct neighbor elements of the

beam (that is, elements that share a node with the contacting element) cannot come in contact with

the same contact body in the same direction. This is to avoid multiple contact constraints being

imposed on a node in that direction.

3. Sliding from one beam element to the next element is defined only if the element has a unique

neighbor element (i.e. a beam cannot slide over a branch).

4. The check for beam contact conditions is always single sided with automatic optimization of

contact constraint equations (ISTYP is ignored)

5. Analytic (SPLINE) option of the contact body is not supported for beam contact bodies (IDSPL

is ignored)

6. If the nodes of a beam element touch a rigid body, a solid or a shell element, then the beam contact

radius (BCBMRAD) is ignored

7. The searching order for deformable contact bodies (ISEARCH) is supported by beam-to-beam

contact, but in general is of little use, since the same constraints will be imposed whether body 1

is touching body 2 or body 2 is touching body 1. However, if contact conditions are ignored due

to remark 2., then reversing the search direction by setting ISEARCH=1 and switching slave and

master bodies may solve the problem.

8. Stress-free initial contact and delayed slide-off are not supported for beam-to-beam contact

(ICOORD is ignored)

9. The glue option that retains initial gaps and overlaps (IGLUE=2), as well the moment carrying

glue options (IGLUE=3 or 4), are not supported for beam-to-beam contact. Each case is treated

as IGLUE=1. However, these options are supported for the nodes of a beam element that touch

a rigid body, a shell or solid element.

10. Since beam elements do not have cross-sectional stresses, beam-to-beam contact separation is

always based on nodal forces:

• IBSEP is ignored by beam-to-beam contact

• FNTOL on BCPARA and BCTABLE is always interpreted as a force

• In general, force-based separation must be used with beam-to-beam contact (IBSEP = 0)

• If stress-based separation is required, then the separation threshold (FNTOL) for beam-to-

beam contact combinations must be explicitly specified on the BCTABLE and the nodes of

the beam elements should not touch other entities

11. Only the bilinear Coulomb friction model (FTYPE=6) is supported

Examples

Following are examples for the Beam-to-Beam contact. Since all of them have been included in the QA

Decks library, they are not listed in this guide.

153CHAPTER 3


Example 6: Crossed Beams (nlc027a.dat)

As an example of the Beam-to-Beam contact in SOL 400, Figure 3-21 shows the undeformed shape only.

This example shows that two crossed beam contacts at one point and then separate.

Figure 3-21 Crossed Beams

• Two contact bodies (all CBEAMs)

• Body 1 clamped at both ends

• Body 2 clamped at one end and loaded by point force in z-direction at the other end

• BCPARA:

• BEAMB=1

• BCBODY

• COPTB=1000 (default)

• BCBMRAD,0.05,ALL

Please refer to Improved Flexibility in Contact (for Shell only in MD Nastran R3), 145, for the details of

COPB=1000.


154

Example 7: Coiled Beams (nlc027b.dat)

Two wires, modeled as cantilever beams, are initially parallel to each other. Figure 3-22 is the deformed

shape after twisting them together.

Figure 3-22 Coiled Beams

• Two initially parallel wires

• Clamped at one end

• Other ends rotated about common center

• Two contact bodies (all CBEAMs)

• BCPARA:

• BEAMB=1

• BCBODY

• COPTB=1000(default)

• BCBMRAD,0.05,ALL

All crossed lines connect points in contact on the beam axes.

155CHAPTER 3


General Shell Edge(-to-Edge and -to-Surface) Contact

To support this capability, the Beam-like contact entities are created automatically on the free and the

hard edges of a shell structure. Note that these created entities don’t add any stiffness to the model.

Beam-to-beam contact is used internally to detect contact between the beam-like entities and to handle

sliding, separation and friction. Contact radii of the beam-like entities are derived from the thickness of

the shell elements (R = T/2).

Input

Since it is Beam-to-Beam contact internally, the BEAMB must be switched on

• BCPARA: BEAMB=1

At the same time, Shell edges must be included in contact description

• COPTB=10010 on BCBODY or COPTS=COPTM=10010 on BCTABLE

The above two inputs are the basic requirements for General Shell Edge contact.

Limitations• Since beam-to-beam contact is used internally, all the same limitations of the Beam-to-Beam

contact are also applied to General Shell-Edge contact

• Only the bilinear Coulomb friction model (FTYPE=6) is supported

• Not available for quadratic shell elements.

Examples

Below are examples for the General Shell-Edge contact. Since all of them have been included in the QA

Decks library, they are not listed in this guide.

Example 8: Shell Free Edge Contact (nlc028a.dat)

As an example of the General Shell Edge contact in SOL 400, Figure 3-23 shows the undeformed shape

only of two contacting shells along the free edges.


156

Figure 3-23 Shell Free Edge Contact

• 2 Contact bodies

(all shell elements, edges do not match)

• Enforced displacement of the top edge of body 2

• BCPARA:

• BEAMB=1

• BCBODY:




Example 9: Thin-Wall Square Boxed Free Edges Contact (nlc028b.dat)

As an example of the General Shell Edge contact in SOL 400, Figure 3-24 shows the undeformed shape

only of two thick walled open square box structures in contact along the free edges.

157CHAPTER 3


Figure 3-24 Thin-Wall Square Boxed Free Edges Contact

• Two shell bodies contacting each other on the edges

• BCPARA:

• BEAMB=1

• BCBODY:




Optimize Contact Constraints

When optimization of contact constraints is activated, the slave and master relation between different

BCBODY’s is based on:

• Softer-or-harder materials (HARDS=2.0 in default on BCTABLE)

• finer-or-coarse meshes

The user can let the program determinate the slave and master relation automatically.


158

Input

This capability is activated when:

• ISTYP=2 on BCBODY

• ISEARCH=0 (Default) on BCTABLE (or no BCTABLE)

Limitations

None.

Examples

See Example 4: Five Irregular Shell Bodies Edge-to-Edge Glue (nlc026a.dat), 148 and Example 5: Five

Irregular Shell Bodies Edge-to-Edge Glue plus the 6th Shell Body as a "Footplate" (nlc026c.dat), 150.

GLUE Control

UNGLUE

With UNGLUE, the user can select some nodes of the contact body for regular contact instead of glue

contact even if the contact table (BCTABLE) says that they should be glued. Those selected nodes will

ignore any glue condition and do regular contact instead.

Input

The following inputs are required for this capability

• UNGLUE (or BCONTACT) Case Control command. Its format is as follows

Selects the grids should use standard contact instead of glued contact in glued bodies.

Format:

UNGLUE=n

• UNGLUE Bulk Data entryI

This entry is only necessary if glued contact has been specified and some of the grids should use

standard contact instead of glued contact.

UNGLUE (SOL 400) Contact Body Unglue Selection

UNGLUE (SOL 400) Contact Body

159CHAPTER 3


• IGLUE(=1, 2, 3 or 4) on BCTABLE

In the same rule as BCMOVE and BCHANGE, the user can still use the ID from BCONTACT Case

Control command to select UNGLUE Bulk Data entries but UNGLUE Case Control command always

dominates the selection of it.

Limitations

UNGLUE is ignored by Permanent Glue.

Breaking Glue

When a glued contact node breaks due to the breaking criterion, then it will internally switch to the

unglue option.

Input

The basic requirements for this capability are listed here.

• IGLUE > 0 on BCTABLE

• JGLUE = 2 on BCTABLE

• 4 new entries (SN, ST, m, n) on BCTABLE under “BKGL” keyword

1 2 3 4 5 6 7 8 9 10

UNGLUE ID BID ID1 THRU ID2 BY N

ID3 THRU ID4 ID5 ID6

ID Identification number referenced by a SUBCASE or STEP Case Control command. See

Remark 1. (Integer > 0, no Default)

BID Identification number of the specified BCBODY (Integer > 0, no Default)

IDi ID list of Grids (Integer > 0, no Default)

1 2 3 4 5 6 7 8 9 10




“FBSH” FRLIM BIAS SLIDE HARDS COPTS1 COPTM1

“BKGL” BGST BGSN BGM BGN

“HHHB” HCT HCV HNC BNC EMISS HBL



160

where

The Breaking Criteria is

Limitations

Nodes must be glued first during the analysis. Only when they are released due to the breaking criterion

will they switch to do regular contact.

Miscellaneous Items• BCONTACT=ALLBODY Case Control Command

• In MD Nastran R2, Case Control command BCONTACT=SID is required to all 3D Contact

analysis.

• With the new option, BCONTACT=ALLBODY, BCTABLE Bulk Data entries are not

required anymore. All BCBODY’s defined in the file will be searched for contact. All entries

on BCTABLE will take the default values.

• Case Control Commands BCMOVE and BCHANGE

• In MD Nastran R2, BCMOVE and BCHANGE Bulk Data entries shared the same ID with

BCTABLE controlled by BCONTACT Case Control command.









IDMA8 IDMA9 ...

“BKGL” New keyword for BreaKing GLue

BGSN(SN) Maximum normal stress for Breaking Glue (Real, Default 0.0)

BGST(ST) Maximum tangential stress for Breaking Glue (Real, Default 0.0)

BGM(m) The first exponent for Breaking Glue (Real, Default 2.0)

BGN (n) The second exponent for Breaking Glue (Real, Default 2.0)

1 2 3 4 5 6 7 8 9 10

σN

SNJJJJJJJ

⎝ ⎠⎛ ⎞

n σT

STJJJJJJ

⎝ ⎠⎛ ⎞

m

H 1.0>

161CHAPTER 3


• With the new Case Control commands BCMOVE and BCHANGE, they can have their own

ID’s at each STEP.

• User can still use the ID from BCONTACT Case Control command to select BCMOVE

(and/or BCHANGE) Bulk Data entries but BCMOVE and BCHANGE Case Control

commands always dominate their selection.

• Input: Refer to MD Nastran Quick Reference Guide

• Restart in 3D Contact

• In MD Nastran R2, 3D Contact cannot run restart jobs.

• In MD Nastran R3, the 3D Contact supports restart capability but only with the model using

traditional Nastran elements (Elements not referred to a PSHLN1, PSHLN2, PSLDN1, and

etc. entry).

• MPC with Contact Logic Improvement

• This improvement will prevent that Grids having M-set degrees of freedom to be constrained

by the contact component.

• The M-set Grids of MPC equations will be neglected in the contact search.

• Separation Logic Improvement

• The separation check will be skipped after 5 consecutive iterations when the members in the

chattering set are not changed

• Improved separation message when chattering is detected.

MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

162

Explicit Nonlinear - SOL 700

Introduction

MD Nastran R3 SOL 700 is the third release of powerful Explicit Nonlinear Solution available in

MD Nastran and offers an advanced technology to analyze transient dynamic events of short duration

with severe geometric and material nonlinearities.

MD Nastran SOL 700 allows users to work within one common modeling environment using the same

Bulk Data interface. The NVH, linear and nonlinear models can be used for explicit applications such as

crash, crush, and drop test, blade out and bird strike simulations. This dramatically reduces the time spent

to build different models for implicit and explicit analysis and prevents the users from making mistakes

because of unfamiliarity between different programs.

New Capabilities in Explicit Nonlinear - SOL 700

MD Nastran R3 SOL 700 has been dramatically improved to include the following new capabilities in

this release:

1. Advanced Fluid Structure Interaction (FSI) – Broadband applications

2. Parallel FSI based on Distributed Memory Parallel Technology

3. Advanced Composites based on micromechanical failure and damage capability

4. SPH Method – Smooth Particle Hydro-Dynamics

5. Sheet Metal Forming with springback capability

6. Integrated, Multi-disciplinary Fan Blade Out (FBO) and Rotor Dynamics simulation

7. Analysis Chaining:

• Implicit to Explicit (Prestress)

• Explicit to Explicit (Multiple Droptest)

• Explicit to Implicit (springback)

8. New element and material models

9. FAA Hybrid II and III Dummies

Advanced Fluid Structure Interaction (FSI)

The FSI capability was first introduced in SOL 700 with the MD Nastran R2 release and was limited to

airbags and occupant safety simulation. With MD Nastran R3, full capabilities of advanced Dytran FSI

technology are implemented in SOL 700 which will allow users to simulate complex, broadband FSI

applications such as:

• Sloshing

• Blasts and Explosives

163CHAPTER 3


• Hydroplaning

• Fluid-filled bottle droptest

• Fuel tank sloshing and crush

• Fuel pumps

• Aircraft crashworthiness on water

• Bird Strike with fluid bird

• Weapon Design

• Under Water Shock Analysis (UNDEX)

• Many more

The analysis of the physical behavior of fluids and gases is best solved using a Eulerian approach. The

nature of the behavior of these types of materials is represented in a natural way using a finite volume

description based on the Euler equations of motion. Accurate solver(s) are available in MD Nastran R3

Fluid Filled Bottles

Courtesy - Nampak

Crash with Airbags on Water

Bird Strike


164

SOL 700 that allows you to analyze the behavior of fluids and gases, coupled to structures if necessary

and defines the fluxes of mass, momentum and energy, the conserved problem quantities.

The objective of fluid-structure interaction using the coupling algorithm is to enable the material modeled

in Eulerian and Lagrangian meshes to interact. Initially, the two solvers are entirely separate. Lagrangian

elements that lie within an Eulerian mesh do not affect the flow of the Eulerian material and no forces

are transferred from the Eulerian material back to the Lagrangian structure. The coupling algorithm

computes the interaction between the two sets of elements. It thus enables complex fluid-structure

interaction problems to be analyzed.

The FSI in MD Nastran R3 SOL 700 is based on the advanced Finite Volume (Eulerian) and Coupling

technologies of Dytran while the structural part is co-simulated based on LS-DYNA solver. The

following FSI technologies are now available in SOL 700:

• Single Material Hydrodynamic

• Single Material Hydrodynamics with Strength

• Multi-Material Hydrodynamics

• Multi-Material Hydrodynamics with Strength

• General Coupling

• Porosity Models

• Closed Volume

• Fast Coupling

• Multiple Eulerian Domains with Multiple Coupling Surfaces

• Coupling surface with Failure

• Coupling Surfaces with Porous Holes

• Flow between Eulerian domains

• Deactivation

Shaped Charge

165CHAPTER 3


• Multiple Adaptive Euler

• Standard Euler Solver

• Roe Solver

• Riemann Solver

• Special techniques for Fluid-filled containers

• Hot filling for plastic bottles

• Mesh Box with non-uniform Euler

• Graded Mesh

• Hydrostatic boundary conditions for UNDEX

• Skin Friction

In addition numerous material models are added that are highlighted in the new material and element

sections (see Section 9). For a more detailed discussion of the FSI theories and capabilities, please refer

to MD Nastran Explicit Nonlinear (SOL 700) User’s Guide.

Parallel FSI

With the release of MD Nastran R3 SOL 700, we are pleased to introduce the long awaited Parallel FSI

capability. The Parallel FSI is based on the Distributed Memory Parallel (DMP) technology and will

dramatically increase the performance and reduce the simulation time of the CPU intensive FSI

applications. The MD Nastran R3 Parallel FSI capability is limited to single material hydro-dynamics

and general coupling using the MESH box. Please refer to the MD Nastran Explicit Nonlinear (SOL 700)

User’s Guide for a detailed discussion of Parallel FSI capability.

Sloshing

Hydroplaning


166

Figure 3-25

This is a sloshing simulation which was run up to 4 CPUs and shows dramatic speed-ups. Cache

Coherency with the Euler cubes is the explanation for the super linear scaling as indicated in the picture.

The speed-up can also be observed on 2 and 4 CPU runs when the Euler cubes are used (1cpu-cache

result). As shown in Figure 3-25, even if the cache coherency is taken out, the scaling is still impressive

- 1.62 (2cpu) and 2.41 (4cpu).

Advanced Composites

Two major, advanced composite capabilities are added to MD Nastran R3 SOL 700 to support the

Progressive Failure Analysis (PFA) and honeycomb material behavior. The first capability is based on

prediction of delamination and failure of composite shell structures and the second capability will allow

accurate simulation of honeycomb material for both shells and solid structures.

The MD Nastran R3 SOL 700 PFA capability will allow users to study the delamination and failure of

plies, matrix, fiber and interlaminate plies of composites structures at micro-mechanic levels.

New material models and numerous failure criteria are introduced to support the new composite

capability. These materials are common and consistent between SOL 400 and SOL 700.

167CHAPTER 3


Please see Progressive Failure Analysis with a Micromechanical Module, 138.

Smooth Particle Hydrodynamics (SPH) Method

Smooth Particle Hydrodynamics (SPH) is another important capability that is implemented in

MD Nastran R3 SOL 700. The SPH method is known to be an effective technique in certain class of

problems where there is a presence of highly deformable material with complex erosion properties. The

SPH method is basically a meshless lagrangian technique to model fluid flow problems such as

crashworthiness on water or soft soil, high velocity impact, penetration and perforation problems. See

the MD Nastran Explicit Nonlinear (SOL 700) User’s Guide for more details.

Sheet Metal Forming (SMF) with Spring-back

Sheet metal forming is a complex application and requires tailored material properties and special

contact features such as draw bead models to predict the deep drawing of the sheet metal and the spring-

back effect after the dies are removed. The deep drawing is simulated by SOL 700 explicit solver and

then results are transferred to the implicit solver to reduce the computation time for the spring-back

effect.

High Velocity Impact

Courtesy - CEI Ensight


168

Four new material models are introduced in the MD Nastran R3 SOL 700 which are tailored for SMF:

MATD036: This model was developed by Barlat and Lian [1989] for modeling sheets with anisotropic

materials under plane stress conditions. This material allows the use of the Lankford parameters for the

definition of the anisotropy.

MATD037: This model is for simulating sheet forming processes with anisotropic material. Only

transverse anisotropy can be considered. Optionally an arbitrary dependency of stress and effective

plastic strain can be defined via a load curve. This plasticity model is fully iterative and is available only

for shell elements.

MATD039: This model is for simulating sheet forming processes with anisotropic material. Only

transverse anisotropy can be considered. Optionally, an arbitrary dependency of stress and effective

plastic strain can be defined via a table. A Forming Limit Diagram (FLD) can be defined using a table

and is used to compute the maximum strain ratio which can be post processed. This plasticity model is

fully iterative and is available only for shell elements.

MATD190: This model was developed by Barlat and Lian [1989] for modeling sheets with anisotropic

materials under plane stress conditions. This material allows the use of the Lankford parameters for the

definition of the anisotropy. This particular development is due to Barlat and Lian [1989]. It has been

modified to include a failure criterion based on the Forming Limit Diagram. The curve can be input as

a table, or calculated based on the n-value and sheet thickness.

In addition, four new contact methods are introduced for Metal Forming contact behavior (BCTABLE):

METHOD = FORMNS: Forming nodes to surfaces

METHOD = FORM1SS: Forming one way surface to surface

METHOD = FORM2SS: Forming surface to surface

169CHAPTER 3


METHOD=DRAWBEAD: The draw bead is defined two ways:

1. A consecutive list of slave nodes that lie along the bead using BCGRID

2. A set of property ID’s of beams that lie along the draw bead using BCPROP.

Additional features that are available for draw bead include:

• TIDRF TABLEID for draw bead bending force

• TIDNF TABLEID for draw bead normal force

• DBDTH Draw bead depth

• DFSCL Scale factor for TIDRF load curve

• NUMINT Number of equally spaced integration points along the draw bead

Springback simulation – Springback simulation is a chained analysis where the results of sheet forming

and deep drawing from the explicit run are used as a pre-condition in the implicit solver for springback

simulation. The methodology below describes the analysis steps for SMF and follow up springback

simulation:

• 1st run: drawing simulation with SOL 700 explicit solver

• Use the SEQROUT Bulk Data entry to generate a file with nodes, elements and stresses at

the end of the job. This file will be used for a subsequent analysis

• File = JobName.dytr.nastin

• 2nd run: springback analysis with SOL 700 implicit solver

• Use the INCLUDE Bulk Data entry to include prestress file for the structure

(JobName.dytr.nastin)

• Use the SPRBCK Bulk Data entry to activate the implicit springback analysis

• Use the SEQROUT Bulk Data entry to write a file with nodes, elements and element stresses

at the end of the job, which can also be used for a subsequent analysis

The trimming features are not supported in MD Nastran R3 and will be included in future releases.

Integrated Fan Blade Out (FBO) and Rotor Dynamics (RD) simulation

The FBO-RD solution in MD Nastran R3 presents an efficient multi-disciplinary, integrated implicit-

explicit-implicit analysis process for more accurate simulation of engine fan blade-out condition using


170

MD Nastran. FBO event is extremely nonlinear due to heavy wide cord fan blades incorporated for new

generation of high by-pass ratio jet engines to meet airframe manufacturers’ demand for higher thrust

engines with improved performance and optimum weight. Analytical procedures are used by airframe

and engine manufacturers to support design of propulsion installation and adjacent wing structures.

Until now the industry standard practice has been primarily focused on the application of the various

point solutions to predict pre-stressing of the fan blades, fan blade out analysis and standalone rotor

dynamics simulation. However, with MD Nastran R3, the FBO-RD simulation process is automated. The

new FBO-RD solution offers an integrated, multi-disciplinary simulation capability in MD Nastran to

streamline the FBO event from prestressing of fan blades to blade-out on a fine-meshed finite element

model, typically used by engine manufacturers to rotor dynamics simulation using a much coarser mesh

as used by airframe companies, all in one common modeling environment. This process can result in

much higher levels of accuracy and dramatically reduce cost of analysis and design process.

The engine manufacturers typically use a fine and detailed finite element model of the engine to conduct

an explicit FBO simulation. The analysis objective is to generate the loads for the airframe manufacturers

to compute the mass unbalance and conduct an implicit rotor dynamics simulation to predict the engine

stability. Even though the engine is the same but the simulation models are mostly company-confidential

and are not shared among manufacturers. For this reason, the airframe companies construct their own

finite element model of the engine for rotor dynamics analysis which usually has a much coarser mesh

than the FBO model.

171CHAPTER 3


One of the problems of the current practice has been the FBO loads that are generated by the explicit

solver, are not directly shared and rather approximated and normalized before it is sent to airframe

manufactures. The problem is exacerbated by the fact the location and exact timing of the FBO loads on

the surrounding structure are missing, forcing the airframe companies to approximate the location of

applied loads in the coarse mesh model for RD simulation. These loads are usually on the conservative

side, resulting in over-design.

The MD Nastran R3 will allow the companies “share” the same Nastran database that includes accurate

time history of FBO loads, both impact and rub loads, as well as their applied location, as computed by

MD Nastran SOL 700 explicit solver. A new entry called “BLDOUT” defines blade out force output

information and mapping criteria for a combined SOL 700 – SOL 400 Blade-out analysis (used both in

the SOL 700 and subsequent SOL 400 analyses).

Further, it will also allow the airframe manufacturers to read those loads from the database and map them

correctly on a coarse mesh model for rotor dynamic simulation performed by MD Nastran R3 SOL 400.

The FBO load mapping on the coarse mesh, time steps synchronization between explicit and implicit

models, are completely automated in SOL 400. The integrated FBO-RD in MD Nastran R3 offers the

first “Industry Standard” solution and will facilitate a common modeling and analysis environment to

achieve high fidelity results while dramatically reducing the product design cycle.

Please consult MD Nastran R3 SOL 700 User’s Guide for more details.

Typical FBO Loads

Whirl Diagram from Rotor Dynamics


172

Analysis Chaining

Some of the automated analysis chaining have already been discussed such as FBO-RD simulation which

is an implicit-explicit-implicit chaining. There are basically three types of analysis chaining that are

available in SOL 700:

1. Implicit to Explicit (Prestressing etc.)

2. Explicit to Explicit (Multiple droptests etc.)

3. Explicit to Implicit (Springback etc.)

Implicit to Explicit Chaining (Prestress)

The prestressing was available and discussed in MD Nastran R2 and is supported by using the “PRSTRS”

entry at the beginning of the run. The results of the prestress will then be written in a file called NASINIT

for subsequent runs.

Explicit to Explicit (Multiple Droptest etc.)

The user will perform a regular impact analysis. By adding a specific output, after the simulation has

finished an intermediate file “nastin” is generated. This file holds information of the deformed shape of

model together with new thicknesses, stresses and strains of all shells. The nastin file contains GRID,

CQUAD4, CTRIA3 (with thinknesses) and ISTSxx describing the stress state of each solid, shell and

beam element. This file can be included in a new model, which has a different impact scenario. See the

following figure for schematic representation of process flow.

173CHAPTER 3


Explicit to Implicit (Springback etc.)

The user first will perform a regular stamping analysis by SOL 700 explicit solver. By adding a specific

output request in the model called “SEQROUT”, SOL 700 will generate an intermediate file “nastin” for

subsequent springback analysis. This file holds information of the deformed shape of model together

with new thicknesses, stresses and strains of all shells. This file can be included in a new model for

springback simulation using the SOL 700 implicit solver.

Combined Chaining – Certain applications requires an implicit-explicit-implicit chaining such as sheet

metal forming where the sheet metal might be pre-stressed prior to the actual deep drawing operation and

the follow up springback effect. Under those scenarios, the user first will perform a regular implicit pre-

stress analysis by using the “PRSTRS” flag to generate the NASINIT file. Next, the results of the

NASINIT file are read in the SOL 700 explicit solver while an entry called “SEQROUT” is used to save

the results of the stamping analysis. By using different subcases, contacts can be defined to predict the

multi-stage interactions of the different parts and bodies. By adding a specific output, after the simulation

has finished an intermediate file NASTIN is generated. This file holds information of the deformed shape

of model together with new thicknesses, stresses and strains of all shells. This file can be included in a

new model, which defines the spring back analysis. If the user has also added the specific entries, the

spring back analysis will generate new NASTIN file which holds the same information of the new

stabilized shape.


174

New Materials and Elements

With the complete implementation of FSI technology in MD Nastran R3, numerous material models and

elements are introduced to simulate the complex behavior of fluids, gases and their interaction with the

surrounding structure. These include various Equations of State, Yield, Shear and Failure models in

addition to different types of Eulerian elements and properties. In addition new models are added to

support SMF capabilities that are highlighted in previous sections. A complete list of these new

capabilities is out of the scope of the release notes. Please refer to the MD Nastran Quick Reference Guide

for a detailed description. The MD Nastran Explicit Nonlinear (SOL 700) User’s Guide includes the

theoretical background of FSI technology and offers numerous examples.

Support for FAA Hybrid II and III Dummy Models

MD Nastran R3 SOL 700 supports two new dummies that are tailored for aerospace and defense

applications. These are Federal Aviation Administration (FAA) Hybrid II and Hybrid III dummies that

are developed in native MD Nastran SOL 700 format and are available from Engineering Technology

Associates (ETA).

175CHAPTER 3


New SOL 700 Bulk Data Entries and Parameters

Table 3-2 contains new Bulk Data entries for SOL 700 in MD Nastran R3. More details can be found in

the MD Nastran Quick Reference Guide.

Table 3-2 New Bulk Data Entries for SOL 700

New for MD Nastran R3 (SOL 700)

Bulk Data Entries Description

ABINFL Defines an inflator model suited for airbag analyses. The inflator model is

defined as part of the GBAG or COUPLE surface.

BARRIER Defines a barrier for transport in an Eulerian mesh.

BLDOUT Defines blade out force output information and mapping criteria

CMARKB2 Defines a 2-noded marker beam element by means of connecting two grid

points.

CMARKN1 Defines a 1-noded marker element on a grid point.

COUOPT Defines the interaction factor and a pressure load from the covered side acting

on a BSURF.

COUP1FL Defines the surrounding variables when a segment of a coupling surface fails.

COUPINT Defines the interaction between two coupling surfaces.

COUPLE Defines a coupling surface that acts as the interface between an Eulerian (finite

volume) and a Lagrangian (finite element) domain.

CSPH Purpose: Defines a SPH particle.

CYLINDR Cylindrical shape used in the initial condition definition on the TICEUL entry.

DBREG Defines a drawbead region.

DETSPH Defines the ignition point from which a spherical detonation wave travels,

causing the reaction of high explosive materials.


176

EOSIG Defines the properties of Ignition and Growth equation of state and the reaction

rate equation used to model high explosives.

EOSJWL Defines the properties of a JWL equation of state commonly used to calculate

the pressure p of the detonation products of high explosives

EOSMG Defines the properties of a Mie-Gruneisen equation of state commonly used to

calculate the pressure p in high strain rate processes.

EOSTAIT Defines the properties of an equation of state based on the Tait model in

combination with a cavitation model where the pressure p is defined as

follows:

FAILJC Defines the properties of the Johnson-Cook failure model.

FAILMPS Defines the properties of a failure model where failure occurs when the

equivalent plastic strain exceeds the specified value.

FFCONTR Defines the pressure within a closed volume. Intended for the use in (partially)

filled containers, where dynamic fluid effects are negligible, e.g. top loading

and hot filling.

FLOWDEF Definition of default Eulerian flow boundary condition.

FLOW Defines the properties of a material for the boundaries of an Eulerian mesh.

FLOWSPH Purpose: Define a flow of particles. This option applies to continuum domains

modeled with SPH particles.

FLOWT Defines the material properties for the in- or outflow of material trough the

boundary of an Euler mesh. Inflow velocity and material properties can be

chosen time dependent.

GBAGCOU Defines a switch from full gas dynamics to uniform pressure formulation.

GBAG Defines the pressure within an enclosed volume.

HEATLOS Defines the heat-transfer model to be used with GBAG or COUPLE.

HTRCONV Defines the heat transfer through convection for a COUPLE and/or GBAG

surface.

Convection is heat transfer from the air bag to the environment through the air

bag surface.

HTRRAD Defines the heat transfer through radiation for a COUPLE and/or GBAG

surface.

Radiation is heat transfer from the air bag to the environment through the air

bag surface.

HYDSTAT Initializes the Euler element densities in accordance to a hydrostatic pressure

profile.




177CHAPTER 3


INFLTR Defines the inflator characteristics of a COUPLE and/or GBAG subsurface.

INFLCG Defines the cold gas-inflator characteristics of a COUPLE and/or GBAG

subsurface

INFLGAS Defines a thermically ideal gas to be used with a standard or hybrid inflator.

INFLHB Defines the hybrid-inflator characteristics of a COUPLE and/or GBAG

subsurface.

INFLTNK Defines the Tanktest-inflator characteristics of a COUPLE and/or GBAG

subsurface

INITGAS Specifies the initial gas composition inside a gasbag or Euler coupling surface.

LEAKAGE Defines the porosity model to be used with GBAG or COUPLE.

MATDEUL Defines a complete constitutive model as a combination of an equation of state,

a shear model, a yield model, a failure model, a spall model (PMIN), and

corotational frame.

MESH Defines a mesh.

PERMEAB Defines the permeability of a COUPLE and/or GBAG (sub)surface.

Permeability is the velocity of gasflow through a (sub)surface and is defined as

a linear or tabular function of the pressure difference over the surface.

PERMGBG Defines a permeable area of a COUPLE and/or GBAG surface, connected to

another GBAG.

The velocity of the gas flow through the surface is defined as a linear or tabular

function of the pressure difference.

PEULER1 Eulerian element properties. The initial conditions of these elements are

defined in geometric regions.

PEULER Defines the properties of Eulerian elements.

PMARKER Defines the behavior of the marker element in the FV domain.

PMINC Defines a spallation model where the minimum pressure is constant.

PORFCPL Defines an interaction between two coupling surfaces through a hole.

PORFGBG Defines a hole in a couple and/or GBAG (sub)surface, connected to another

GBAG.

PORFLOW Defines the material properties for the in- or outflow of an Eulerian mesh

through a porous area of the couple surface.

PORFLWT Defines a time dependent flow trough a porous area of the couple surface.

PORHOLE Defines a hole in a COUPLE and/or GBAG surface.

PORHYDS Prescribes a hydrostatic pressure profile on a porous BSURF.





178

PSPH Purpose: Define properties for SPH particles.

SEQROUT –

Sequential Run

Output generation

Purpose: At the end of an explicit simulation write out the initial state to a file

that can be used for a subsequent explicit SOL 700 run.

SHREL Defines an elastic shear model with a constant shear modulus.

SHRPOL Defines an elastic shear model with a polynomial shear modulus.

SPHERE Spherical shape used in the initial condition definition on the TICEUL entry.

SPRBCK Activates springback analysis tailored for sheet metal forming.

SURFINI Defines a surface that is used for initialization of regions of an Eulerian mesh.

TICEL Defines the initial values of element variables at the beginning of the analysis.

TICEUL Defines the initial value sets for Eulerian regions. The Eulerian regions are

defined by geometric shapes.

TICREG Defines the initial value sets for Eulerian regions. The Eulerian regions are

defined by geometric shapes.

TICVAL Defines the initial values of an Eulerian geometric region.

YLDHY Defines a yield model with zero yield stress.

YLDJC Defines a Johnson-Cook yield model where the yield stress is a function of

effective plastic strain, strain rate, and temperature.

YLDMC Defines a Mohr-Coulomb yield model.

YLDMSS Defines the yield model for snow material. This entry must be used in

combination with MATDEUL, EOSPOL and SHREL.

YLDPOL Defines a polynomial yield model where the yield stress is a function of

effective plastic strain.

YLDRPL Defines a rate power law yield model where the yield stress is a function of

effective plastic strain and strain rate.

YLDSG Defines the Steinberg-Guinan yield model where the yield stress is a function

of effective plastic strain, pressure and temperature.

YLDTM Defines the Tanimura-Mimura yield model where the yield stress is a function

of effective plastic strain, strain rate and temperature.

YLDVM Defines a bilinear or piecewise-linear yield model with isotropic hardening,

using the von Mises yield criterion.

YLDZA Defines the Zerilli-Armstrong yield model where the yield stress is a function

of effective plastic strain, strain rate and temperature.




179CHAPTER 3


Spotweld Rupture

Stress – SPWRS

Purpose: Define a static stress rupture table for shell elements connected to

spot weld beam elements using the constrained contact option:

METHOD=SPOTWELD. This table will not work with other contact types.

Data, which is defined in this table, is used by the stress based spot weld failure

model developed by Toyota Motor Corporation. See MATDSWx entries

where this option is activated by using MATDSW6 and OPT=RS.

MATD036 Modeling sheets with anisotropic materials under plane stress conditions

MATD037 Simulating sheet forming processes with anisotropic material

MATD039 Simulating sheet forming processes with anisotropic material

MATD078 – Soil and

concrete material

Purpose: This model permits concrete and soil to be efficiently modeled.

MATD145 – Schwer

Murray CAP Model

Purpose: The Schwer & Murray Cap Model, a.k.a. Continuous Surface Cap

Model, is a three invariant extension of the Geological Cap Model (MATD025)

that also includes viscoplasticity for rate effects and damage mechanics to

model strain softening. The model is appropriate for geomaterials including

soils, concrete, and rocks.

MATD190 This model was developed by Barlat and Lian [1989] for modeling sheets with

anisotropic materials under plane stress conditions. The material allows the use

of the Lankford parameters for the definition of the anisotropy. It has been

modified to include a failure criterion based on the Forming Limit Diagram.

The curve can be input as a table, or calculated based on the n-value and sheet

thickness.

MATD016 – Pseudo

Tensor

Purpose: This model has been used to analyze buried steel reinforced concrete

structures subjected to impulsive loadings.

SPHSYM Purpose: Define a symmetry plane for SPH. This option applies to continuum

domains modeled with SPH particles.

SPHDEF Purpose: Provide controls for computing SPH particles.

EOSGRUN Purpose: The Gruneisen equation of state.





180



Table 3-3 New Parameters For SOL 700

MATD053 Purpose: This allows the modeling of low density, closed cell polyurethane

foam. It is for simulating impact limiters in automotive applications. The

effect of the confined air pressure is included with the air being treated as an

ideal gas. The general behavior is isotropic with uncoupled components of the

stress tensor.

MATD116 Purpose: This material is for modeling the elastic responses of composite

layups that have an arbitrary number of layers through the shell thickness. A

pre-integration is used to compute the extensional, bending, and coupling

stiffness for use with the Belytschko-Tsay resultant shell formulation. This

material model must be used with the user defined integration rule for shells,

see *INTEGRATION_SHELL, which allows the elastic constants to change

from integration point to integration point. Since the stresses are not computed

in the resultant formulation, the stresses output to the binary databases for the

resultant elements are zero. Note that this shell does not use laminated shell

theory and that storage is allocated for just one integration point (as reported in

D3HSP) regardless of the layers defined in the integration rule.

MATD163 Purpose: Crushable foam with optional damping, tension cutoff, and strain rate

effects. Unloading is fully elastic. Tension is treated as elastic-perfectly-

plastic at the tension cut-off value.


Parameters Description

AXIALSYM Enables an efficient and accurate 2d axial symmetry for Eulerian materials. A

much larger time step becomes possible by not taking into account the mesh-size

in circumferential direction.

BLADEDEL Option to whether SOL 700 blade out scratch files such as ncforc are deleted or

not at the end of the run.

BLADESET Parameter to set the ID of the UNBALNC entry for SOL 700 blade out

computations.

BLDRSTRT Option to restart SOL 700 blade out analysis after the BINOUT to NCFORCE

conversion so that regeneration of the BINOUT, D2PLOT and NCFORCE files

is not required.




181CHAPTER 3


BLDTHETA Parameter to set the value of “THETA” on the UNBALNC entry for SOL 700

blade out computations.

COPOR Activates contact based porosity.

DELCLUMP This parameter prevents small clumps in the Euler mesh from determining the

time step and prevents the leakage of small masses to isolated regions.

DYNINT Defines the size of the integer memory in words.

DYNREAL Defines the size of the float memory in words.

EULBND Defines boundary treatment for Euler boundaries.

EULBULKL Defines the default value of the linear bulk viscosity coefficient for Eulerian

materials.

EULBULKQ Defines the default value of the quadratic bulk viscosity coefficient for Eulerian

materials.

EULBULKT Defines the default type of bulk viscosity for Eulerian materials.

EULSTRES Defines the update logic for stresses when material is transported in Euler

elements.

EULTRAN Sets the definition of the face velocity used in the transport scheme of the Multi-

material solver and the single material strength solver.

FASTCOUP Defines the fast coupling algorithm.

FBLEND Eulerian elements with uncovered fractions smaller than FBLEND are blended

with adjacent elements to form a clump so that they do not control the time step.

FMULT Defines the dimension of the multimaterial element array.

GRADMESH Glues fine meshes to coarse meshes. See the section on Graded meshes in the user

manual for further information.

HYDROBOD Defines a body force for single hydro material in Euler.

ISOL70GO Option to determine whether SOL 700 blade out analysis continues past its

normal stopping point in the GP1 module.

LIMITER Defines the type and the spatial accuracy of scheme used in the Euler solver based

on the ideas of Prof. Philip Roe.

MICRO Defines the accuracy of the initial conditions in Eulerian elements, when using the

geometrical shape definition.

RKSCHEME Defines the type of time-integration scheme used in the Riemann solution-based

Euler solvers.

ROHYDRO Defines the minimum density for hydrodynamic, single-material Eulerian

elements.

ROMULTI Defines the minimum density for multimaterial Eulerian elements.




182

ROSTR Defines the minimum density for single-material Eulerian elements with shear

strength.

VELCUT Defines the minimum velocity in Eulerian meshes.

VELMAX Defines the maximum velocity in Eulerian meshes.

CONTACT Change defaults for computation with contact surfaces.



183CHAPTER 3


Arc-Length Methods (Pre-release)

Introduction

In nonlinear static analysis, when the loading response beyond the critical limit (post buckling status),

the conventional Newton-Raphson Method usually cannot be used to analyze the structure. The Arc-

Length Method(s), which allows the nonlinear solver to find solutions to most of these kinds of unstable

problems, is now available in SOL 400. The concept of this method is to modulate the applied loads in

order to produce solutions with displacement increments of manageable size for a given load step.

Benefits

Although the post-buckling state is not usually allowed in the structure design, the prediction of such

response becomes much more interesting to engineers in past decades. In the design process for instance,

it may be desirable to trace the response of the snap-through or post-buckling behavior. The Arc-Length

Method allow solutions in the unstable regime for such class of problems.

The Arc-Length analysis has been merged into the current SOL 400 solution algorithm which takes

advantage of the following:

• Share the extensive enhancements for the nonlinear large strain and material behavior.

• Improved nonlinear iteration algorithms make solution easier and faster to converge. These

includes

• ADAPT, AUTO, ITER, SEMI, FNT, and PFNT methods

• Bisection Algorithm

• Quasi-Newton (BFGS) method

• Allow boundary condition change between STEPs.

Method and Theory

The theory of the Arc-Length Method is described in the MSC Nastran Handbook for Nonlinear

Analysis, Version 67, Section 3.7. Unlike the Newton-Raphson Method, whose load increment is fixed

during the iterations, the Arc-Length Method has varied load increment at each iteration. Sometimes we

also call it as the Control Increment (C.I.) method whose displacement increment is limited by the

constraint equations. Three different types of the constraint equations are available in the Arc-Length

Method in SOL 400. They are

1. The Crisfield's Method (TYPE=CRIS),

2. The Modified Riks' Methos (TYPE=MRIK), and

3. The Original Riks' Method (TYPE=RIKS).

Please refer to the MSC Nastran Handbook for Nonlinear Analysis, Version 67, Section 3.7 for the details

of these equations.

MD Nastran R3 Release Guide Arc-Length Methods (Pre-release)

184

It would be difficult to estimate a proper arc-length for multi-degree-of-freedom problems. The initial

arc-length is determined by the program that is mainly based on the original number of load increment

(NINC on NLPARM Bulk Data entry) and the load increment in the current loadcase (SUBCASE or

STEP). It is to be continuously updated at every increment using the information gathered during the

preceding converged increment.

Inputs

The existing Bulk Data entry NLPCI, which allows the user to define a set of parameters to control the

Arc-Length Method(s), is used to trigger on the Arc-Length Method as usual. See the MD Nastran Quick

Reference Guide for details. All the input entries are the same as before except that the filed 7, SCALE,

is not supported in SOL 400. This value is computed in the code automatically now but does not allow

users to change it.

The NLPCI Bulk Data entry is selected by the Case Control command NLPARM=ID. There must also

be an NLPARM Bulk Data entry with the same ID.

Outputs

There are no new outputs associated with this feature other than informational and diagnostic messages.

Note that

1. Because of the new format of the “Nonlinear Iteration Module Output” table in SOL 400, the load

factor of each iteration can be easily found in the first field now.

2. The field INTOUT, on the NLPARM Bulk Data entry, controls the output in the following ways

• =YES, output processed for every computed load increment

• =NO, output processed for the last load of the SUBCASE or STEP.

• =ALL, output processed for every computed and user-specified load increment.

Limitations

Considering that the Arc-Length method only supports the ANALYSIS=NLSTAT in SOL 400, the

following limitations exist in MD Nastran R3

1. Restart is not supported

2. Enforce Motion is not supported

3. 3D Contact is not supported

4. CASI solver is not supported

5. Creep Analysis is not supported

6. Heat Transfer is not supported

7. Line Search and NLADAPT are not supported

185CHAPTER 3


Example - nla011b.dat

A spherical shell with an initial imperfection, which was introduced by making the radius of curvature

near the apex greater than the shell radius, was analyzed. The shell was subjected to an external uniform

pressure, while the periphery was clamped. The problem was assumed to remain axisymmetric

geometry and loading throughout the deformation. The material was elasto-plastic with von Mises yield

criterion and kinematic hardening. The large displacement effect was also included in the analysis. The

detailed input of the model is attached at the end.

There were 3 STEPs' in this model. The external pressure was gradually increased from 2000 psi, 3000

psi to 4000 psi at the end of each STEP. The linear buckling load was around 3300 psi; therefore, the

first 2 STEPs' only required the Newton-Raphson method (NLPARM Bulk Data entry only without

NLCPI) because the stiffness matrix was still positive definite. Since the bucking occurred in the 3rd

STEP, the NLPCI Bulk Data entry was added into it by using Crisfield constraint equation. Note that if

the Arc-Length Method did not apply to the third STEP, the solution diverged.

Figure 3-26 shows the deformed shape and Figure 3-27 the central-load vs. deflection curve.

Figure 3-26 Deformed Shape of Imperfect Spherical Shell


186

Figure 3-27 Load-Deflection Curve of Imperfect Spherical Shell (Grid 100 is the Central

Point)

ID MSC, NLA011B $SOL 400 $TIME 5CENDECHO=UNSORT SET 1 = 100 DISP = ALL OLOAD=ALL SPC=10SUBCASE 1 STEP 1 LOAD=20 NLPARM=2 STEP 2 LOAD=30 NLPARM=2 STEP 3 LOAD=40 NLPARM=5OUTPUT(XYPLOT) CSCALE = 1.5 PLOTTER NAST XTITLE = LOAD FACTOR YTITLE = DISPLACEMENT XYPLOT DISP RESP/100(T3)BEGIN BULKPARAM,POST,-1$ DEFINE SPHERICAL COORDINATE SYSTEMSCORD2S 100 0. 0. 0. 0. 0. 1. +C2S1

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

3.00E+00

3.50E+00

-8.00E-02 -6.00E-02 -4.00E-02 -2.00E-02 0.00E+00

DISPLACEMENT OF GD 100

LO

AD

FA

CT

OR

187CHAPTER 3


+C2S1 1. 0. 1.CORD2S 200 0. 0. -.32908 0. 0. 1. +C2S2+C2S2 1. 0. 1.$ DEFINE PLOT ELEMENTGRID 1000 0. 0. 0. 123456PLOTEL 1000 1000 100$ GEOMETRYGRDSET 100 345GRID 100 200 1.1506 0. 0. 0 12456GRID 101 200 1.1506 0.715 -5.GRID 102 200 1.1506 0.715 5.GRID 103 200 1.1506 1.43 -5.GRID 104 200 1.1506 1.43 5.GRID 105 200 1.1506 2.145 -5.GRID 106 200 1.1506 2.145 5.GRID 107 200 1.1506 2.86 -5.GRID 108 200 1.1506 2.86 5.GRID 109 200 1.1506 3.575 -5.GRID 110 200 1.1506 3.575 5.GRID 111 200 1.1506 4.29 -5.GRID 112 200 1.1506 4.29 5.GRID 113 200 1.1506 5.005 -5.GRID 114 200 1.1506 5.005 5.GRID 115 200 1.1506 5.72 -5.GRID 116 200 1.1506 5.72 5.GRID 117 200 1.1506 6.435 -5.GRID 118 200 1.1506 6.435 5.GRID 119 100 0.8251 10. -5.GRID 120 100 0.8251 10. 5.GRID 121 100 0.8251 11.48 -5.GRID 122 100 0.8251 11.48 5.GRID 123 100 0.8251 12.96 -5.GRID 124 100 0.8251 12.96 5.GRID 125 100 0.8251 14.44 -5.GRID 126 100 0.8251 14.44 5.GRID 127 100 0.8251 15.92 -5.GRID 128 100 0.8251 15.92 5.GRID 129 100 0.8251 17.40 -5.GRID 130 100 0.8251 17.40 5.GRID 131 100 0.8251 18.8806 -5.GRID 132 100 0.8251 18.8806 5.$ CONNECTIVITYCTRIA3 10 2 100 101 102CQUAD4 11 2 101 103 104 102CQUAD4 12 2 103 105 106 104CQUAD4 13 2 105 107 108 106CQUAD4 14 2 107 109 110 108CQUAD4 15 2 109 111 112 110CQUAD4 16 2 111 113 114 112CQUAD4 17 2 113 115 116 114CQUAD4 18 2 115 117 118 116CQUAD4 19 2 117 119 120 118CQUAD4 20 2 119 121 122 120CQUAD4 21 2 121 123 124 122CQUAD4 22 2 123 125 126 124CQUAD4 23 2 125 127 128 126CQUAD4 24 2 127 129 130 128CQUAD4 25 2 129 131 132 130$ ELEMENT PROPERTIESPSHELL 2 1 0.0251 1


188

MAT1 1 10.8+6 0.3MATS1 1 PLASTIC 1.225+6 1 2 7.8+4$ BOUNDARY AND LOADING CONDITIONSSPC1 10 123456 131 132PLOAD2 20 -2000. 10 THRU 25PLOAD2 30 -3000. 10 THRU 25PLOAD2 40 -4000. 10 THRU 25$ PARAMETERSPARAM LGDISP 1$ SOLUTION CONTROLNLPARM 2 2 AUTONLPARM 5 5 AUTO YESNLPCI 5 ARC$ENDDATA

189CHAPTER 3


Analysis Chaining

Introduction

The analysis chaining was released in MD Nastran R2. In that release, the analysis chaining was only

supported for nonlinear static analysis and nonlinear transient analysis. In this release, this capability is

greatly expanded and is discussed in the following sub-sections. In order for completeness, some of the

information may have been previously presented in MD Nastran R2, and repeated here.

Input

The combination of SUBCASE, STEP, ANALYSIS and NLIC four Case Control commands provide a

mechanism for defining the multiple load steps, running multiple independent load cases, specifying

multiple and mixed types of analyses, and altering the natural load sequence in one job.

SUBCASE and STEP define load cases for a job. SUBCASE defines multiple load cases, which are

independent from each other, i.e., the load history is not passed from one SUBCASE to next. In a

SUBCASE, a number of STEPs can be defined. The solution of one STEP is a continuation of the

solution of its previous STEP.

The user can specify the type of analysis for each SUBCASE and/or STEP by using the Case Control

command ANALYSIS. ANALYSIS is discussed in Analysis Type, 189.

The Case Control command NLIC will alter the natural load sequence and it has the following formats:

NLIC SUBCASE i, STEP j, INCREMENT k

How to used this command is explained in the following example.

Analysis Type

The analysis type for the analysis chaining is defined by the Case Control command;

ANALYSIS = “analysis type”

In MD Nastran R3, the following analysis types are available:

• STATICS – linear static analysis,

• NLSTATICS – nonlinear static analysis,

• NLTRAN – nonlinear transient analysis,

• MODES – normal modes analysis,

• DCEIG – direct complex eigenvalue analysis,

• MCEIG – modal complex eigenvalue analysis,

• Brake Squeal Analysis – the Case Control command BSQUEAL is used to request the brake

squeal analysis. ANALYSIS = DCEIG or MCEIG can be used. See the following example.

MD Nastran R3 Release Guide Analysis Chaining

190

• HSTAT – steady state heat transfer analysis,

• HTRAN – transient heat transfer analysis.

The default is ANALYSIS=NLSTATICS.

NLSTATICS, NLTRAN, and STATICS are normal linear or nonlinear analysis. MODES, DCEIG,

MCEIG, and BSQUEAL are perturbation analysis, which is discussed in Examples of Linear Perturbation

and Brake Squeal Analyses, 102. HSTAT and HTRAN are heat transfer analyses, which are discussed in

SOL 400 Advanced Heat Transfer, 77.

Examples

The following examples illustrate the manner in which the SUBCASE, STEP, ANALYSIS, and NLIC

commands are used.

• With one SUBCASE and multiple steps, each step defines the total external load and other

characteristics for the step, which will be applied by the completion of the step. The solution of

any STEP is a continuation of the solution of its previous STEP. The following is a typical

example:

SUBCASE 1 $ This line can be omittedSTEP 10ANALYSIS = NLSTATNLPARM = 100LOAD = 10

STEP 20ANALYSIS = NLSTATNLPARM = 100LOAD = 20

STEP 30TSTEPNL = 200ANALYSIS = NLTRANDLOAD = 30

In the above example, the solution will be continues from step 10 to step 20 and step 30.

• Multiple SUBCASEs may be executed in one job where the types of analysis, loads and

boundary conditions can be changed. All SUBCASE’s are independent from each other, i.e., no

load history information is transmitted from one SUBCASE to the next. At the start of each

SUBCASE, the displacements, stresses and strains throughout the model are zero if there is no

initial condition specified. For example:

SUBCASE 1ANALYSIS = NLSTAT $ This line can be omitted

NLPARM = 100STEP 110LOAD = 110

STEP 120LOAD = 120

SUBCASE 2ANALYSIS = NLTRANTSTEPNL = 200

191CHAPTER 3


STEP 210DLOAD = 210

STEP 220DLOAD = 220

In above example, the solutions of SUBCASE 1 and SUBCASE 2 are independent of each other.

In case that the solution divergence is detected in a step, SOL 400 will terminate the solution of

the current subcase and jump to the next subcase.

• A case control command placed below the step level allows that command to vary from on step

to another. If it is placed above the step level, the command becomes the default for all steps in

the subcase. Most of the case control commands, which can be placed below the subcase level,

can also placed below the step level. For example, all steps in above examples use the same Case

Control command NLPARM = 100 in SUBCASE 1 and TSTEPNL = 200 in SUBCASE 2.

• NLIC command will alter the load pass. In the following case, the transient step 30 uses the

static analysis of step 10 at load factor 0.5 as its preload.

SUBCASE 1STEP 10ANALYSIS = NLSTATLOAD = 10NLAPRM = 110

STEP 20ANALYSIS = NLSTATLOAD = 20NLPARM = 120

STEP 30NLIC STEP 10, LOADFAC 0.5ANALYSIS = NLTRANDLOAD = 30TSTEPNL = 130

In order for step 30 to point to load factor 0.5 of step 10, the data at load factor 0.5 must have

been saved. This is done by the INTOUT field on the NLPARM Bulk Data entry.

• This section gives an example of chaining across the subcase boundary. In the following

example, both the transient analysis of SUBCASE 2 and SUBCASE 3 use the static analysis of

SUBCASE 1 at load factor 0.5 as their preload.

SUBCASE 1 STEP 10ANALYSIS = NLSTATLOAD = 10

SUBCASE 2STEP 20 NLIC SUBCASE 1, STEP 10, LOADFAC 0.5ANALYSIS = NLTRANDLOAD = 20

SUBCASE 3STEP 20NLIC SUBCASE 1, STEP 10, LOADFAC 0.5ANALYSIS = NLTRANDLOAD = 30


192

• This section gives an example for the perturbation analysis. In following example, the normal

modes analyses have been performed at load factor of 0.25 and 0.75 of the nonlinear static of

STEP 10.

SUBCASE 1STEP 10ANALYSIS = NLSTATLOAD = 10

STEP 20 NLIC STEP 10, LOADFAC 0.25ANALYSIS = MODESMETHOD = 20

STEP 30NLIC STEP 10, LOADFAC 0.75ANALYSIS = MODESMETHOD = 20

• This section gives an example of brake squeal analysis.

SUBCASE 3STEP 1LABEL = Nonlinear Static StepNLPARM = 3BCONTACT = 1SPC = 2LOAD = 4

STEP 2LABEL = Modal Brake Squeal with NLIC at 0.5ANALYSIS = MCEIGBSQUEAL = 989NLIC STEP 1 LOADFAC 0.5SPC = 2CMETHOD = 1METHOD = 2AUTOSPC(noprint)= yesRESVEC = NO

The second step requests a brake squeal analysis. The BSQUEAL Case Control command

requests a brake squeal analysis and it is performed at load factor of 0.5 of the first step. The

analysis method can be either DCEIG or MCEIG. For details, please refer to Examples of Linear

Perturbation and Brake Squeal Analyses, 102.

• This section gives an example of heat to structure chaining.

SUBCASE 1STEP 1ANALYSIS = HSTATNLPARM = 1SPC = 1LOAD = 2THERMAL = ALLFLUX = ALLTSTRU = 200

STEP 2ANALYSIS=NLSTATNLPARM = 3

193CHAPTER 3


SPC = 5 TEMP(load)= 200 LOAD = 13STEP 3ANALYSIS=NLSTATNLPARM = 2SPC = 5TEMP(load)= 200LOAD = 14

In the previous example, the temperature results of steady state heat transfer analysis are used in

the structural steps. The temperature ID 200 specified in command TSTRU=200 in STEP 1 is

passed to STEP 2 and STEP 3 in command TEMP(LOAD)=200. This means that temperature

results of STEP 1 in used in STEP 2 and STEP 3 as temperature load.

Legal Chaining Type

In this section, we will discuss which types of analysis chaining are legal for MD Nastran R3.

Let us define the symbol “NLSTAT � NLTRAN” means the case control structure giving by the

following:

STEP 1ANALYSIS = NLSTATLOAD = 1

STEP 2NLIC STEP 1, LOADFAC 0.5ANALYSIS = NLTRANDLOAD = 2

In MD Nastran R3, the following types of analysis chaining are legal:

NLSTATICS or STATICS � NLTRAN

NLSTATICS or STATICS � NLSTATIC or STATICS

NLSTATICS or STATICS � MODES, DCEIG, MCEIG, or BSQUEAL

HSTAT � NLSTATICS or STATICS

The above information can also be presented in the table format as:

STAT NLST NLTR MODE DCEI MCEI BSQU HSTA HTRA

STAT� Y Y Y Y Y Y Y

NLST� X X X Z Z Z Z

NLTR� Y

HSTA� Y Y Y

HTRA� Y


194

The symbols in previous table have the following meanings:

• X – full analysis chaining capabilities are supported as given in input and example sections

previously.

• Y – the NLIC Case Control command is not supported, so the chained step is limited to chain to

the end of the previous analysis step

• Z - chaining across a subcase boundary is not supported. This means that NLIC can only

reference the steps in the same subcase.

• Blank – Chaining not supported in MD Nastran R3.

Limitations

For heat transfer analysis, the following limitations exist:

• If analysis chaining is used, only a single subcase is allowed in the Case Control packet.

All the above limitations and gaps in the table of allowable chaining will be remedied in future releases.

Chapter 4: Implicit Nonlinear MD Nastran R3 Nastran Release Guide

4 Implicit Nonlinear

� Implicit Nonlinear - SOL 600


Implicit Nonlinear - SOL 600

196


The following is a discussion of the new additions and improvements made for MD Nastran R3.

Support of Large Grid and Element IDs

The largest addition to SOL 600 for MD Nastran R3 is the addition of a capability to support very large

grid and element IDs. Up to 10-digit IDs may now be used for grids and elements when SOL 600 is used,

however to be compatible with other solution sequences, IDs should not normally exceed a value of

99999999. Large IDs may be specified separately for grids, elements, or both items. Large ID capability

is not the default for MD Nastran R3 and, if it is needed for a particular model, it must be activated by

placing one of the following items shown in bold on the SOL 600,ID (p. 137) in the MD Nastran Quick

Reference Guide (most other items are omitted to prevent confusion):

SOL 600,SID MRENUMBR= MRENUELE= MRENUGRD=

Please see parameters, MRENUMBR, 771, MRENUELE, 769, and MRENUGRD (p. 770) in the MD

Nastran Quick Reference Guide. These key words are only required if the number of digits is greater

than seven.

Multiple RFORCE Entries in the Same Subcase

SOL 600 now supports multiple RFORCE entries in the same subcase so that different portions of the

structure can rotate with different angular velocities, or even in different directions. To accomplish this,

the two or more RFORCE entries should have the same SID (see below) and field 4 of the each

continuation entry should specify IDRF which points to a SET 3 entry designating which elements apply

to that particular RFORCE entry.

RFORCE (addition to the RFORCE entry for SOL 600)

Format:

1 2 3 4 5 6 7 8 9 10

RFORCE SID G CID A R1 R2 R3 METHOD

RACC MB IDRF

IDRF (SOL 600

only)

ID indicating to which portion of the structure this particular RFORCE entry applies.

It is possible to have multiple RFORCE entries in the same subcase for SOL 600 to

represent different portions of the structure with different rotational velocities. IDRF

corresponds to a SET3 entry specifying the elements with this acceleration.

197CHAPTER 4

Implicit Nonlinear

BCONTACT Case Control Command Clarification

Normally, only one form of this entry may be used in any given analysis. The exception, for SOL 600

only, is that BCONTACT=NONE may now be used for any subcase desired and/or for increment zero

and some other form such as BCONTACT=N used for the other subcases. This allows some subcases to

have contact and others to have no contact. Analysis restarts must use the same form as the original run

BCONTACT=ALLxxx cannot be mixed with

BCONTACT=NONE or BCONTACT=N in the same input file.

BCTABLE Bulk Data Entry Additions

Several new fields have been made in the BCTABLE entry to clarify which shell surfaces may contact

for SOLs 101, 400 and 600 and to add new information for SOL 700. For further details please see,

Advanced Integrated Nonlinear and Contact (Ch. 3). The new fields are shown in bold:

Format:

For detailed descriptions on the new fields and Remarks 22 and 23 see BCTABLE (SOLs

101/400/600/700) (p. 1090) in the MD Nastran Quick Reference Guide.

1 2 3 4 5 6 7 8 9 10




FBSH FRLIM BIAS SLIDE HARDS COPTS1 COPTM1

BKGL BGST BGSN BGM BGN

HHHB HCT HCV HNC BNC EMISS HBL









FTBID VC SMOOTH FLANGL PENMAX THKOPT SHLTHK

SLDTHK SLDSTF

DBID TIDRF TIDNF DBDTH DFSCL NUMINT


IDMA8 IDMA9 ...



198

Other BCTABLE Clarifications

If the user leaves IDSLAVE and IDMAST blank, then NGROUP is normally required and continuation

entries are usually expected for NGROUP SLAVE/MASTER combinations. Exceptions are (a) for

SOL 700 where self-contact may be designated using a slave IDSLA1 of zero and no MASTER entry

and (b) for SOL 600 if no contact is desired in increment zero or a particular subcase, fields 1 and 2 of

the primary BCTABLE entry for that subcase is entered, all other fields left blank and no continuation

lines are entered. The SOL 600 no contact condition may be achieved in either of two ways - set Case

Control BCONTACT=ID and enter a matching BCTABLE with that ID in field 2 and all other fields

blank or set BCONTACT=NONE and do not enter BCTABLE for that subcase.

New Triangular Plane Stress Element

The MRALIAS parameter or the ALIASM option may be used to specify that a 3-node plane stress

element is to be used by specifying type 201.

New Solid Shell Element

A new solid shell element (CSSHL) has been added to SOL 600. The solid shell is normally used for

contact problems where contact occurs on both the top and bottom faces. This element may be used with

either homogeneous properties or by referencing a PCOMP or PCOMPG.

CSSHL (SOL 600)

Defines the connection for a Solid Shell with 6 or 8 grid points.

Format:

Examples:

1 2 3 4 5 6 7 8 9 10

CSSHL EID PID G1 G2 G3 G4 G5 G6

G7 G8

CSSHL 44 11 1 2 3 4 5 6 quad

7 8 quad

CSSHL 51 22 11 12 13 21 22 tria

23 tria

CSSHL 51 22 11 12 13 13 21 22 tria

23 23 tria

Note: The second and third examples are equivalent to each other.

199CHAPTER 4

Implicit Nonlinear

See CSSHL (SOL 600) (p. 1367) in the MD Nastran Quick Reference Guide Nastran Quick Reference

Guide for additional details. An example is tpl model hextqb-sshl2.dat

PSSHL (SOL 600)

Defines the properties for Solid Shell (CSSHL) elements.

Format:

Example:

New Penta 15 Solid Element

Support for Penta 15 elements with mid-side nodes has been available in previous releases but they were

formed using hexa 20 elements with a collapsed side. This formulation is not as accurate as the new true

penta 15 formulation. The old collapsed side formulation is no longer used starting with this release and

the new formulation is used automatically. There are no changes to the input data required.

Field Contents

EID Element identification number. (1 < Integer < 1E11, Required)

PID Property identification of a PSHELL, PCOMP, or PCOMPG entry. (Integer > 0,

Required). Note that the MID2 entry on the PSHELL or PCOMP is ignored.

Gi Grid point identification number of connection points. (Integer or blank, for quad

shapes all eight values are required, for triangle shapes only G4 and G8 may be left

blank in which case G4=G3 and G8=G7.)

1 2 3 4 5 6 7 8 9 10

PSSHL PID MID IT SF

PSSHL 11 33 .8333

Field Contents

PID Property identification number. (Integer > 0, Required)

MID Identification of a MAT1xxx entry. All MAT entries available in SOL 600 can be

specified except for hyperelaastic materials. (Integer > 0)

IT Transition thickness - Enter only if a solid shell is attached to a standard shell (such

as CQUAD4), in which case TT is the thickness of the standard shell. (Real, Default

= 0.0)

SF Transverse shear factor - Leave blank if transverse shear is not to be considered.

(Real or blank, if entered SF must range between 0.0 and 1.0)



200

MARCOUT – t16 Output Results Changes

All output quantities supported by Marc are available in the SOL 600 t16 file and may be specified using

the MARCOUT Bulk Data entry. Additions for this release are as follows:

Please note that for SOL 600, MD Nastran Case Control commands such as SET ID=, DISP=,

STRESS=, STRAIN= only control the output in the .op2, .xdb, punch, .f06 and/or jid.marc.out file(s).

The Case Control requests do not affect the. t16 output.

Limiting t16 Output to Selected Elements or Grids

For large nonlinear models the output can become very large. Sometimes only a certain portion of the

structure is of concern. The following new entry may be used in SOL 600 to specify which elements or

nodes should be output. The default is all elements and nodes will be output if the entry is not made. This

entry may be used in combination with MARCOUT or the default MARCOUTs may be used.

MT16SEL – Limits elements and/or grid results to selected elements or grids for t16 and t19 file results

Format

E-USER 1st user-defined element post code(s) are generated by user subroutine plotv.f

E-USER1 2nd user-defined element post code(s)

E-USER2 3rd user-defined element post code(s)

E-USER3 4th user-defined element post code(s)

E-USER99 100th user-defined element post code(s)

These outputs are only available in the .t16 file, not in .op2, .xdb, .f06, punch. A

maximum number of 100 user-defined element post codes may be entered for SOL 600.

N-USER 1st user-defined nodal post code are generated by user subroutine upstnd.f

N-USER1 2nd user-defined nodal post code are generated by user subroutine upstnd.f

N-USER2 3rd user-defined nodal post code are generated by user subroutine upstnd.f

N-USER3 4th user-defined nodal post code are generated by user subroutine upstnd.f

N-USER4 5th user-defined nodal post code are generated by user subroutine upstnd.f

N-USER99 100th user-defined nodal post code are generated by user subroutine upstnd.f, etc.

User-defined outputs are only available in the .t16 file, not in .op2, .xdb, .f06, punch. A

maximum of 100 user-defined nodal post codes may be entered for SOL 600.

1 2 3 4 5 6 7 8 9 10

MT16SEL TYPE ID1 THRU ID2 BY ID3

201CHAPTER 4

Implicit Nonlinear

Example:

See MT16SEL (SOL 600) (p. 2239) in the MD Nastran Quick Reference Guide for more details.

Analytical Contact Threshold Angle

Starting with this release it is possible to define analytical contact threshold angles for different subcases.

To do so, include the following entry:

Defines automatic analytical contact threshold angle for multiple subcases - SOL 600 only.

Format:

Example:

Please see SANGLE (SOL 600) (p. 2684) in the MD Nastran Quick Reference Guide for more details. An

example using SANGLE is TPL model sangle1a.dat.

Additions to NLSTRAT

The following additions have been made to the NLSTRAT entry to support heat transfer analyses which

was introduced in the previous release.

MT16SEL GRID 1 THRU 100 BY 5

ELEM 100 THRU 500 BY 2

1 2 3 4 5 6 7 8 9 10

SANGLE IDC IDB Angle IDC IDB Angle

SANGLE 1 4 50.0 1 6

2 4 -1.0 2 6 55.0

Field Contents

IDC Identification number of a SUBCASE Case Control command. (Integer, no Default) To

enter a value corresponding to Marc’s increment zero, set IDC=0.

IDB Identification of a contact body (must be the same as a BCBODY ID) (Integer,

no Default)

Angle Threshold automatic analytical contact angle (SANGLE). (Real, Default = 60.0)

A value of -1.0 turns off analytical

PLANKS Planks second constant (Real, Default=14387.69 microMK) PARAMETERS (4,6)

CLIGHT Speed of light in a vacuum (Real, Default=2.9979E14 micor M/s) PARAMETERS

(4,7)

RAPMAX Maximum change in the incremental displacement in a Newton-Raphson iteration

(Real, Default = 1.0E30) PARAMETERS (4,8)



202

Generalized Alpha Dynamic Integration Method

For previous releases, several numerical integration methods were available for dynamic analysis. One

additional method, called the Generalized Alpha or Hilber-Hughes Taylor Method has been added. This

method is sometimes superior to the others for difficult dynamics problems, particularly those involving

contact. The single step Houbolt method is still the default for this release, but the new method may

become the default in subsequence releases. To select any of these methods, enter the following bulk

data parameter:

MHOUBOLT

Integer, Default = 0, MD Nastran Implicit Nonlinear (SOL 600) only.

If MHOUBOLT=0, SOL 600 transient dynamics will use the single step Houbolt numerical

integration method.

MHOUBOLT=1, SOL 600 transient dynamics will use the Newmark Beta numerical integration method.

MHOUBOLT=2, SOL 600 transient dynamics will use the standard multi-step Houbolt numerical

integration method.

MHOUBOLT=7, SOL 600 transient dynamics will use the generalized alpha (Hilber-Hughes Taylor)

numerical integration method.

For additional information, see Advanced Integrated Nonlinear and Contact (Ch. 3).

MATVP Material Property Entry

The MATVP entry has completely changed so that both SOL 400 and 600 may use the same entry. Please

refer to MATVE (SOLs 400/600) (p. 2165) in the MD Nastran Quick Reference Guide for the new

description and be sure to update any existing input files that have an older entry and need to be run with

this release. An example is TPL model vcreep.dat.

FISTIF Initial friction stiffness for model 6 used in first cycle of an increment to define the

friction stiffness matrix in cases where a touching node has a zero normal force and

the amount of sliding does not exceed the elastic sticking limit (Real, Default = 0.0 in

which case the program calculates it) PARAMETERS (5,1)

SNGMIN Minimum value that indicates a singularity if a direct solver is used (Real, Default =

0.0 in which case the value is set internally by the program) PARAMETERS (5,2)

RTMAX Maximum change in temperature per iteration in radiation simulations (Real, Default

= 10 times the maximum error in temperature estimate or 100.0) PARAMETERS (5,3)

203CHAPTER 4

Implicit Nonlinear

MATSMA Shape Memory Alloy Material Property Entry

A new shape memory allow material property entry is now available for use both in SOL 400 and 600.

Please see MATSMA (SOLs 400/600) (p. 2132) in the MD Nastran Quick Reference Guide for a full

description of this entry.

Nonlinear Elastic Orthotropic Materials

An orthotropic material model that allows the user to enter the nine material parameters as a function of

strain and temperature is now available. This is defined through the MATNLE6 and TABLE3Di options.

Composite Integration Methods to Reduce Computer Time

SOL 600 allows composite materials to be fully nonlinear. The properties of each layer may have

plasticity and/or have properties that vary with temperature. Often analyses are conducted where the

material properties are assumed to remain linear and are at a constant temperature. For such cases,

computer time can be reduced by significant amounts by taking these factors into account. A new entry,

PCOMPF, is available to specify which elements can use the faster integration methods. This entry is

shown below and an example is compos1-fast3.dat in the tpl directory.

Format:

Alternate Formats:

1 2 3 4 5 6 7 8 9 10

PCOMPF INT PID1 THRU PID2 BY N

1 2 3 4 5 6 7 8 9 10

PCOMPF INT PID PID PID1 THRU PID2 PID3 THRU

PID4 PID5 TO PID6 PID PID PID PID7

THRU PID8 BY N

1 2 3 4 5 6 7 8 9 10

PCOMPF INT ALL

Field Contents

PID1 Property identification number. (0 < Integer < 10000000) corresponds to a matching

PCOMP or PCOMPG entry.

INT INT=1, (Default), conventional through the thickness integration of each layer, allows

all available material behavior through the thickness.



204

INT=2, linear elastic material, fast-integrated through the thickness - thermal strains

and temperature dependent material properties are not allowed.

INT=3, linear elastic material, fast integrated through the thickness, temperature

dependent elasticity, and thermal strains are allowed.

Field Contents

205CHAPTER 4

Implicit Nonlinear

New SOL 600 Bulk Data Entries and Parameters



Table 4-2 contains new Parameters for SOL 600 in MD Nastran R3. More details can be found in the

MD Nastran Quick Reference Guide.




CSSHL Defines the connection for a solid shell with 6 or 8 grid points.

MATSMA Material properties for shape memory alloys (SOLs 400 and 600 only)

MATNLE6 Properties for nonlinear orthotropic elastic material

MT16SEL Limits elements and/or grid results to selected elements or grids for t16

and t19 file results

PSSHL Defines the properties for solid shell (CSSHL) elements.

SANGLE Defines automatic analytical contact threshold angle for multiple

subcases.

Table 4-2 New Parameters for SOL 600



MARCMATT (Integer) Determines if Marc input file will be created with materials using the

table-driven formats or not (Default = -1 if parameter is not entered)

MARROUTT Determines whether an inconsistent set of outputs between the Marc t16 file

(selected using MARCOUT) and standard Nastran output selected using Case

Control requests (and param,post) is allowed or not (Default = -1 if parameter is

not entered)

MBENDCAP Determines how PBEND internal pressure will be treated for SOL 600, (Default

= 1 if this parameter is not entered).

MDAREAMD Option to modify or not modify all DAREA entries which are not associated with

any other loads (DAREA entries that supply the actual load)

MFORCOR1 Option to correct forces entered twice (at the same node) in multiple subcases.

MINVASHF Inverse power “auto sift” value.

MINVCITR Inverse power method, number of iterations.

MINVCSHF Inverse power shift frequency in Hz.



206

MINVCTOL Inverse power convergence tolerance.

MINVFMAX Inverse power max frequency to extract in Hz.

MINVNMOD Inverse power max number of modes to extract.

MRENUELE It is best if MRENUELE is specified in the SOL entry. Some models will not have

memory allocated properly if this parameter is placed in the bulk data.

(Integer) Determines if SOL 600 elements will be renumbered or not (Default = -1

if parameter is not entered and MRENUELE is not entered on the SOL 600 entry)

MRENUGRD It is best if MRENUGRD is specified in the SOL entry. Some models will not

have memory allocated properly if this parameter is placed in the bulk data.

(Integer) Determines if SOL 600 grid id’s will be renumbered or not (Default = -1

if parameter is not entered and MRENUGRD is not entered on the SOL 600

entry)

MRENUMBR Determines if both grid and element IDs for SOL 600 will be renumbered or not.

MRPELAST Determines whether PELAST will be skipped or cause the job to abort for

SOL 600, (default = -1 if parameter is not entered). SOL 600 does not support

PELAST. PBUSHT along with CBUSH and PBUSH should be used instead.

MRPREFER Determines to output SOL 600 stresses on the t16 file in the standard Marc

coordinate system for the element or the “preferred” (layer) coordinate system

when the model contains composite elements.

MSPEEDCB Determines whether CBEAM increased speed options are to be applied. This

option may be necessary for models with a large number of beams whose element

ID’s are large.

MTABLD1M Option to modify or not to modify all TABLED1 entries which do not start with

the first point of (0.0, 0.0)

MTABLD1T Specifies the second time value of all TABLED1 entries that do not start with the

first point being (0.0, 0.0) if PARAM,MTABLD1M=1.

MULRFORC Option to activate multiple RFORCE entries for different portions of the model in

the same subcase.

Table 4-2 New Parameters for SOL 600



Chapter 5: NVH and Acoustics MD Nastran R3 Release Guide

5 NVH and Acoustics

� NVH Enhancements

� Enhancements to the Frequency Response Function (FRF) and FRF

Based Assembly (FBA) Feature

� Enhancements to ADAMSMNF Case Control Command


NVH Enhancements

208

NVH Enhancements

ACMS with Acoustic External Superelement Creation

The ACMS feature (see the DOMAINSOLVER ACMS (PARTOPT=DOF) Executive Control statement

in the MD Nastran Quick Reference Guide) is now fully integrated with the creation of an external

acoustic superelement which contains both the fluid cavity and the fluid-structural boundary. External

superelement creation is requested with the EXTSEOUT Case Control command. For an acoustic

external superelement, the component modes and their associated reduced stiffness, mass, etc. matrices

are computed separately for the fluid and structure. If QSETi and SPOINT Bulk Data entries are used

to define the generalized coordinates then there must be a sufficient number to accommodate both the

fluid and structure modes. If there are insufficient generalized coordinates then the program will truncate

both the fluid and structural modes proportionally. It is for this reason that PARAM,AUTOQSET,YES is

strongly recommended to avoid potential modal truncation. Fluid points may also be specified on the

boundary of the superelement using the ASETi entry. However, free-fixed or free-free fluid or structure

boundaries are not permitted with ACMS.

Multiple RANDOM Looping

Prior to this release, only one set of RANDPS Bulk Data entries could be selected per run. In other

words, the RANDOM Case Control command could only reference a single RANDPS set identification

number (SID). In this version multiple SIDs may be specified on the SET command if its identification

number is in turn referenced on a RANDOM command. For example;

SET 1000 = 101 103 107 110RANDOM = 1000

where 101, 103, 107, and 110 refer to multiple RANDPS SIDs. It should be noted for this type of usage

the SET id must be unique with respect to all RANDPS SIDs; e.g., 1000 is not an SID on any RANDPS

entry.

Sparse OUTPUT4 Format for External Superelement Creation

The sparse OUTPUT4 format option is now used for EXTSEOUT (MATRIXOP4=unit) Case Control

command. This will result in significant disk space reduction of the resulting op4 file.

Binary op2 and op4 Compatibility Robustness

Starting in version V2004 r3, binary op2 and op4 files could be read across dissimilar platforms.

However, several errors were encountered since V2004 r3 and are now corrected in MD Nastran R3.

209CHAPTER 5

NVH and Acoustics

Merged Superelement Results

PARAM, FULLSEDR, YES may be specified in a superelement analysis to merge several types of

results (displacements, stresses, etc.) across all superelements into a single non-superelement results

format. FULLSEDR is intended for superelement models which contain unique IDs across all element

and grid points. FULLSEDR benefits third party post-processing programs which have difficulty

digesting superelement results in the op2 or .pch files.


Enhancements to the Frequency Response Function (FRF) and FRF Based Assembly (FBA) Feature

210


Introduction

The FRF / FBA (Frequency Response Function / FRF Based Assembly) capability was first introduced

in MD Nastran R2. This capability facilitates the computation of the FRFs of individual components and

also the subsequent computation of the FRFs of an assembly of such components from their individual

FRFs.

The capability available in MD Nastran R2 had several limitations that were pointed out in the MD

Nastran R2 Release Guide. These limitations have been eliminated in MD Nastran R3.

The enhancements made in MD Nastran R3 are discussed in the following sections. These changes also

involved enhancements to the FRF Case Control command and the addition of seven new Bulk Data

entries (FBADLAY, FBALOAD, FBAPHAS, FRFCONN, FRFFLEX, FRFRELS and FRFSPC1) related

to FRF/FBA usage. The descriptions of the expanded FRF Case Control command and the new Bulk

Data entries are given in the MD Nastran R3 Quick Reference Guide.

Names for FRF Components

The name of an FRF component is now as much a characteristic as its identification number (ID). The

FRF Case Control command has been enhanced so that the COMPNAME keyword (which was optional

earlier) is now required if the COMPID keyword is specified or vice versa.

Interchangeable COMPID/COMPNAME Fields in All Bulk Data Entries Meant for FBA Use

All Bulk Data entries meant for use in the FBA process are designed so that the FRF components can be

identified either by their component IDs or by their component names. These items can be used

interchangeably. This feature offers great convenience and flexibility to users.

User Load Specification in the FBA Process

It is now possible to specify user loads in the FBA process. In order to facilitate this, three new Bulk

Data entries FBALOAD, FBADLAY and FBAPHAS have been introduced. These entries define loads

by referencing points in the FRF components that comprise the FRF assembly.

Responses to Unit Loads and User Specified Loads

It is now possible to get responses not only to unit loads, but also to user specified loads in both FRF

generation runs and in the FBA process. This is meaningful if the user specifies a dynamic load in a FRF

211CHAPTER 5

NVH and Acoustics

or FBA job via a DLOAD Case Control command. To facilitate this, the XITOUT keyword in the FRF

Case Control command has been expanded. Details are given below.

FRF Case Control XITOUT Keyword

Possible values are UNIT, UNITALL, USER and USERTOTL. Their meanings are given below:

XITOUT = UNIT

• Generates output for all user specified unit loads (either explicitly via FRFXIT/FRFXIT1 Bulk

Data entries or implicitly via the DLOAD Case Control command)

XITOUT = UNITALL

• Generates output not only for all user specified unit loads (either explicitly via

FRFXIT/FRFXIT1 Bulk Data entries or implicitly via the DLOAD Case Control command), but

also for unit loads applied automatically by the program at all connection points in the set

specified by the FRF Case Control CONNPTS keyword

XITOUT = USER

• Meaningful only if there is a DLOAD Case Control command

• If the specified dynamic load involves loads on N DOFs in the model, the program

automatically generates output for (N+1) load cases. The first N of these load cases represent

loads on each of the N DOFs separately and individually and the (N+1)th load case represents

the total applied load.

XITOUT = USERTOTL

• Meaningful only if there is a DLOAD Case Control command

• Generates output only for the total applied load, corresponding to the (N+1)th load case

mentioned previously.

If N = 1 in the above discussion, then XITOUT = USER and XITOUT = USERTOTL will both generate

output only for the total applied load.

The prior scenario is in contrast to standard SOL 108 / SOL 111 jobs wherein the output is generated

only for the total applied load (just like XITOUT = USERTOTL).

The output generated by the XITOUT = USER option described is perfectly well suited for TPA

(Transfer Path Analysis) studies since it allows for the examination of the effects on the response of the

system due to loads on individual DOFs as well as due to the total applied load.

XITOUT Keyword Defaults

• XITOUT = UNIT is the default if there is no DLOAD Case Control command.

• XITOUT = USER is the default if there is a DLOAD Case Control command.

If the user specifies XITOUT = USER or XITOUT = USERTOTL, but there is no DLOAD Case

Control command, the program issues a warning message and assumes XITOUT = UNIT.



212

Connection of Scalar Points and Explicit Connection of Coincident Grid Points

It is now possible to connect scalar points of FRF components and also to specify the explicit connection

of coincident grid points. The latter feature is particularly helpful to handle cases wherein an FRF

component may have two or more coincident grid points among its connection points. A new Bulk Data

entry called FRFCONN has been introduced for this purpose. This entry is analogous to the SECONCT

entry employed in superelement analysis.

Flexible Connection of Degrees-of-Freedom

The connections in the FBA process are no longer restricted to rigid connections. The enhancements

allow for flexible connections between DOFs of coincident grid points or those of scalar points. Elastic

(K), damping (B) and non-uniform structural damping (Ge) properties may be specified for these

connections for use in the FBA process. These properties may be specified either as constant values (that

are independent of the forcing frequency) or as frequency dependent values. A new Bulk Data entry

called FRFFLEX has been introduced for this purpose.

Release of Connection Degrees-of-Freedom

It is now possible to release specific DOFs of connection grid points in the FBA process. A new Bulk

Data entry called FRFRELS has been introduced for this purpose.

Grounding of Connection Degrees-of-Freedom

It is now possible to specify single-point constraints for DOFs of connection points in the FBA process.

A new Bulk Data entry called FRFSPC1 has been introduced for this purpose. This entry is selected by

the SPC Case Control command.

Handling of Coincident Connection Grid Points of FRF Components in the FBA Process

As part of the enhancements, the program now examines each FRF component in the FBA process for

the existence of coincident connection grid points. If such points exist, the program performs the

following tasks:

• Outputs a list of such points for each FRF component in the FBA process.

• Examines each coincident connection grid point to ensure that it is referenced either on an

FRFCONN Bulk Data entry or all six (6) of its DOFs are released by being referenced on an

FRFRELS Bulk Data entry. If this condition is met, the program continues the execution.

Otherwise, the program terminates the execution with a User Fatal Message (UFM).

The above design ensures that coincident connection grid points will NOT be automatically combined

with other such points, leading possibly to invalid, unwanted or inadvertent connections. Instead, the

design ensures that such points will be combined only via explicit user directives.

213CHAPTER 5

NVH and Acoustics

Handling of Displacement (or Local) Coordinate Systems at Connection Grid Points of FRF Components in the FBA Process

When the program connects two or more grid points of the FRF components in the FBA process, it

examines the displacement (or local) coordinate systems of each of those connection points to ensure that

they all represent the same coordinate system transformations with respect to the basic coordinate

system. If this condition is not met, the program terminates the job with a User Fatal Message (UFM).

The previous requirement is necessary to ensure proper results from the FBA process.

FRFs for PLOTEL Grid Points

The program logic has been enhanced so that, if COMPID/COMPNAME is specified in the FRF Case

Control command, then FRFs are automatically computed for all grid points referenced on PLOTEL

Bulk Data entries regardless of any other user requests. With this enhancement, the specific points for

which FRFs are computed in a FRF generation run comprise the following:

• All points specified via DISP, VELO and ACCE requests

• All grid points referenced on PLOTEL Bulk Data entries

• All points associated with elements for which STRESS/FORCE requests are specified

• All points where unit loads are applied (either explicitly via FRFXIT/FRFXIT1 Bulk Data

entries or implicitly via the DLOAD Case Control command)

• All points comprising the set referenced by the CONNPTS keyword in the FRF Case Control

command

Summary of the Enhancements

The enhancements made in MD Nastran R3 for the FRF/FBA capability represent significant

improvements over what was available in MD Nastran R2. These improvements make the feature an

excellent tool for practical situations and a viable alternative to traditional superelement analysis for

NVH studies. In particular, the results generated for user specified loads are very well suited for

subsequent processing by visualization tools.


Enhancements to ADAMSMNF Case Control Command

214

Enhancements to ADAMSMNF Case Control Command

The general goal of this enhancement is to provide MD Nastran database access for ADAMS/FLEX

MNF, i.e., Modal Neutral File-type, data storage and/or processing. This will allow you to persist

multiple flexible bodies in the same database instead of generating multiple “MNF” files. Moreover, tests

show that you will experience up to 30 times faster data access speeds if the MNF data is stored in a MD

Nastran database compared to the same data stored in an MNF file.

This enhancement is implemented in the ADAMSMNF Case Control command using a new option

keyword as shown below:

ADAMSMNF FLEXBODY=YES EXPORT=MNF/DB/BOTH

It should be noted that at this time MD Nastran databases may not be shared among binary incompatible

machines. That is, if you generate a database on a 32-bit Big Endian platform, e.g., HPUX, SUN, and

would like to read the data on a 32-bit Little Endian platform, e.g., WINDOWS, LINUX, then you must

convert the database using the “DBUNLOAD/DBLOAD” procedure.

Chapter 6: Numerical Methods and High Performance Computing MD Nastran R3 Release Guide

=

6 Numerical Methods and High

Performance Computing

� Linear and Nonlinear Contact Analysis

� High Performance Iterative Solver Now Available for Nonlinear

Transient Analysis

� Matrix Based Iterative Solver Now Available for Nonlinear Static

Analysis

� Factor Matrix Caching for Lanczos and Nonlinear Transient Analysis

with NLAUTO

� New TAUCS Indefinite Solver Improves Lanczos Performance

� Shared Memory Parallel (SMP) Scalability Improvements for Static

Analysis

� New MAXRATIO Information Output

� New SPARSESOLVER MDTSTATS Information Output


Linear and Nonlinear Contact Analysis216

Linear and Nonlinear Contact Analysis

Introduction

Linear and nonlinear contact analysis is available in MD Nastran SOL 101 and SOL 400. The CASI

element based iterative solver was integrated into contact analysis for the MD Nastran R2.1 release. This

enhancement enabled efficient computation for the solution of equations for contact

with solid models.

Contact between two or more solid bodies, over a varying contact area, involves significant

computational cost. The original implementation of contact in MD Nastran utilized previously existing

functional and computational tools. For MD Nastran R3, new computational tools and procedures have

been implemented, resulting in improved performance.

Benefits

Users should observe improved computational efficiency and performance for both linear and nonlinear

contact analysis, especially for solid models using the CASI element based iterative solver.

Inputs

To select the CASI iterative solver, specify the SMETHOD command in the Case Control Section.

SMETHOD = ELEMENT

To modify parameters for the CASI solver, specify the ID of an ITER Bulk Data entry:

SMETHOD = 10

For example, to specify a convergence tolerance of 1.0e-4 for the CASI solver:

ITER, 10PRECOND=CASI, ITSEPS=1.0E-4

The user interface for the CASI iterative solver for contact analysis is the same as it is for linear static

analysis in SOL 101. Refer to the Case Control command SMETHOD, 457 and the Bulk Data entry ITER,

1772 in the MD Nastran Quick Reference Guide for more information.


Significant reduction is observed in disk I/O and scratch disk capacity requirements. This results in

reduced elapsed analysis times for systems with minimal memory and/or relatively slow scratch disk

drive performance.

A[ ] x{ } b{ }Z

217CHAPTER 6

Numerical Methods and High Performance Computing

Demonstration Example

Examples are taken from actual models from industry. The models are proprietary, so they may not be

displayed. However, the basic model characteristics are shown along with the performance comparison.

Example 1

Analysis type: Linear contact

Number of grid points: 817,556

Number of solid elements: 525,741

Number of iterations: 3

Compute platform used: IBM AIX POWER5

Disk I/O (GB) Scratch Disk Required (GB)

MD Nastran R2 268.1 31.9


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Linear and Nonlinear Contact Analysis218

Example 2

Analysis type: Nonlinear contact





Disk I/O (GB) Scratch Disk Required (GB)



Nonlinear contact example

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219CHAPTER 6


High Performance Iterative Solver Now Available for Nonlinear Transient Analysis

Introduction

Nonlinear analysis is available in MD Nastran SOLs 400 and 101. At each nonlinear iteration, a solution

of the equations is performed using sparse direct factorization and forward-backward

substitution (FBS). For large models composed primarily of solid finite elements, the bulk of the

solution time is spent computing . For MD Nastran R2.1 structural static analysis, iterative

solutions are available to compute for models that will benefit from an iterative solution, such as

solid models. For MD Nastran R3, the CASI element-based iterative solver is now available for use in

non-linear transient structural analysis.

Benefits

Users may experience significant performance increases by selecting an iterative solver for nonlinear

analysis of large solid models. Depending on the number of nonlinear iterations in the overall analysis,

the anticipated speedup is from two to five times.

Inputs

To select an iterative solver, specify the SMETHOD command in the Case Control Section. The

following SMETHOD command selects the CASI element-based iterative solver:

SMETHOD = ELEMENT

(To select a matrix-based iterative solver, specify SMETHOD = MATRIX.) The ELEMENT solver

generally results in the best performance. To modify the specific parameter settings for one of the

preceding iterative solvers, the SMETHOD command can specify the ID of an ITER Bulk Data entry.

The user interface for the iterative solver is the same as it is for linear static analysis in SOL 101. Refer

to the Case Control command SMETHOD, 457 and the Bulk Data entry ITER, 1772 in the MD Nastran

Quick Reference Guide, for more information.

Outputs

There are no new engineering outputs associated with this feature other than informational and

diagnostic messages. In addition, a “PCS” output text file contains additional diagnostic output.


The element-based iterative solution option is primarily intended for use in nonlinear contact analysis of

large solid models exceeding one million DOFs. There may be no performance gain if one substitutes

A[ ] x{ } b{ }Z

x{ }

x{ }


High Performance Iterative Solver Now Available for Nonlinear Transient Analysis220

the CASI solver for direct solution (DECOMP/FBS) in situations where many FBS operations are

performed using the factor matrix from a single decomposition. This situation arises for simple linear

transient analysis.

The CASI solver is not designed to handle indefinite coefficient matrices. If a solution fails, the

NLSOLV module automatically switches to the direct sparse solver method to continue the solution

process. Differential stiffness effects and follower stiffness can produce an indefinite and possibly

unsymmetrical coefficient matrix.

Due to the unsymmetrical nature of the follower stiffness matrix, use caution when follower stiffness is

present and the SMETHOD is ELEMENT or selects the CASI solver. By default, the presence of any of

the MOMENTi, FORCEi, PLOADi, and RFORCE Bulk Data entries causes automatic generation of

follower stiffness. If CASI is specified and follower-stiffness is present, it is automatically

symmetricized. In cases where this is not acceptable, PARAM,FOLLOWK,NO must be specified in the

Bulk Data Section. However, this will alter the analysis results by not including follower stiffness.

Currently, follower stiffness resulting from RFORCE, PLOADX and GRAV loadings cannot be handled

by the CASI solver interface. Therefore, the presence of these Bulk Data entries will generate User Fatal

Message 9192 unless PARAM,FOLLOWK,NO is also specified.

221CHAPTER 6


Matrix Based Iterative Solver Now Available for Nonlinear Static Analysis

Introduction

For symmetric linear systems, the matrix-based iterative solver was introduced in MD Nastran R2.1 for

nonlinear structural static analysis for (SOL 101 and SOL 400). In MD Nastran R3, the matrix-based

iterative solver is also available for unsymmetric systems in nonlinear static and transient structural

analysis. Certain applications in nonlinear static analysis (SOL 400) result in unsymmetric systems to

be solved inside the nonlinear solution module. These examples include:

• Heat transfer analysis with advection (one-directional fluid flow) or radiation

• Follower-force stiffness

• Friction force stiffness

• Damping matrices

• Transfer functions

For solid modeling applications, the default unsymmetric direct factorization and solve provide

numerical stability. However, the performance characteristics of this solver are sub-optimal. Typically,

for solid models, an iterative solver proves to be significantly faster than a direct solver.

Benefits

For MD Nastran R3, the Nastran matrix-based unsymmetric iterative solver is available in the nonlinear

solution module in SOL 400. This solver can provide up to two times speedup compared to the

equivalent direct unsymmetric solver.

In order to maintain desired performance, unsymmetric nonlinear systems are often “symmetricized”.

This can have the desired effect on performance, while sacrificing some degree of numerical and

engineering integrity. The availability of the Nastran matrix-based iterative solver substantially lowers

the performance penalty for solving a true unsymmetric system for large solid models.

Method and Theory

The Jacobi (default) and Cholesky preconditioning methods with and without scaling are available. BIC

preconditioning (the default preconditioning method for symmetric systems) is not available for

unsymmetric systems. If BIC is chosen by the user, the program automatically switches to Jacobi

preconditioning without scaling. Similarly, the element-based CASI iterative solver is not available for

unsymmetric systems, and the program will switch automatically to Jacobi preconditioning without

scaling if it is chosen.


Matrix Based Iterative Solver Now Available for Nonlinear Static Analysis222

Inputs

There is no change to the iterative solver interface. The matrix-based iterative solver is specified by the

Case Control command

SMETHOD = matrix

or

SMETHOD = k

where k is the ID of an ITER Bulk Data entry. For more information please refer to the Case Control

command SMETHOD, 457 and the Bulk Data entry ITER, 1772 in the MD Nastran Quick Reference

Guide. The program will decide automatically whether the symmetric or unsymmetric path is taken.

Outputs

Diagnostic output is available according to the options on the ITER Bulk Data entry.


The Nastran matrix-based iterative solver is best suited for large solid models that yield unsymmetric

nonlinear solutions.

Demonstration Examples

Below are three examples using heat transfer analysis, demonstrating the significant benefits of the

matrix-based iterative solver for this type of problem.

Both examples were run with the default preconditioner, Jacobi without scaling. Both examples require

solutions of unsymmetric linear systems in SOL 400.

Example 1:

When run with SMETHOD=matrix in MD Nastran R2, this job fails in the iterative solver because only

the direct method works for unsymmetric systems in SOL 400. In MD Nastran R3, the command

SMETHOD=matrix will result in significant performance improvements.

Analysis type: Heat transfer with radiation





223CHAPTER 6


Example 2:

When run with SMETHOD=matrix in MD Nastran R2, this job fails in the iterative solver because only

the direct method works for unsymmetric systems in NLSOLV. In MD Nastran R3, the command

SMETHOD=matrix will result in significant performance improvements.

Analysis type: Heat transfer





Heat transfer example

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Matrix Based Iterative Solver Now Available for Nonlinear Static Analysis224

Example 3:

Analysis type: Heat transfer with radiation






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225CHAPTER 6


Factor Matrix Caching for Lanczos and Nonlinear Transient Analysis with NLAUTO

Introduction

In solution sequences where many linear systems are solved using the same coefficient matrix, the FBS

time can be significant when the factor matrix is stored out of core. Examples include dynamic solution

sequences which use the Lanczos method and nonlinear transient response. In MD Nastran R3, new

logic has been introduced to cache as much of the factor as possible in memory.

Benefits

The reduced I/O can cut the elapsed time for FBS by five to 30 percent, depending on the size of the

factor matrix, the number of right-hand sides, and the amount of memory available.

Method and Theory

The underlying method has not changed; only the memory usage. Previously, only the minimum amount

of factor data needed to perform the FBS was read from the factor data block each time and FBS was

required. Now, as much of the factor as possible is cached in memory between FBS calls, reducing the

I/O required.

Inputs

For Lanczos, no input is required, except when running on Linux IA64. This option has not been

beneficial on Linux IA64, but it can be turned-on setting SYSTEM cell 146 to -1. For nonlinear transient

analysis, the factor caching logic must be activated by setting SYSTEM(146) to -1. For comparison

purposes, the factor-caching logic can be deactivated by setting SYSTEM(146)=+1.

Outputs

A new System Information Message 4157 will appear in the. f04 file:

In addition, when SYSTEM cell 166 to 2, additional time stamps “FBSI BGN” and “FBSI END” appear

in the .f04 file.

MEMORY REQUIREMENTS FOR IN-CORE FACTOR OPTION: AVAILABLE MEMORY: 229909 KWORDS NUMBER OF TOTAL FRONTS: 42935 NUMBER OF FRONTS WHICH FIT IN CORE: 14225 EST MEMORY FOR ENTIRE FACTOR TO IN CORE: 586268 KWORDS


Factor Matrix Caching for Lanczos and Nonlinear Transient Analysis with NLAUTO226


It is difficult to estimate the amount of memory to specify for a given model so that most of the factor

can be cached. The “estimate” program can give a starting point. A rule of thumb would be to give 3

times the amount of memory recommended in the “estimate” output, but no more than 75% of the

physical memory available on the machine.


Example 1:

The following example is a nonlinear transient analysis model, with approximately 4000 dof which

performs approximately 34,000 FBS operations. The analysis was run on a workstation with two dual-

core 64-bit Pentium Xeon processors running at 3GHz, 8GB of physical memory and a 4-way striped

SCSI disk array. The job was submitted with mem=4gb. Specifying system(146)=-1 reduces total I/O by

11% and results in a 10% overall performance improvement in elapsed time.

Nonlinear Transient Performance

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227CHAPTER 6


Example 2:

The following example is a powertrain model with 160,000 grids and 940,000 degrees of freedom.

Twenty mode shapes are required using Lanczos. A total of 14 FBS operations are performed. The job

is run on workstation with two dual-core 64-bit Pentium Xeon processors running at 3GHz, 8GB of

physical memory. The job is submitted with mem=6gb. By caching the factor, the total FBS time is

reduced by 30%, resulting in a 13% reduction in the overall READ time.

Lanczos Performance Improvement

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New TAUCS Indefinite Solver Improves Lanczos Performance228

New TAUCS Indefinite Solver Improves Lanczos Performance

Introduction

A new symmetric indefinite factorization method from the TAUCS software project

www.tau.ac.il/~stoledo/taucs/ has been integrated into MD Nastran R3. It is available in the DCMP,

DECOMP, SOLVE, RMG2, SDR2, and READ modules, with the main focus on the READ module. The

new solver keeps all data in memory.

Benefits

The new method can significantly improve the factorization and FBS time, particularly in the Lanczos

procedure, for problems which fit in memory. In this release, the method is only recommended on the

Linux x86_64 platforms (Intel EM64T and AMD Opteron).

Method and Theory

The new method is based on a hybrid left-looking /supernodal multifrontal technique, with emphasis on

data locality.

Inputs

The new method can be selected by setting SYSTEM cell 166 to 16384.

Outputs

The following information is printed in the .f04 file.


In this release, this method has only been tuned for the Linux x86_64 platform (Intel EM64T/AMD

Opteron) and is only recommended for that platform. This method must keep all data in memory, so it

is recommended that it be submitted with 75% of the physical memory available.

Elimination tree depth is 7043 Symbolic Analysis of LDL^T: 1.53e+08 nonzeros, 9.48e+10 flops, 1.40e+09 bytes in L Relaxed Analysis of LDL^T: 1.80e+08 nonzeros, 1.14e+11 flops, 1.72e+09 bytes in L Symbolic Analysis = 3.415 seconds (3.411 cpu)12:07:41 1:05 15753.0 24.0 61.1 6.5 TAUD END12:07:47 1:11 16890.0 1137.0 66.7 5.5 TAUD BGN Using blocked update in dense factorization. Supernodal Left-Looking LDL^T = 49.121 seconds (48.390 cpu) Post Analysis of LDL^T: 1.80e+08 nonzeros, 1.14e+11 flops, 1.72e+09 bytes in L

www.tau.ac.il/~stoledo/taucs/%20

229CHAPTER 6



A normal modes computation has been performed using the default factorization method (SPDC) and

the new TAUCS method on the following models. The jobs are run on a workstation with two dual-core

64-bit Pentium Xeon processors running at 3GHz, 8GB of physical memory. Each job was submitted

with mem=6gb.

Model Grids DOF Modes Factorizations FBS’s

Powertrain 160,000 940,000 20 2 14

Rotor 197,000 592,000 8 2 8

Viga 139,000 413,000 5 2 5

Van 103,000 584,000 73 2 43

Lanczos Performance

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Shared Memory Parallel (SMP) Scalability Improvements for Static Analysis230

Shared Memory Parallel (SMP) Scalability Improvements for Static Analysis

Introduction

In solution sequences where a linear system must be solved with a large number of right-hand sides,

several passes over the factor matrix may be needed to compute all of the solution vectors. This

performance enhancements keeps as much of the factor matrix as possible in memory to reduce the I/O,

improve overall performance, particularly SMP performance.

Benefits

The performance of any large FBS with many right-hand sides will be improved by as much as 30%. For

example, superelement models with static (Guyan) reduction, statics models with many load cases, and

heat transfer models with radiation will benefit from this enhancement.

Method and Theory

The underlying method has not changed; only the memory usage. Previously, only the minimum amount

of factor data need to perform the FBS was read from the factor data block during each FBS pass. Now,

as much of the factor as possible is cached in memory between FBS passes, reducing the I/O required.

Inputs

The feature is automatically activated on all platforms except Linux IA64 when enough memory is

available to store at least 32 right-hand side vectors, and when the factor and right-hand side have the

same data type (both real or both complex). The minimum number of right-hand sides required to

activate the feature can be overridden with the value of SYSTEM cell 70.

Outputs

A system information message is printed in the .f04 file if any part of the factor is cached:

Guidance and Limitations1. This feature is not available on the Linux IA64 platform.

*** SYSTEM INFORMATION MESSAGE 4157 (PREFAC1) A PORTION OF THE SPARSE FACTOR HAS BEEN CACHED IN MEMORY FOR THE FBS. 34435 FRONTAL MATRICES OUT OF A TOTAL OF 37881 ARE STORED IN MEMORY. MEMORY AVAILABLE: 412 M WORDS ESTIMATED ADDITIONAL MEMORY NEEDED TO STORE THE ENTIRE FACTOR: 281 M WORDS

231CHAPTER 6


2. This feature requires additional memory. The recommended amount is three times the amount

specified by the “estimate” program plus enough to hold 32 right-hand side vectors.


The following example is a linear statics model of a car body with 42,000 grid points, 246,000 degrees

of freedom, and 8,300 load cases. The job was run on an IBM pSeries workstation with 8 1.9GHz

power5 processors, and 8GB of physical memory.

Linear Static Performance

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New MAXRATIO Information Output232

New MAXRATIO Information Output

Introduction

A new interface is now available for analysts to better control the generation of matrix diagonal term ratio

statistics produced by the sparse symmetric matrix decomposition process in the DCMP module. The

matrix diagonal term ratio statistics are sometimes useful in determining the quality of the matrix

decomposition process. In general, for linear static analysis, high or negative ratios indicate a loss of

accuracy and could be indicative of a modeling error. The MAXRATIO functionality was a pre-release

capability in the MD Nastran R2.1 release. For MD Nastran R3 this is now a production capability.

Benefits

The new interface provides analysts with more control over the process than the existing method of

supplying a value for the MAXRATIO DMAP parameter. In addition, a new output data option is

available in the form of a simple bar chart that provides a more comprehensive view of the ratio data.

Method and Theory

No new theory is involved. The method simply involves the computation of a ratio defined as the original

matrix diagonal term divided by the decomposed matrix diagonal term. These ratios are placed in a table

together with the external identifier associated with the row/column of the term. This table is then

processed according to the options requested by the user.

Inputs

The matrix diagonal term ratio output options are controlled by keywords specified on the

SPARSESOLVER Executive Control statement. See New SPARSESOLVER MDTSTATS Information

Output, 236 for a complete description of this statement.

Outputs

The matrix diagonal term ratios can be presented in two different views. The first view is the table view,

in which each ratio is listed together with the external identifier of the row/column of the matrix, as well

as the original input matrix diagonal term. This format is virtually identical to that produced by the

previous version when any ratio exceeds the value of the MAXRATIO input parameter.

The second view of the ratios is statistical in nature. It is similar to a bar chart. A series of bar segments

are generated. There are two options for specifying the segment widths of the bars. The default option

uses powers of 10 as the widths (e.g., 10.0 to 100.0, and 100.0 to 1000.0). The second option allows the

user to specify how many segments are desired. The program will compute the segment width using the

maximum and minimum ratios. For each bar in the chart, the total number of terms in the range is

tabulated together with a visual indication of the percentage number of terms in that particular bar.

233CHAPTER 6


Note that when negative matrix diagonal term ratios are detected, they will always be output if the

TABLE option is specified.

These new views of the ratios do not replace any existing diagnostics generated by the DCMP module if

a problem is detected. Under these conditions, output from the table view may duplicate previous output

generated by DCMP module error processing.


The matrix diagonal term ratio statistics are sometimes useful in determining the quality of the matrix

decomposition process. In general, high ratios indicate a loss of accuracy. The feature can be used by

taking all of the program defaults for the various control variables. These defaults produce both the table

and bar outputs. The table is limited to 25 ratios that exceed 1.0E+05. The bar chart uses powers of ten

for segment widths. This can be done by adding

SPARSESOLVER DCMP (MDTRATIO)

to the Executive Control Section of the input data file.

The use of this new feature is currently limited to sparse symmetric matrix operations in the DCMP

module.

If there are scalar-type points present in the problem, the degrees of freedom associated with these points

will be grouped into the results for the translational degrees of freedom output.


A simple example is presented that demonstrates the use of some of the new features available for output

of the matrix diagonal term ratios. The SPARSESOLVER Executive Control statement is used to specify

the desired features. The example is for demonstration purposes only, and is not representative any

particular modeling situation. The model data consists of a simple plate structure subject to an end load.

Example Input Data$$ Example problem to demonstrate matrix diagonal term ratios$id test,casesol 101SPARSESOLVER DCMP (MDTRATIO) cendspc=100load=1000disp=allbegin bulkgrdset,,,,,,,6cquad4,101,101,1,2,52,51cquad4,102,101,2,3,53,52cquad4,103,101,3,4,54,53cquad4,104,101,4,5,55,54


New MAXRATIO Information Output234

cquad4,105,101,5,6,56,55cquad4,106,101,6,7,57,56cquad4,107,101,7,8,58,57cquad4,108,101,8,9,59,58cquad4,109,101,9,10,60,59cquadr,1101,101,1,2,52,51cquadr,1102,101,2,3,53,52cquadr,1103,101,3,4,54,53cquadr,1104,101,4,5,55,54cquadr,1105,101,5,6,56,55cquadr,1106,101,6,7,57,56cquadr,1107,101,7,8,58,57cquadr,1108,101,8,9,59,58cquadr,1109,101,9,10,60,59grid, 1,, 0.0,0.0,0.0grid, 2,, 1.0,0.0,0.0grid, 3,, 2.0,0.0,0.0grid, 4,, 3.0,0.0,0.0grid, 5,, 4.0,0.0,0.0grid, 6,, 5.0,0.0,0.0grid, 7,, 6.0,0.0,0.0grid, 8,, 7.0,0.0,0.0grid, 9,, 8.0,0.0,0.0grid,10,, 9.0,0.0,0.0grid,51,, 0.0,1.0,0.0grid,52,, 2.4,1.0,0.0grid,53,, 3.5,1.0,0.0grid,54,, 4.6,1.0,0.0grid,55,, 5.7,1.0,0.0grid,56,, 6.8,1.0,0.0grid,57,, 7.9,1.0,0.0grid,58,, 9.0,1.0,0.0grid,59,,10.1,1.0,0.0grid,60,,11.2,1.0,0.0$ctria3,201,101,101,102,151ctria3,202,101,102,152,151ctria3,203,101,102,103,152ctria3,204,101,103,153,152ctria3,205,101,103,104,153ctria3,206,101,104,154,153ctria3,207,101,104,105,154ctria3,208,101,105,155,154ctriar,1201,101,101,102,151ctriar,1202,101,102,152,151ctriar,1203,101,102,103,152ctriar,1204,101,103,153,152ctriar,1205,101,103,104,153ctriar,1206,101,104,154,153ctriar,1207,101,104,105,154ctriar,1208,101,105,155,154grid,101,, 0.0,0.0,0.0grid,102,, 1.0,0.0,0.0grid,103,, 2.0,0.0,0.0grid,104,, 3.0,0.0,0.0grid,105,, 4.0,0.0,0.0grid,151,, 0.0,1.0,0.0grid,152,, 3.4,1.0,0.0grid,153,, 4.5,1.0,0.0grid,154,, 5.6,1.0,0.0

235CHAPTER 6


grid,155,, 6.7,1.0,0.0$pshell,101,1,0.05,1mat1,1,10.+6,,0.33spc1,100,123,1,101spc1,100,3,5,55,105,155spc1,100,1,55,155spc1,100,2,1,101force,1000,10,,1000.0,1.0,0.0,0.0force,1000,60,,1000.0,1.0,0.0,0.0force,1000,105,,1000.0,1.0,0.0,0.0force,1000,155,,1000.0,1.0,0.0,0.0enddata

Example Output

The output generated by the example is shown as follows. Notice that there are two separate sections of

output: one for translational degrees of freedom, and one for rotational degrees of freedom. Within each

section, both a bar chart and table of matrix diagonal term ratios are output.

TRANSLATIONAL DOF DIAGONAL TERM RATIO STATISTICS CHART FOLLOWS FOR THE DECOMPOSITION OF MATRIX KLL ------------------------------------------------|--------------------------------------------------------------------------- DIAGONAL TERM RATIO RANGE #TERMS % TOT |MAXIMUM RATIO = 6.90963E+02 MINIMUM RATIO = 1.00000E+00 ------------------------------------------------|--------------------------------------------------------------------------- 1.0000E+00 TO 1.0000E+01 62 79.49 |**************************************************************************> 1.0000E+01 TO 1.0000E+02 12 15.38 |*************** 1.0000E+02 TO 1.0000E+03 4 5.13 |***** 00 MATRIX/FACTOR DIAGONAL TERMS RATIO SUMMARY TABLE FOR TRANSLATIONAL DOF SORTED ON DIAGONAL RATIO GRID POINT ID DEGREE OF FREEDOM MATRIX/FACTOR DIAGONAL RATIO MATRIX DIAGONAL (TOP 1 RATIOS>MAXRAT= 6.90963E+02) 58 T3 6.90963E+02 5.65535E+04 ROTATIONAL DOF DIAGONAL TERM RATIO STATISTICS CHART FOLLOWS FOR THE DECOMPOSITION OF MATRIX KLL ------------------------------------------------|--------------------------------------------------------------------------- DIAGONAL TERM RATIO RANGE #TERMS % TOT |MAXIMUM RATIO = 3.35974E+02 MINIMUM RATIO = 1.00000E+00 ------------------------------------------------|--------------------------------------------------------------------------- 1.0000E+00 TO 1.0000E+01 38 63.33 |*************************************************************** 1.0000E+01 TO 1.0000E+02 18 30.00 |****************************** 1.0000E+02 TO 1.0000E+03 4 6.67 |*******

00 MATRIX/FACTOR DIAGONAL TERMS RATIO SUMMARY TABLE FOR ROTATIONAL DOF SORTED ON DIAGONAL RATIO GRID POINT ID DEGREE OF FREEDOM MATRIX/FACTOR DIAGONAL RATIO MATRIX DIAGONAL (TOP 1 RATIOS>MAXRAT= 3.35974E+02) 58 R2 3.35974E+02 2.14135E+04


New SPARSESOLVER MDTSTATS Information Output236

New SPARSESOLVER MDTSTATS Information Output

Introduction

A new interface is now available to control the generation of matrix diagonal term statistics for the input

matrix to the sparse symmetric matrix decomposition process in the DCMP module. The matrix diagonal

term statistics can be useful in determining the quality of the model in regions that produce unusually

large or small terms. In general, for linear static analysis, model degrees of freedom with small

stiffnesses could indicate areas where loads will produce large displacements. This feature complements

the MDTRATIO option that controls MAXRATIO output described previously. The SPARSESOLVER

MDTSTATS functionality was a pre-release capability in the MD Nastran R2.1 release. For MD Nastran

R3 this is now a production capability.

Benefits

The new interface provides another means of identifying potential modeling errors other than monitoring

the MAXRATIO statistics. One of the new output data options is a simple bar chart that provides a more

comprehensive view of the diagonal term data.

Method and Theory

No new theory is involved. The method involves adding the original matrix diagonal term to the ratio

table where the computation of the ratio is defined to be the original matrix diagonal term divided by the

decomposed matrix diagonal term. These terms are placed together in a table with the external identifier

associated with the row/column of the term. This table is then processed according to the options

requested by the user.

Inputs

The matrix diagonal term statistical output options are controlled by keywords specified on the

SPARSESOLVER Executive Control statement. See the MD Nastran Quick Reference Guide for a

complete description of this statement.

Outputs

The matrix diagonal term statistics can be presented in two different views. The first is the table view in

which each diagonal term is listed together with the external identifier of the row/column of the matrix,

as well as with the Aii/Lii diagonal term ratio. This format is almost identical to that produced now when

any ratio exceeds the value of the MAXRATIO input parameter. The second view of the diagonal terms

is statistical in nature, similar to a bar chart. A series of bar segments is generated. There are two options

for specifying the segment widths of the bars. The default option uses powers of 10 as the widths (e.g.,

10.0 to 100.0, and 100.0 to 1000.0). The second option allows the user to specify how many segments

are desired. The program will compute the segment width using the maximum and minimum diagonal

237CHAPTER 6


terms. For each bar in the chart, the total number of terms in the range is tabulated together with a visual

indication of the percentage number of terms in that particular bar.

These new views of the diagonal terms do not replace any existing diagnostics generated by the DCMP

module if a problem is detected. Under these conditions, output from the table view may duplicate

previous output generated by DCMP module error processing.


The matrix diagonal term statistics are sometimes useful in determining areas of the model that may pose

problems during the decomposition process, or afterwards during the solution of equations that produce

displacements. In general, unusually large or small values could indicate a modeling problem. The

feature can be used by taking all of the program defaults for the various control variables. These defaults

produce both the table and bar outputs. The table is limited to the 25 largest terms that exceed 1.0E+10,

and the 25 smallest terms less than 1.0. The bar chart uses powers of ten for segment widths. This can

be done by adding

SPARSESOLVER DCMP ( MDTSTATS )

to the Executive Control Section of the input data file.

The use of this new feature is currently limited to sparse symmetric matrix operations in the DCMP

module.

If there are scalar-type points present in the problem, the degrees of freedom associated with these points

will be grouped into the results for the translational degrees of freedom output.


A simple example is presented that demonstrates the use of some of the new features available for output

of the matrix diagonal term statistics. The SPARSESOLVER Executive Control statement is used to

specify the desired features. The example problem is used for demonstration purposes only, and is not

representative of any particular model. The model data consists of a simple plate structure subject to an

end load. The model properties have been designed to indicate a potential problem in the bending

properties at grid points 4 and/or 54.

Example Input Data$$ Example problem to demonstrate matrix diagonal term statistics$id test,casesol 101$ Note: SPARSOLVER DCMP options must be enclosed in ()$ Note also that MDTSTATS options must also be enclosed in their own ()SPARSESOLVER DCMP ( MDTSTATS = ( CHART, TABLET, NMAXVALT=10, MAXVALT=1.0e+08,



NMINVALT=20, MINVALT=1.0, TABLER, NMINVALR=30, MINVALR=100.0 ) )cendspc=100load=1000disp=allbegin bulkgrdset,,,,,,,6cquad4,101,101,1,2,52,51cquad4,102,101,2,3,53,52cquad4,103,102,3,4,54,53cquad4,104,102,4,5,55,54cquad4,105,101,5,6,56,55cquad4,106,101,6,7,57,56cquad4,107,101,7,8,58,57cquad4,108,101,8,9,59,58cquad4,109,101,9,10,60,59cquadr,1101,101,1,2,52,51cquadr,1102,101,2,3,53,52cquadr,1103,102,3,4,54,53cquadr,1104,102,4,5,55,54cquadr,1105,101,5,6,56,55cquadr,1106,101,6,7,57,56cquadr,1107,101,7,8,58,57cquadr,1108,101,8,9,59,58cquadr,1109,101,9,10,60,59grid, 1,, 0.0,0.0,0.0grid, 2,, 1.0,0.0,0.0grid, 3,, 2.0,0.0,0.0grid, 4,, 3.0,0.0,0.0grid, 5,, 4.0,0.0,0.0grid, 6,, 5.0,0.0,0.0grid, 7,, 6.0,0.0,0.0grid, 8,, 7.0,0.0,0.0grid, 9,, 8.0,0.0,0.0grid,10,, 9.0,0.0,0.0grid,51,, 0.0,1.0,0.0grid,52,, 2.4,1.0,0.0grid,53,, 3.5,1.0,0.0grid,54,, 4.6,1.0,0.0grid,55,, 5.7,1.0,0.0grid,56,, 6.8,1.0,0.0grid,57,, 7.9,1.0,0.0grid,58,, 9.0,1.0,0.0grid,59,,10.1,1.0,0.0grid,60,,11.2,1.0,0.0$ctria3,201,101,101,102,151ctria3,202,101,102,152,151ctria3,203,101,102,103,152ctria3,204,101,103,153,152ctria3,205,101,103,104,153ctria3,206,101,104,154,153ctria3,207,101,104,105,154

239CHAPTER 6


ctria3,208,101,105,155,154ctriar,1201,101,101,102,151ctriar,1202,101,102,152,151ctriar,1203,101,102,103,152ctriar,1204,101,103,153,152ctriar,1205,101,103,104,153ctriar,1206,101,104,154,153ctriar,1207,101,104,105,154ctriar,1208,101,105,155,154grid,101,, 0.0,0.0,0.0grid,102,, 1.0,0.0,0.0grid,103,, 2.0,0.0,0.0grid,104,, 3.0,0.0,0.0grid,105,, 4.0,0.0,0.0grid,151,, 0.0,1.0,0.0grid,152,, 3.4,1.0,0.0grid,153,, 4.5,1.0,0.0grid,154,, 5.6,1.0,0.0grid,155,, 6.7,1.0,0.0$pshell,101,1,0.05,1pshell,102,1,0.05,2mat1,1,10.+6,,0.33mat1,2,10.+1,,0.33spc1,100,123,1,101spc1,100,3,5,55,105,155spc1,100,1,55,155spc1,100,2,1,101force,1000,10,,1000.0,1.0,0.0,0.0force,1000,60,,1000.0,1.0,0.0,0.0force,1000,105,,1000.0,1.0,0.0,0.0force,1000,155,,1000.0,1.0,0.0,0.0enddata

Example Output

The output generated by the example is shown as follows. There are two separate sections of output: one

for translational degrees of freedom and one for rotational. Within each section, both a bar chart and

table of matrix diagonal terms are output.

=============================================================================================================================== TRANSLATIONAL DOF Aii DIAGONAL TERMS STATISTICS CHART FOLLOWS FOR MATRIX KLL Matrix Trace(Aii) = 1.27351E+08 ------------------------------------------------|--------------------------------------------------------------------------- | MAXIMUM VALUE = 5.94121E+06 MINIMUM VALUE = 4.07806E-01 MATRIX DIAGONAL TERM RANGE #TERMS % TOT | GRID ID = 104, DOF = T2 GRID ID = 54, DOF = T3 ------------------------------------------------|--------------------------------------------------------------------------- 1.0000E-01 TO 1.0000E+00 2 2.56 |*** 1.0000E+03 TO 1.0000E+04 2 2.56 |*** 1.0000E+04 TO 1.0000E+05 18 23.08 |*********************** 1.0000E+05 TO 1.0000E+06 6 7.69 |******** 1.0000E+06 TO 1.0000E+07 50 64.10 |**************************************************************** ===============================================================================================================================



0 MATRIX/FACTOR DIAGONAL TERMS SUMMARY TABLE FOR TRANSLATIONAL DOF SORTED ON Aii DIAGONAL GRID POINT ID DEGREE OF FREEDOM Aii TERM Lii TERM Aii/Lii RATIO (TOP 1 VALUES > 5.94121E+06) 104 T2 5.94121E+06 3.57301E+06 1.66280E+00

0 MATRIX/FACTOR DIAGONAL TERMS SUMMARY TABLE FOR TRANSLATIONAL DOF SORTED ON Aii DIAGONAL GRID POINT ID DEGREE OF FREEDOM Aii TERM Lii TERM Aii/Lii RATIO (TOP 2 VALUES < 1.00000E+00) 54 T3 4.07806E-01 4.07806E-01 1.00000E+00 4 T3 4.70350E-01 2.84250E-01 1.65471E+00

=============================================================================================================================== ROTATIONAL DOF Aii DIAGONAL TERMS STATISTICS CHART FOLLOWS FOR MATRIX KLL Matrix Trace(Aii) = 4.52211E+05 ------------------------------------------------|--------------------------------------------------------------------------- | MAXIMUM VALUE = 2.34493E+04 MINIMUM VALUE = 4.71107E-02 MATRIX DIAGONAL TERM RANGE #TERMS % TOT | GRID ID = 9, DOF = R2 GRID ID = 54, DOF = R1 ------------------------------------------------|--------------------------------------------------------------------------- 1.0000E-02 TO 1.0000E-01 2 3.33 |*** 1.0000E-01 TO 1.0000E+00 2 3.33 |*** 1.0000E+02 TO 1.0000E+03 3 5.00 |***** 1.0000E+03 TO 1.0000E+04 36 60.00 |************************************************************ 1.0000E+04 TO 1.0000E+05 17 28.33 |**************************** ===============================================================================================================================

0 MATRIX/FACTOR DIAGONAL TERMS SUMMARY TABLE FOR ROTATIONAL DOF SORTED ON Aii DIAGONAL GRID POINT ID DEGREE OF FREEDOM Aii TERM Lii TERM Aii/Lii RATIO (TOP 1 VALUES > 2.34493E+04) 9 R2 2.34493E+04 4.87230E+03 4.81277E+00

0 MATRIX/FACTOR DIAGONAL TERMS SUMMARY TABLE FOR ROTATIONAL DOF SORTED ON Aii DIAGONAL GRID POINT ID DEGREE OF FREEDOM Aii TERM Lii TERM Aii/Lii RATIO (TOP 4 VALUES < 1.00000E+02) 54 R1 4.71107E-02 3.08701E-02 1.52610E+00 4 R1 4.71334E-02 9.03202E-03 5.21847E+00 54 R2 1.48139E-01 8.62427E-02 1.71770E+00 4 R2 1.48232E-01 7.96377E-02 1.86133E+00

Chapter 7: Upward Compatibility


=

7 Upward Compatibility

� TEMPERATURE Case Control Command

� Improvements in Fluid Eigenvalue Analysis

� FLUID GRID Points and Partitioning

� Distributed Memory Parallel (DMP) Diagnostic Messages

� System Information Message (SIM) 6916


Upward Compatibility

242

TEMPERATURE Case Control Command

According to Remark 8 under the Case Control command TEMPERATURE (Ch. 4) in the MD Nastran

Quick Reference Guide, TEMPERATURE(INITIAL) and TEMPERATURE(MATERIAL) cannot be

specified in the same run and User Fatal Message 633 will be issued. User Fatal Message 633 is also

issued if TEMPERATURE(BOTH) is specified with TEMPERATURE(INIT) and

TEMPERATURE(MATERIAL). However, in MD Nastran R2 and prior, this rule was not enforced when

just TEMPERATURE was specified with TEMPERATURE(INITIAL) or

TEMPERATURE(MATERIAL); and, depending on their relative locations in the Case Control Section,

one of them would be ignored and results will be wrong. For example, the following input file (modified

from TPL problem tempload):

sol 101cendtemp(init) = 10subcase 1 temp = 20 load = 100 spc = 10 disp = allbegin bulkforce,100,3,0,100.0,1.0,0.0,0.0grid, 1,, 0.0,0.0,0.0grid, 2,,10.0,0.0,0.0grid, 3,,20.0,0.0,0.0cbar,1,10,1,2,0.0,0.0,1.0pbar,10,100,1.0,1.0,1.0,1.0mat1,100,1.+4,,0.3,,1.-3rbar,2,2,3,,,,,2.0-4temp,10,1,51.0temp,10,2,52.0temp,10,3,53.0temp,20,1,61.0temp,20,2,62.0temp,20,3,63.0spc1,10,123456,1enddata

produces the following results in versions MD Nastran R2 and prior:

In MD Nastran R3, this rule is now enforced with TEMPERATURE and UFM 633 will be issued. To

avoid User Fatal Message 633 in MD Nastran R3, simply replace TEMPERATURE with

Case Control T1 Displacement at Grid 2 Comment

TEMP(INIT) and TEMP(LOAD) 0.200 Correct answer

TEMP(LOAD) 0.715 Correct answer

TEMP(INIT) and TEMP 0.715 Wrong answer because

TEMP(INIT) is ignored

243CHAPTER 7


TEMPERATURE (LOAD). In MD Nastran R4 or later, the BOTH keyword may be removed from the

documentation and the program as an option of the TEMPERATURE command.



244

Improvements in Fluid Eigenvalue Analysis1. The elemental mass matrix formulation for the 4-noded CTETRA fluid element has been

modified to prevent spurious modes. Changes may be observed in the fluid’s natural frequencies

especially at the higher frequencies. Use NASTRAN SYSTEM(446)=1 to obtain the previous

version’s formulation.

2. Householder method is automatically selected for the fluid’s system modes if the acoustic cavity

is defined in a superelement and there exist fluid boundary points. The Householder method is

more reliable method when there are fluid points on the boundary of an acoustic superelement.

The switch to Householder occurs if the number of estimated fluid modes is less than or equal to

the value of user PARAMeter FLUIDNE (Default=500).

245CHAPTER 7


FLUID GRID Points and Partitioning

The GP4 module processes displacement set definition Bulk Data entries (e.g. ASET/ASET1). During

this process, it performs various integrity tests on the data supplied by users. One of these tests verifies

that the degree-of-freedom (DOF) components exist for the points specified. The allowable components

depend upon the point type. For instance, a GRID point has six degrees of freedom and one may specify

any (or all) of the components one through six. An SPOINT on the other hand has only a single DOF

and one may specify only a blank or zero as the component. One must also remember that for some types

of analysis, a GRID point may have a reduced number of components available. For example, in

acoustics, one can define GRID points attached to fluid that have only a single component DOF. If the

DOF integrity test fails, Nastran issues message 2049 that informs the user of the problem. The severity

of the message depends upon whether one uses the standard input format (e.g. ASET) or the alternative

format (ASET1) for the Bulk Data entry. When one uses the standard format, one defines each point and

DOF component code explicitly and it must exist. Otherwise, GP4 issues a FATAL 2049 message

indicating that the point is missing. When one uses the alternate entry format, GP4 is prepared for the

possibility that one or more points may not exist in THRU ranges defined on the entry. For this case, a

missing point/DOF produces a WARNING 2049 message.

Consider the following Bulk Data entries:

Since point 1130 is a fluid GRID point, it has only a single DOF associated with it. This DOF is

referenced with DOF component 1. Standard format entry #2 and alternate format entry #4 both use the

proper DOF component code and GP4 places the entries in the a-set without generating any messages.

Standard format entry #3 and alternate format entry #5 on the other hand, contain DOF components that

do not exist for the specified point.

Previous versions handle the processing of entries #3 and #5 as follows:

• For entry #3 (ASET), GP4 issues a FATAL message 2049 indicating that it could not find the

point and the job stops.

• For entry #5 (ASET1), GP4 issues a WARNING message 2049 indicating that it could not find

the point and the job continues, BUT, the point is NOT placed in the a-set as requested.

1. GRID,1130,,0.0,0.0,0.0,-1 $ this is a FLUID GRID point (OCID=-1)

2. ASET,1130,1 $ standard format

3. ASET,1130,123456 $ standard format

4. ASET1,1,1130 $ alternate format

5. ASET1,123456,1130 $ alternate format



246

MD Nastran R3 contains a modification to this process for FLUID GRID points and SPOINTs as follows:

• For entry #3 (ASET), GP4 issues a WARNING message 2049 indicating that certain DOFs are

not available at the point, places the one DOF available at the point in the a-set and continues the

job.

• For entry #5 (ASET1), GP4 issues a WARNING message 2049 indicating that certain DOFs are

not available at the point, places the one DOF available at the point in the a-set and continues the

job

Note the difference between MD Nastran R3 and previous versions in this area applies only to FLUID

GRID and SPOINT entries found on displacement set membership (partitioning) definition Bulk Data

entry (ASET, ASET1, OMIT, OMIT1, etc.). Existing bulk data files containing “illegal” specifications

for DOF component codes for FLUID GRIDs and SPOINTs on the partitioning bulk data entries that ran

successfully on previous versions will continue to run, but may produce different results when run with

MD Nastran R3 if a DOF becomes a part of the a-set.

247CHAPTER 7


Distributed Memory Parallel (DMP) Diagnostic Messages

Several DMP diagnostic messages used to indicate one or more of the following keywords MDMODES,

GDMODES, FDMODES, MDACMS, GDSTAT, MDSTAT, FDFREQ in the .f06 and f04 files. They

have been replaced by their proper DOMAINSOLVER description, for example, MDMODES was

replaced by “DOMAINSOLVER MODES (PARTOPT=DOF)”.



248

System Information Message (SIM) 6916

SIM 6916 which looks similar to the example below is no longer printed in the .f06 file unless you set

system(294) to a value greater than zero.

*** SYSTEM INFORMATION MESSAGE 6916 (DFMSYM) DECOMP ORDERING METHOD CHOSEN: BEND, ORDERING METHOD USED: BEND

Chapter 8: Optimization MD Nastran R3 Release Guide

8 Optimization

� Enhancements in DRESP3

� Topometry Optimization

� Topography (Bead or Stamp) Optimization

� Permanent Glued Contact Modeling in SOL 200

� Randomization of an Input Data File

� Random Elimination of Element Types

� Enhancements in SOL 200 Optimization

� Optimization of Nonlinear Structural Responses (Pre-release)


Enhancements in DRESP3

250


Introduction

DRESP3 is a feature of SOL 200 in MD Nastran that allows the user to invoke external software to

calculate design responses that are not available as standard DRESP1 quantities or that cannot be

synthesized using the DRESP2 capability. The DRESP3 is a special purpose capability that requires

some work on the user’s part to function effectively, but it has its adherents who appreciate its ability to

include design responses that are not available from Nastran. Use of this capability has identified three

enhancements for this capability that have been implemented for MD Nastran R3:

1. Provision for a capability to provide analytic gradients for the response

2. The ability to produce multiple response outputs from a single DRESP3 call.

3. Reordering of finite difference sensitivities when the DRESP3 has only DRESP1 flags and there

are more DRESP1 responses in the DRESP3 than there are independent design variables in the

model.

Benefits

Analytical gradients provide a performance benefit as well as more robust results than can be expected

from a finite difference approach to obtaining gradients.

The multiple response requirement arises from a typical scenario where a number of design criteria for a

particular component share a common set of inputs. For example, a panel may have criteria on stress,

buckling and fatigue that share parameters for geometry, properties and internal responses. By evaluating

all of these criteria in a single call, duplicate calculations are avoided and the number of calls to the server

are reduced.

The third enhancement above is for the very special application where there are perhaps thousands of

DRESP1 entries and a few hundred design variables. In this case, it makes sense to do the finite

difference gradient calculation by perturbing all the DRESP1 quantities for a particular design variable

and then calling the DRESP3 evaluator. In this way, the number of call to the evaluator is reduced from

2*NRESP1 to 2*NDVI. When NRESP1 >> NDVI, this can provide a major performance improvement

to the extent it enables performing design tasks that were previously out of reach.

User Inputs

The format of the DRESP3 Bulk Data entry is unchanged. The user is required to modify the two server

subroutines that serve to supply Nastran with the information required to evaluate the DRESP3

responses. These two subroutines are R3SGRT and R3SVALD and have the same names as has been

used in previous releases of this capability. They now have additional inputs and outputs as shown here

by examples.

The R3SGRT now not only checks that the DRESP3 Bulk Data entry is supported by the server, but also

identifies the number of responses that are produced from the server and whether analytic or finite

251CHAPTER 8

Optimization

difference gradient techniques will be used during the sensitivity and optimization evaluations.

Listing 8-1 shows an R3SGRT subroutine that utilizes the new features in solving the DRESP3 example

contained in External Response to Include Alternative Buckling Response (p. 504) in the MD Nastran

Design Sensitivity and Optimization User’s Guide.

Listing 8-1 R3SGRT Subroutine

SUBROUTINE R3SGRT(GRPID,TYPNAM,NRESP, GRDTYP, ERROR)C ----------------------------------------------------------------------CC PURPOSE: VERIFY THE EXTERNAL RESPONSE TYPECC GRPID INPUT INTEGER - GROUP IDC TYPNAM INPUT CHARACTER*8 - NAME OF EXTERNAL RESPONSE TYPEC NRESP OUTPT INTEGER - NUMBER OF RESPONSES FOR THIS DRESP3C GRDTYP OUTPT INTEGER - INTEGER ARRAY OF LENGTH NRESP C INDICATING HOW GRADIENT ARE TO BEC COMPUTEDC = 2 THE USER WILL SUPPLY ANALYTIC C GRADIENTSC = -2 FINITE DIFFERENCE TECHNIQUES ARE USEDC ERROR INPUT/OUTPUT INTEGER -ERROR CODE FOR THE CALL.CC METHODC MATCH THE USER INPUT: TYPNAM WITH THE LIST OF AVAILABLEC EXTERNAL RESPONSE TYPES. IF NO MATCH IS FOUND, SET ERROR CODE.C SPECIFY THE NUMBER OF RESPONSES AND THE GRADIENT TECHNIQUE TO C BE USED FOR EACH CC CALLED BYC R3CGRTCC NOTE:C THE WRITER OF THIS ROUTINE IS RESPONSIBLE TO SPECIFYC NTYPES AND R3TYPE.C ----------------------------------------------------------------------CC VARIABLES PASSED INC INTEGER GRPID, ERROR, NRESP INTEGER GRDTYP(*) CHARACTER*8 TYPNAMCC LOCAL VARIABLESC INTEGER NTYPES, BADTYP PARAMETER(NTYPES=6) CHARACTER*8 R3TYPE(NTYPES)C DATA BADTYP/7554/ DATA R3TYPE/'USEVAR1 ','USEVAR10','USEALL', . 'USEMIXVS','FREQMOD ','EULJOH '/ ERROR = 0 DO 100 ITYPE = 1, NTYPES IF (TYPNAM .EQ. R3TYPE(ITYPE)) THEN NRESP = 2 GRDTYP(1) = 2



252

GRDTYP(2) = 2 GOTO 200 END IF100 CONTINUE ERROR = BADTYP200 CONTINUE RETURN END

This is an update of Listing 7-33 in the and items in bold are highlighted for the following discussion.

There are two additional arguments for the subroutine:

• NRESP – indicates how many responses are to be calculated for this response type

• GRDTYP – indicates how gradients are to be supplied to an optimization or sensitivity analysis.

GRDTYP is a vector of length NRESP. Setting GRDTYP(iresp)=2 specifies that analytic gradients will

be provided while =-2 indicates that finite difference techniques will be required to compute gradient

information. In the Listing 8-1, the user has specified that there are two responses and that analytical

gradients will be supplied for each.

The corresponding R3SVALD subroutine is an update of Listing 7-34 in the MSC.Nastran Design

Sensitivity and Optimization User’s Guide:

Listing 8-2 R3SVALD Subroutine

SUBROUTINE R3SVALD(GRPID,TYPNAM, . NITEMS,ARGLIS, . NSIZE, ARGVAL, . NWRDA8,ARGCHR, . FORG,NRESP,NARG, . DR3VAL,SENVAL, . ERROR)C ----------------------------------------------------------------------CC PURPOSE: COMPUTE THE EXTERNAL RESPONSECC GRPID INPUT INTEGER - GROUP IDC TYPNAM INPUT CHARACTER*8 - NAME OF EXTERNAL RESPONSE TYPEC NITEMS INPUT INTEGER - DIMENSION OF ARRAY ARGLISC NSIZE INPUT INTEGER - DIMENSION OF ARRAY ARGVALC NWRDA8 INPUT INTEGER - DIMENSION OF CHARACTER ARRAY ARGCHRC ARGLIS INPUT INTEGER - ARRAY OF NO. OF ITEMS FOR EACH C ARGUMENT TYPE C ARGVAL INPUT DOUBLE - ARRAY OF ARGUMENT VALUES (EXCEPT C CHARACTERS) C ARGCHR INPUT CHARACTER*8 - ARRAY OF CHARACTER VALUES C NRESP INPUT INTEGER - NUMBER OF RESPONSESC FORG INPUT INTEGER - TYPE OF CALLC = 0 FUNCTION EVALUATIONC = 1 SENSITIVITY EVALUATION C NARG INPUT INTEGER - NUMBER OF ARGUMENTS NEEDING GRADIENTS C DR3VAL OUTPUT DOUBLE - VALUE OF THE EXTERNAL RESPONSESC SENVAL OUTPUT DOUBLE - MATRIX OF THE SENSITIVITY OF THE IRTH C RESPONSE TO THE IARGTH ARGUMENT

C ERROR INPUT/OUTPUT INTEGER -ERROR CODE FOR THE CALL.C

253CHAPTER 8

Optimization

C METHODC A)SET UP VARIOUS PARAMETERS FROM THE ARGUMENT LISTC B)IF FORG = 0 EVALUATE THE EXTERNAL RESPONSE BASED ON THE C GIVEN TYPNAMC C)ELSE IF FORG = 1 EVALUATE THE SENSITIVITIES OF THE EXTERNAL C RESPONSES TO THE ARGUMENTS THAT CAN VARY FOR C THE GIVEN TYPNAM C D)RETURN BADTYP ERROR IF TYPNAM IS NOT MATCHED HERE.CC NSIZE - THE NUMBER OF ARGUMENTS OR VALUES IN A DRESP3 ENTRYCC NSIZE=NV+NC+NR+NNC+NDVP1+NDVP2+NDVC1+NDVC2+NDVM1+NDVM2+NRR2C WHERE: C NV = NUMBER OF DESVARS NR = NUMBER OF DTABLESC NR = NUMBER OF DRESP1S NNC = NUMBER OF DNODE PAIRS C NDVP1 = NUMBER OF DVPREL1S NDVP2 = NUMBER DVPREL2S C NDVC1 = NUMBER OF DVCREL1S NDVC2 = NUMBER DVCREL2S C NDVM1 = NUMBER OF DVMREL1S NDVM2 = NUMBER DVMREL2S C NRR2 = NUMBER OF DRESP2S C NARG = NSIZE - NCCC CALLED BYC VARIOUSC ----------------------------------------------------------------------CC VARIABLES PASSED INC CHARACTER*8 TYPNAM, ARGCHR(NWRDA8) INTEGER FORG , NRESP INTEGER GRPID, NITEMS, NSIZE, ARGLIS(NITEMS), ERROR, NWRDA8 DOUBLE PRECISION ARGVAL(NSIZE), DR3VAL(*), SENVAL(NRESP,*) CCC LOCAL VARIABLESC INTEGER BADTYP, IDBG DOUBLE PRECISION PI, FAC, FACT, SLNDER DOUBLE PRECISION R,L,E,SIGMA,SIGMAC, RGYRAC DATA BADTYP /7554/, BADFG /7555/ C PI = 3.14159 PI2 = PI * PICC THE USER-SUPPLIED EQUATION TO DEFINE THE EXTERNAL RESPONSESC SIGMA = DRESP1, R=DESVAR, L, E AND SIGMAC = DTABLE CONSTANTSCC EULER : EULER= -SIGMA * (L/ RGYRA ) **2 / (PI**2 * E)C RGYRA = R / 2.0CC JOHNSON: JOHNSON = -SIGMA / (SIGMAC * FACTOR )C FACTOR = 1. - SIGMAC * (L/RGYRA)**2 /(4 * PI**2 * E) ERROR = 0CC SET UP PARAMETERS FOR VARIOUS ARGUMENT ITEMSC IF (TYPNAM .EQ. 'EULJOH ') THENC FUNCTION EVALUATION R = ARGVAL(1) L = ARGVAL(2)



254

E = ARGVAL(3) SIGMAC = ARGVAL(4) SIGMA = ARGVAL(5) RGYRA = R / 2.0 SLNDER = L / RGYRA FACT = PI * SQRT(2.0D0 * E / SIGMAC) FAC = 1.0D0 - SIGMAC * (SLNDER) ** 2 /(4.0D0 * PI2 * E ) IF ( FORG .EQ. 0 ) THENC FUNCTION EVALUATION C JOHNSON CRITERION DR3VAL(1) = -SIGMA / (SIGMAC * FAC)C EULER CRITERION DR3VAL(2) = -SIGMA * SLNDER**2 / (PI2 * E *10.0D0) ELSE IF ( FORG .EQ. 1 ) THENC GRADIENT EVALUATION DO 10 IRESP = 1, NRESP DO 20 IARG = 1, NARG SENVAL(IRESP,IARG) = 0.0D0 20 CONTINUE 10 CONTINUE C NOTE THAT ARGVAL(2,3 AND 4) ARE CONSTANT AND THEREFORE HAVE C ZERO SENSITIVITY DSLDR = -SLNDER / R DFACR = -SIGMAC * SLNDER * DSLDR / (2.0D0 *PI2 * E) C SENSITIVITY OF THE FIRST RESPONSE TO THE FIRST ARGUMENT SENVAL(1,1 ) = DFACR * SIGMA / ( SIGMAC * FAC ** 2)C SENSITIVITY OF THE SECOND RESPONSE TO THE FIRST ARGUMENT SENVAL(2,1) = -2.0D0*SIGMA * SLNDER * DSLDR / 1 (PI2 * E * 10.0D0)C SENSITIVITY OF THE FIRST RESPONSE TO THE SECOND ARGUMENT SENVAL(1,2) = - 1.0D0 / (SIGMAC * FAC) C SENSITIVITY OF THE SECOND RESPONSE TO THE SECOND ARGUMENT SENVAL(2,2) = -SLNDER**2 / (PI2 * E* 10.0D0) DO 25 IDBG =1,225 CONTINUE ELSE ERROR = BADFG ENDIF ELSE ERROR = BADTYP END IF RETURN END

There are three new arguments and one modified argument in the calling statement:

• FORG – input integer - flag to indicate whether this call is to perform function evaluations or

gradient evaluations. 0-function, 1-gradient

• NRESP – input integer - indicates how many responses are to be calculated for this response

type

• NARG – input integer -number of arguments requiring gradients

• DR3VAL – output real – vector of responses

• SENVAL, - output real – matrix of sensitivities

255CHAPTER 8

Optimization

DR3VAL is the modified argument in that it previously was a scalar and now is a vector. A comparison

with the listing in the User’s Guide shows that now two responses are being returned (one for the Euler

criteria and one for the Johnson criteria) rather than a single argument which was the most critical of the

two criteria. NARG is used to supply the number of columns in the SENVAL matrix and it is important

to note that any constant terms (i.e, those input using DTABLE) are not included in the count of NARG

even though they are in the ARGVAL vector. SENVAL has NRESP rows and NARG columns.

DR3VAL is output when FORG=0 while SENVAL is output when FORG=1. Additional discussion of

these arguments is provided in Guidelines and Limitations, 255.

Output

.f06 output associated with the DRESP3 has been altered in one subtle respect: a response number field

has been added to the print as a count of which of the multiple responses is associated with the print. As

an example, the

It is seen that a single DRESP3 entry has generated 10 responses. These are 2 responses in each five

elements that have the buckling criteria imposed on them. It is up to the user to decipher that RESP NO.

1 is the Johnson buckling criterion while RESP NO. 2 is the Euler criterion.


Modifying Existing Server Subroutines

The enhanced capability does not require any changes in the input files that have been developed to

utilize the DRESP3, but it does require changes in the R3SGRT and R3SVALD server subroutines. To

retain the current capability for an existing DRESP3, the changes required in the R3SGRT subroutine are

to:

1. Add arguments NRESP and GRDTYP

2. Type NRESP and GRDTYP as integers.

3. Once the appropriate TYPNAM has been selected, add NRESP = 1 and GRDTYP(1) = -2

---- RETAINED DRESP3 RESPONSES ----

----------------------------------------------------------------------------------------------------------------------- INTERNAL DRESP3 RESP RESPONSE GROUP TYPE LOWER UPPER ID ID NO LABEL NAME NAME BOUND VALUE BOUND ------------------------------------------------------------------------------------------------------------------------ 1 32 1 JOHNSON TESTGRP EULJOH N/A 1.4018E+00 1.0000E+00 1 32 2 JOHNSON TESTGRP EULJOH N/A 1.3761E+00 1.0000E+00 2 32 1 JOHNSON TESTGRP EULJOH N/A 1.4018E+00 1.0000E+00 2 32 2 JOHNSON TESTGRP EULJOH N/A 1.3761E+00 1.0000E+00 3 32 1 JOHNSON TESTGRP EULJOH N/A 1.4018E+00 1.0000E+00 3 32 2 JOHNSON TESTGRP EULJOH N/A 1.3761E+00 1.0000E+00 4 32 1 JOHNSON TESTGRP EULJOH N/A 1.4018E+00 1.0000E+00 4 32 2 JOHNSON TESTGRP EULJOH N/A 1.3761E+00 1.0000E+00 5 32 1 JOHNSON TESTGRP EULJOH N/A 1.4018E+00 1.0000E+00 5 32 2 JOHNSON TESTGRP EULJOH N/A 1.3761E+00 1.0000E+00



256

For the R3SVALD subroutine, the changes are to:

1. Add arguments FORG, NRESP, NARG, and SENVAL

2. Type FORG, NRESP and NARG as integers and DR3VAL(*) and SENVAL(NRESP,*) as

double precision

3. Replace the current DR3VAL = statements with DR3VAL(1) =.

4. Since FORG=1 is not supported, it is not necessary to specify any SENVAL output.

Other Guidelines

In R3SGRT, GRDTYP needs to be defined for all NRESP responses and the values must be either 2 or -

2. It is an error if any other value is used.

As mentioned previously, NARG is an input to R3SVALD and this value is determined from all the

DRESP3 arguments minus the constants and the string inputs. If a particular response is not a function

of one of the arguments, it is necessary to explicitly set the corresponding SENVAL output to zero. It is

a good practice to initialize the entire SENVAL array to 0.0.

It is important to realize that the gradients that are provided are for the responses with respect to the

DRESP3 arguments and not (necessarily) the design variables. This takes the burden of performing the

chain rule calculations from the user and uses existing Nastran operations to compute terms such as:

Instead, the R3SVALD subroutine provides the and terms and the remaining operations

are performed within Nastran.

Limitation

There is a current limitation that all GRDTYP’s for a particular TYPE must be the same, either -2 or 2.

The GRDTYP’s do not need to all be the same for all the DRESP3’s in an input file. That is, one can

specify analytic gradients for one TYPE and finite difference gradients for another type.

Validation and Verification

Checking that the gradients are correct is an important and challenging process. Tips for facilitating this

include:

1. Setting DSAPRT(END=SENS) = n will stop the run after printing the sensitivities of the

responses in set n.

2. Setting DSAPRT(START=1) = n will provide sensitivities for the response in set n on the first

design cycle.

3. One can use two different versions of a DRESP3 to have the program check on itself. One would

use finite difference gradients while the second would use analytic gradients. The results should

agree except for numerical rounding due to the finite difference calculation.

dr3

dxJJJJJJJJ

δr3

δxJJJJJJJJZ

δr3

δriJJJJJJJJ∑

δri

δxJJJJJJJH

δr3

δx⁄ δr3

δri

⁄

257CHAPTER 8

Optimization

Examples

Three test cases are discussed here. The first of these is ds13grad and is a variation of the dsoug13

example in External Response to Include Alternative Buckling Response (Ch. 7) in the MD Nastran

Design Sensitivity and Optimization User’s Guide. The R3SGRT and R3SVALD subroutines listed

above are used in this example.

The second example is dresp3aa is a test example to demonstrate all the types of arguments that can be

included in a DRESP3. The DRESP3 input in this example is:

Listing 8-3 ds13grad

$ F101 = X1DRESP3 101 EXTERNR3TESTGRP USEVAR1 DESVAR 1 DTABLE CONST DRESP1 808 DNODE 2 1 DVPREL1 1 DVCREL1 3 DVMREL1 5 DVPREL2 2 DVCREL2 4 DVMREL2 6 DRESP2 909 $ F102 = R2DRESP3 102 EXTERNR3TESTGRP USEVAR10 DESVAR 1 DTABLE CONST DRESP1 808 DNODE 2 1 DVPREL1 1 DVCREL1 3 DVMREL1 5 DVPREL2 2 DVCREL2 4 DVMREL2 6 DRESP2 909 $ F103 = F(X1,CONST,R1,G,DVP1,DVC1,DVM1,DVP2,DVC2,DVM2,R2)$234567DRESP3 103 EXTERNR3TESTGRP USEALL DESVAR 1 DTABLE CONST DRESP1 808 DNODE 2 1 DVPREL1 1 DVCREL1 3 DVMREL1 5 DVPREL2 2 DVCREL2 4 DVMREL2 6 DRESP2 909 $ F104 = F(X,g,P1,C1,M1,p2,R2)DRESP3 104 EXTERNR3TESTGRP USEMIXVS DESVAR 1 DTABLE CONST DRESP1 808 DNODE 2 1



258

DVPREL1 1 DVCREL1 3 DVMREL1 5 DVPREL2 2 DVCREL2 4 DVMREL2 6 DRESP2 909 USRDATA thisisa teststringforaddingxxx$ F105 = F(X,R1)DRESP3 105 EXTERNR3TESTGRP FREQMOD DESVAR 1 DRESP1 505

The relevant part of the R3SGRT subroutine that goes with this input file is:

Listing 8-4 dresp3aa

nresp = 1 IF (TYPNAM .EQ. 'FREQMOD' ) then grdtyp(1) = 2 Else if (typnam .eq. 'USEVAR1' ) then grdtyp(1) = -2 ELSE IF (TYPNAM .EQ. 'USEVAR10') THEN grdtyp(1) = 2 ELSE IF (TYPNAM .EQ. 'USEALL') THEN grdtyp(1) = -2 ELSE IF (TYPNAM .EQ. 'USEMIXVS') THEN grdtyp(1) = 2 else ERROR = BADTYP endif

There is a single response for each DRESP3 and analytic gradients are to be provided for

TYPNAM=’FREQMOD’,USEVAR10’ and ‘USEMIXVS’

The relevant part of the R3SVALD subroutine is:

Listing 8-5 dresp3sig

if ( forg .eq. 1 ) thenc gradient evaluation do 10 iresp = 1, nresp do 20 iarg = 1, narg senval(iresp,iarg) = 0.0d0 20 continue 10 continue Endif IF (TYPNAM .NE. 'FREQMOD') THEN x = argval(1) const = argval(2) r1 = argval(3) g = argval(4) p1 = argval(5) c1 = argval(6) m1 = argval(7) p2 = argval(8) c2 = argval(9) m2 = argval(10)

259CHAPTER 8

Optimization

r2 = argval(11) END IF IF (TYPNAM .EQ. 'USEVAR1') THEN dr3val(1) = x+r1+r2 ELSE IF (TYPNAM .EQ. 'USEVAR10') THEN if ( forg .eq. 0 ) then dr3val(1) = r2 else senval(1,9) = 1.0d0 endif ELSE IF (TYPNAM .EQ. 'USEALL') THEN dr3val(1) = x+const+r1+g+p1+c1+m1+p2+c2+m2+r2 ELSE IF (TYPNAM .EQ. 'USEMIXVS') THEN if ( forg .eq. 0 ) then dr3val(1) = x+g+p1+c1+m1+p2+r2 else senval(1,1) = 1.0d0 senval(1,3) = 1.0d0 senval(1,4) = 1.0d0 senval(1,5) = 1.0d0 senval(1,6) = 1.0d0 senval(1,9) = 1.0d0 endif ELSE IF (TYPNAM .EQ. 'FREQMOD') THEN x = argval(1) r1 = argval(2) if ( forg .eq. 0 ) then dr3val(1) = x*r1 else senval(1,1) = r1 senval(1,2) = x endif ELSE ERROR = BADTYP END IF

It is expedient to zero out all the gradient values, whether they are needed or not. For the TYPNAM’s

that don’t support analytic gradients, it is only necessary to provide the response value in DR3VAL(1).

For the TYPNAM’s that do support analytic gradients, an if test on FORG is provided. For FORG=0, a

function evaluation is made while a gradient evaluation is made for FORG=1. Note that for TYPNAM=

‘USEVAR10’, the input file shows 11 inputs, 1 for each of the available “Flags” while the actual response

shown in R3SVALD only uses the DRESP2 argument, the eleventh ARGVAL. Furthermore, the gradient

calculation has a single non-zero result: senval(1,9) = 1.0d0, indicating that the sensitivity of the first

response to the ninth argument that can vary is 1.0. The constant term in the ARGVAL list and the

undesigned DNODE do not count as one of the NARG sensitivity arguments, hence the discrepancy

between eleven and nine.

A final example is entitled dresp3sig and demonstrates the feature that reorders the sensitivity

calculations when NRESP1>>NDVI. In this case, there are 181 DRESP1’s and 10 DESVAR’s so the

criteria is satisfied. The job has two DRESP3’s that have the same arguments but one has

TYPNAM=RSS and the other has TYPNAM=RSSA. The RSS response has its gradients calculated

using finite difference techniques while the RSSA uses analytical gradients. Since these are the same

response, the test case serves to demonstrate that the same sensitivity information is generated using

analytic or finite difference gradient techniques. The problem is too small to make any assessment of

the performance gains that have resulted from the third enhancement mentioned in the Introduction, 250.


Topometry Optimization

260


Introduction

Topometry optimization is an element-by-element sizing optimization. Unlike conventional sizing

optimization where all elements referencing a property entry are grouped as one design variable, each

designable element has an independent design variable in topometry optimization. Since element-by-

element optimization has many design variables, it may find a better design than conventional sizing

optimization. In previous versions of Nastran, the user can use the design variable Bulk Data entry

DESVAR and the relation of model property and design variables Bulk Data entry DVxREL1 to support

element-by-element sizing optimization. However, with this approach the user must generate a unique

property data entry for each element and perhaps prepare thousands of DESVAR and DVPREL1 entries.

With the topometry optimization capability released in MD Nastran R3, the user can utilize a new Bulk

Data entry, TOMVAR, to select designable regions (model property or material property identification

number), design parameters (such as thickness of PSHELLs, or Young’s Modulus of materials), input

initial values, lower and upper bounds to perform element-by-element sizing optimization. The MD

Nastran program internally generates DESVAR and DVPREL1 (and/or DVMREL1) for each designed

element. The implementation provides a very simple user interface to do element-by-element sizing

design optimization. In addition, topometry optimization supports the fully stressed design algorithm in

MD Nastran. FSD is very efficient for certain problems with many stress constraints.

Topometry optimization released in MD Nastran R3 can be applied to all elements that can be resized

through Bulk Data entries DVPREL1 and DVMREL1. Those element types include not only volume-

based elements like CQUAD4 but also non-volume elements like CWELD, CBUSH, and CFAST.

Topology optimization is another element-by-element optimization technology. However, topology

optimization and topometry optimization are fundamentally different. Topology optimization is a “0” or

“1” discrete element-by-element optimization methodology. Topology optimization can be used to

decide which element should be retained and which element should be discarded from the design space.

One the other hand, topometry optimization aims to get a continuous variation of the designed properties.

Although topometry optimization is not recommended for topology optimization tasks, it is observed

topometry optimization can be used to get “similar topological results” for some cases. It is particularly

useful for non-structural elements like CELAS, CFAST, and CBUSH that MD Nastran topology

optimization does not support.

In a single optimization problem, it is allowable to resize (or shape, topology) certain properties while

topometry optimizing other properties.

Benefits• Topometry optimization is easy-to-use. One TOMVAR Bulk Data entry replaces many

thousands of DESVAR and DVxREL1 entries for large element-by-element design optimization

problems.

• Topometry optimization is good to identify critical design regions.

261CHAPTER 8

Optimization

• Topometry optimization is good to locate where to add/or remove material to improve structural

performance.

• Topometry optimization is good for finding the optimal location of spot welds. In particular,

topometry optimization is very useful for some properties that MD Nastran topology does not

support; for example, PDAMP, PELAS, PMASS, PBUSH, PVISC, PGAP, PACBAR, and

PFAST.

Input

The TOMVAR Bulk Data entry is used to select a topometry designable region and designed property

name. The initial, lower, and upper bound of the designed property value are also specified on the

topometry entry. The program automatically generates one design variable for each element

referencing a property PID. The relationship between design variables and the element property

given by

where is the analysis model property value for the ith element. NE is the total number of elements

referencing to the property PID. The user must input an initial value (such as the analysis model input

property value). The default of lower bound (XLB) on is , and default of upper bound on

(XUB) is .

The topometry Bulk Data entry is:

Format:

Example:

Design all element's thickness referencing PSHELL ID = 5 with initial design = 10.0 ( input

element thickness), lower bound and upper bound .

Example:

Design all element's Young Modulus referred by PSHELL ID = 100 with initial design XINIT = 3.E+5,

XLB=1.0, and XUB= 1.0E+6.

N 2 3 4 5 6 7 8 9 10

TOMVAR ID TYPE PID PNAME

/FID

XINIT XLB XUB DELXV

TOMVAR 10 PSHELL 5 T 10.0

DVi

DVi

Pi

Pi DViZ i 1 NE,Z

XLB DVi XUB≤ ≤

Pi

DVi

0.5 DVi

⋅

DVi

1.5 DVi

⋅

t0

10.0Z

0.5 t0

⋅ 1.5 t0

⋅



262

Remarks:

1. Multiple TOMVAR’s are allowed in a single file.

2. Property name and FID > 0 can be used for element property values just like a Bulk Data entry

DVPREL1. Only property name can be used for material property values like DVMREL1. If a

property name is shared by both property and material (such as “A” for PROD and MAT1), this

name is taken as a material name. The user must provide a FID for property name (FID=4 for

PROD). PCOMP, PCOMPG, PBEAML, PBARL, PBMSECT, PBRSECT are not supported. If

material property name is selected, PSHELL (with multiple MID inputs) must reference a unique

material ID.

3. Combined topometry, topography, topology, sizing, and shape optimization is supported in a

single file. However, topometry and topology cannot reference the same property ID. It is possible

to topometry certain elements while sizing others. It is allowed to simultaneously design the same

elements with topometry and desvar (sizing and/or shape) variables but topometry and sizing

cannot reference the same property name.

4. The design response DRESP1=FRMASS (fractional mass) can be used for topometry

optimization. The initial FRMASS is defined as1.0 at the initial design specified on a TOPVAR

entry. For non-volume elements like CELAS, a artificial mass = 1.0 is assumed for each element.

TOMVAR 10 PSHELL 100 E 3.E+5 1.0 1.E+6

Field Contents

ID Unique topometry design region identification number. (Integer > 0)

TYPE Property entry type. Used with PID to identify the elements to be designed.

(Character: “PBAR”, “PSHELL”, “PSOLID”, etc. see Remark 2.)

PID Property entry identifier (Integer > 0). This PID must be unique for PIDs referenced

by other TOPVAR, DVPREL1, DVPREL2, DVMREL1, and DVMREL2 entries.

(Integer > 0). See Remark 2.

PNAME/FID Property name or property material name, such as “T”, “A”, “E”, and “GE”, or field

position of the property entry or word position in the element property table of the

analysis model. Property names that begin with an integer such as 12I/T**3 may

only be referenced by field position. (Character or Integer > 0. see Remark 2.)

XINIT Initial value. (Real or blank, no default). Typically, XINIT is defined to match the

mass target constraint (so the initial design does not have violated constraints) or the

analysis model input property value.

XLB Lower bound. (Real or blank; Default = blank). The default is XLB=0.5*XINIT.

XUB Upper bound. (Real or blank; Default = blank). The default is XLB=1.5*XINIT.

DELXV Fractional change allowed for the design variable during approximate optimization.

(Real > 0.0; Default = 0.5. See Remark 3.).

263CHAPTER 8

Optimization

Output

A regular SOL 200 summary table is produced. In addition, a Patran element result file jobname.des

contains the optimal design values for each element. This Patran element result file can be imported to

Patran a third party post-processor to display topometry optimization results. Two parameters DESCPH

and DESPCH1 are used to specify in SOL 200 when the optimized topometry results are written to the

jobname.des.

Guidelines and Limitations• BIGDOT is the default optimizer of topometry optimization since topometry optimization

usually involves many thousands of design variables. BIGDOT requires a Topology

Optimization license. For SOL 200 design optimization clients without access to topology

optimization, optimizer MSCADS, method=4 (SUMT) is recommended through the

optimization control Bulk Data entry DOPTPRM.

• Since SOL 200 adjoint design sensitivity analysis method does not support element responses

(such as stress), a direct design sensitivity analysis method is automatically selected for

problems with element response constraints. In this case, topometry optimization with element

response constraints are slow due to many design variables. Fully stressed design (FSD) can be

used for certain problems.

• Topology optimization can be used for analysis model properties PDAMP, PELAS, PMASS,

PBUSH, PVISC, PGAP, NSM, NSM1, PACBAR and PFAST. Topology optimization is limited

to analysis properties that can reference material property MAT1.

• P2 > 13 on DOPTPRM prints design variables in *.f06.

Example 1 - Three-bar Truss (tomex1.dat)

A simple sizing optimization example three-bar truss (a TPL file DSOUG1.dat) is used here to

demonstrate topometry optimization solved by the fully stressed design algorithm. Figure 8-1 shows the

three-bar truss that must be built to withstand two separate loading conditions. The objective is to

minimize structural weight and subjected to displacement and stress constraints. The sizing design

variables are the cross-sectional areas. The detailed descriptions of analysis model and design

DESPCH DESPCH specifies when the topometry optimized design values are written to the

element result history file jobname.des. The Default = 0 writes the last design cycle

only. DESPCH < 0 never. DEPSCH1 > 0 at every design cycle that is a multiple of

DESPCH and the last design cycle.

DESPCH1 DESPCH1 > 0, write all topometry designed and non-designed element values to the

element result history file jobname.des. 1.0 is assigned to the non-designed element

value. DESPCH1 < 0, write all topometry designed element values to the element

result history file jobname.des.



264

optimization model can be seen in Chapter 7 of the MD Nastran Design Sensitivity and Optimization

User's Guide.

Figure 8-1 Three Bar Truss

The goal of this example is to show an alternate method of setting design variables by a TOMVAR entry.

The objective and constraints are not changed. In conventional sizing optimization, the set of DESVAR

and DVPREL1 entries define the relations Ai=1.0Xi (i=1, 2, 3) where A is the rod element cross-

sectional area and X is the design variable. In DSOUG1.dat, we have:

$...DESIGN VARIABLE DEFINITION$DESVAR ID LABEL XINIT XLB XUB DELXV(OPTIONAL)DESVAR 1 A1 1.0 0.1 100.0DESVAR 2 A2 2.0 0.1 100.0DESVAR 3 A3 1.0 0.1 100.0$$...DEFINITION OF DESIGN VARIABLE TO ANALYSIS MODEL PARAMETER $RELATIONS$DVPREL1 ID TYPE PID NAME PMIN PMAX C0 +$+ DVID1 COEF1 DVID2 COEF2 ...DVPREL1 10 PROD 11 A 1 1.0

DVPREL1 20 PROD 12 A 2 1.0DVPREL1 30 PROD 13 A 3 1.0

In DSOUG1.dat, rod elements 11 and 12 have different property groups. Then, the DLINK entry is used

to explicitly link the design variables 1 and 3 together. In this example, we try to do element-by-element

optimization. Thus, we take three design variables (rod element cross-sectional areas) as independent

variables. The rod elements 1 and 3 have the same property group (PROD=1). TOMVAR entry 1

265CHAPTER 8

Optimization

(Listing 8-6) is used to define two independent design variables with an initial value = 1.0 (and element

cross-sectional area = 1.0) for rod element 11 and 13 respectively. This is equivalent to four entries in

DSOUG1.dat:

DESVAR 1 A1 1.0 0.1 100.0DESVAR 3 A3 2.0 0.1 100.0DVPREL1 10 PROD 11 A 1 1.0DVPREL1 30 PROD 13 A 3 1.0

TOMVAR entry 2 (Listing 8-6) is used to define one independent design variable with an initial value =

2.0 (and element cross-sectional area = 2.0) for rod element 12. This is equivalent to two entries in

DSOUG1.dat:

DESVAR 2 A2 2.0 0.1 100.0DVPREL1 20 PROD 12 A 2 1.0

Input

The input data for this example is given in Listing 8-6.

Listing 8-6 Input File for Example 1

ID MSC TOMEX1 $ TIME 10 $SOL 200 $ OPTIMIZATIONCENDTITLE = THREE BAR TRUSS TOPOMETRY OPTIMIZATION SUBTITLE = 3 CROSS SECTIONAL AREAS AS DESIGN VARIABLESECHO = SORTSPC = 100DISP = ALLSTRESS = ALLDESOBJ(MIN) = 20 $ (DESIGN OBJECTIVE = DRESP ID)DESSUB = 21 $ DEFINE CONSTRAINT SET FOR BOTH SUBCASESANALYSIS = STATICSSUBCASE 1 LABEL = LOAD CONDITION 1 LOAD = 300SUBCASE 2 LABEL = LOAD CONDITION 2 LOAD = 310BEGIN BULK$$------------------------------------------------------------------------$ ANALYSIS MODEL$------------------------------------------------------------------------$$ GRID DATA$ 2 3 4 5 6 7 8 9 10GRID 1 -10.0 0.0 0.0GRID 2 0.0 0.0 0.0GRID 3 10.0 0.0 0.0GRID 4 0.0 -10.0 0.0$ SUPPORT DATA



266

SPC1 100 123456 1THRU3$ ELEMENT DATACROD 1 11 1 4CROD 2 12 2 4CROD 3 11 3 4$ PROPERTY DATAPROD 11 1 1.0PROD 12 1 2.0MAT1 1 1.0E+7 0.33 0.1$ EXTERNAL LOADS DATAFORCE 300 4 20000. 0.8 -0.6FORCE 310 4 20000. -0.8 -0.6$$------------------------------------------------------------------------$ DESIGN MODEL$------------------------------------------------------------------------$$...DESIGN TOPOMETRY DESIGN DEFINITION$TOMVAR, ID, PRYPE, PID, PNAME, XINIT, XLB, XUB, DELXV(OPTIONAL)TOMVAR, 1 , PROD, 11, 4 , 1., .1 , 100.0TOMVAR, 2 , PROD, 12, 4 , 2., .1 , 100.0$$...STRUCTURAL RESPONSE IDENTIFICATION$DRESP1 ID LABEL RTYPE PTYPE REGION ATTA ATTB ATT1 +$+ ATT2 ...DRESP1 20 W WEIGHTDRESP1 21 U4 DISP 12 4DRESP1 23 S1 STRESS PROD 2 1112$...CONSTRAINTS$DCONSTR DCID RID LALLOW UALLOWDCONSTR 21 21 -0.20 0.20DCONSTR 21 23 -15000. 20000.$$...OPTIMIZATION CONTROL (FULLY STRESSED DESIGN):$DOPTPRM FSDMAX 20 DESMAX 0 P1 1 P2 15$$.......2.......3.......4.......5.......6.......7.......8.......9.......0ENDDATA

267CHAPTER 8

Optimization

Output

A regular SOL 200 output can be found as:

Example 2 – Car Model Topometry Design

A real complex example car body is used here to demonstrate topometry optimization for graphical post-

processing. This example also shows that SOL 200 is able to deal with very large optimization problems.

The objective is to minimize structural compliance and keep weight unchanged. SOL 200 produces an

element thickness distribution file *.des that can be used by Patran or other post-processors to view

topometry optimization results.

*************************************************************** S U M M A R Y O F D E S I G N C Y C L E H I S T O R Y ***************************************************************

(HARD CONVERGENCE ACHIEVED)

NUMBER OF FINITE ELEMENT ANALYSES COMPLETED 17 NUMBER OF FULLY STRESSED DESIGN CYCLES COMPLETED 16 NUMBER OF OPTIMIZATIONS W.R.T. APPROXIMATE MODELS 0

OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY-------------------------------------------------------------------------------------------------------------------------------- OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT-------------------------------------------------------------------------------------------------------------------------------

INITIAL 4.828427E+00 -3.234952E-01

1 FSD 3.862742E+00 N/A -1.543690E-01 2 FSD 3.225798E+00 N/A -7.883203E-03 .

16 FSD 2.741757E+00 N/A 1.664062E-04

DESIGN VARIABLE HISTORY ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- INTERNAL | EXTERNAL | | DV. ID. | ELEMENT ID | LABEL | INITIAL : 1 : 2 : 3 : 4 : 5 : ------------------------------------------------------------------------------------------------------------------------------------------------------------------ 1 | 1 | TOMVAR | 1.0000E+00 : 8.0000E-01 : 6.8794E-01 : 6.8306E-01 : 6.9978E-01 : 7.2284E-01 : 2 | 2 | TOMVAR | 2.0000E+00 : 1.6000E+00 : 1.2800E+00 : 1.0240E+00 : 8.1920E-01 : 6.5536E-01 : 3 | 3 | TOMVAR | 1.0000E+00 : 8.0000E-01 : 6.8794E-01 : 6.8306E-01 : 6.9978E-01 : 7.2284E-01 : -------------------------------------------------------------------------------------------------------------------------------



268

Figure 8-2 Optimal Thickness Distribution of Car Model - Note that this figure is meaningful

only when viewed in color.

269CHAPTER 8

Optimization

Topography (Bead or Stamp) Optimization

Introduction

Topography optimization (also called bead or stamp optimization) is used to generate a design proposal

for reinforcement bead patterns. In MD Nastran R3, topography optimization is treated as a special shape

optimization and built on SOL 200 shape optimization technology. In topography optimization, finite

element grids are moved in as normal vectors to the shell surface or the user's given direction. New

algorithms were developed to generate shape design variables and shape basis vectors automatically

based on the user's provided bead dimension (minimum bead width, maximum bead height, and draw

angle). Since many design variables are generated in the topography optimization, the adjoint design

sensitivity analysis method and large scale optimizer play key roles in solving topography optimization

problems.

Benefits• Topography optimization is particularly powerful for designing sheet metal parts.

• Topography optimization can be used for all SOL 200 analysis types such as statics, normal

modes, buckling, complex eigenvalue, dynamic frequency response, and aeroelastic analyses.

Input

The BEADVAR Bulk Data entry is used to define topography design regions.

N 2 3 4 5 6 7 8 9 10

BEADVAR ID PTYPE PID MW MH ANG BF SKIP

“DESVAR” NORM/XD YD ZD CID XLB XUB DELXV

“GRID” NGSET DGSET

Field Contents

ID Unique topography design region identification number. (Integer > 0)

PTYPE Property entry type. Used with PID to identify the element nodes to be

designed. (Character: “PSHELL”, “PSHEAR”, “PCOMP”, or

“PCOMPG”.)

PID Property entry identifier. See Remark 1. (Integer > 0)

MW Minimum bead width. This parameter controls the width of the beads. The

recommended value is between 1.5 and 2.5 times the average element

width. See Remark 2. (Real > 0.0)

MH Maximum bead height (Real > 0.0). This parameter sets the maximum

height of the beads when XUB=1.0 (as Default). See Remark 2.



270

ANG Draw angle in degrees (0.0 < Real < 90.0). This parameter controls the

angle of the sides of the beads. The recommended value is between 60 and

75 degrees.

BF Buffer zone ('yes' or 'no'; Default='yes'). This parameter creates a buffer

zone between elements in the topography design region and elements

outside the design region when BF='yes'. See Remark 3.

SKIP Boundary skip (“bc”, “load”, “both”, or “none”; Default = “both”). This

parameter indicates which element nodes are excluded from the design

region. “bc” indicates all nodes referenced by “SPC” and “SPC1” are

omitted from the design region. "load" indicates all nodes referenced by

“FORCE”, “FORCE1”, “FORCE2”, “MOMENT”, “MOMENT1”,

“MOMENT2”, and “SPCD” are omitted from the design region. “both”

indicates nodes with either “bc” or “load” are omitted from the design

region. “none” indicates all nodes associated with elements referencing

PID specified in field 4 are in the design region.

“DESVAR” Indicates that this line defines bead design variables that are automatically

generated.

NORM/XD, YD, ZD Bead vector (draw direction). Norm indicates the shape variables are

created in the normal directions to the elements. If XD, YD, and ZD are

provided, the shape variables are created in the direction specified by the

xyz vector defied by XD/YD/ZD that is given in the basic coordinate

system or CID. See Remark 4. (Character or Real, Default = blank = norm).

CID Coordinate system ID used for specifying draw direction (Blank or Integer

> 0; Default = blank = basic coordinate system)

XLB Lower bound. (Real < XUB or blank; Default = blank = 0.0). This ensures

the lower bound on grid movement equal to XLB*MH. See Remark 5.

XUB Upper bound. (Real > XLB or blank; Default = 1.0). This sets the upper

bound of the beads equal to XUB*MH. See Remark 5.

DELXV Fractional change allowed for the design variable during approximate

optimization. See Remark 3. (Real > 0.0; Default = 0.2)

“GRID” Indicates this line defines what element nodes can be added and/or removed

from topography design regions.

NGSET All grids listed on Bulk Data entry SET1 = NGSET are removed from

topography design regions.

DGSET All grids listed on Bulk Data entry SET1 = DGSET are added to topography

design regions.

Field Contents

271CHAPTER 8

Optimization

Remarks:

1. Multiple BEADVAR’s are allowed in a single file. Combined topometry, topology, topography,

sizing, and shape optimization is supported in a single file.

2. The user can provide allowable bead dimensions.

Bead Dimensions

3. It is recommended to set buffer zone = yes to maintain a good quality of mesh during topography

optimization.

4. The grids moves in the normal direction. All element grids referenced by one BEADVAR entry

must follow the right hand rule.

MW

MH

ANG

Design elements

Buffer zone

Nondesign elements

No buffer zone

Nondesign elements

Element Normal

Element normal vectors

Baseline surfaceOptimizedsurface



272

5. To force the grids to move only in the positive bead vector direction (one side of the surface), use

XLB = 0.0. To force the grids to move only in the negative bead vector direction (another side of

the surface), use XUB = 0.0. To allow girds to move in both positive and negative bead vector

directions, use XLB < 0.0 and XUB > 0.0. For example,

6. The jobname.op2 has topography results (shape change) that can be viewed in Patran. The text

file jobname.pch also has updated grid coordinates that can be copied to replace the grids in the

original file, and imported to Patran on other post-processors to view topography optimization

results.

Outputs

A regular SOL 200 design history summary table is produced. The jobname.op2 (with PARAM,POST,-

1) and jobname.pch can be imported to Patran and other post-processors to view topography optimization

results.

User defined draw vector

Baseline surfaceOptimizedsurface

User’s Provided Draw Direction

Bead Vector

Bead Vector

Optimized SurfaceBase Surface

(a) XLB = 0.0 and XUB = 1.0 (b) XLB = -1.0 and XUB = 0.0 (c) XLB = -1.0 and XUB = 1.0

Optimized Surface

273CHAPTER 8

Optimization

Guidelines and Limitations• BIGDOT is the default optimizer of topography optimization since topography optimization

usually involves many design variables. BIGDOT requires a Topology Optimization license. For

SOL 200 design optimization clients without access to topology optimization, the optimizer

MSCADS method=4 (SUMT) is recommended through the optimization Bulk Data entry

DOPTPRM.

• Since SOL 200 adjoint design sensitivity analysis method does not support element responses

(such as stress), a direct design sensitivity analysis method is automatically selected for

problems with element response constraints. In this case, topography optimization with element

response constraints are slow.

• Since adjoint design sensitivity analysis does not support rigid body elements (RBE1, RBE2,

RBE3, RROD, RBAR, RTRPLT, RSPLINE), all grids connected to rigid body elements must be

fixed in topography optimization for static and dynamic frequency response analyses.

• The minimum bead width and maximum bead height have significant effects on optimal

designs. A smaller minimum bead width results in more small beads.

• Mesh distortion is a challenge for topography optimization. It is recommended that a relatively

coarse mesh be used for highly curved areas.

• P2 > 13 on DOPTPRM prints design variables in *.f06

Example 3 – A Square (togex1.dat)

A square model shown in Figure 8-3 is used to demonstrate MD Nastran R3 topography optimization

capabilities. The square is modeled with quadrilateral plate elements (CQUAD4) and is fixed at all four

edges. The objective is to maximize the first frequency of the structure with a given bead dimension

(minimum bead width = 10.0, maximum bead height = 20.0, draw angle = 70.0).

Figure 8-3 A Square



274

Input

The input data for this example is given in Listing 8-7. The Bulk Data entry 1 defines the topography

designable region. It is noticed that element normals are used for bead vectors (draw direction) and all

grids associated with the boundary condition are fixed during optimization. PARAM, POST, -1 outputs

results for Patran.

Listing 8-7 Input File for Example 2

$Topography opt example one SOL 200CENDTITLE = MD Nastran job created on 28-Nov-07 ECHO = NONE$ Direct Text Input for Global Case Control DataDESOBJ(MAX) = 1SUBCASE 1$ Subcase name : Default SUBTITLE=Default SPC = 2 METHOD = 1 DISPLACEMENT(SORT1,REAL,PLOT)=ALL ANALYSIS=MODESBEGIN BULKEIGRL,1,,,20$ Direct Text Input for Bulk Data$ Elements and Element Properties for region : ps1$$ BEADVAR, ID, TYPE, PID, MW, MH, ANG, BF, SKIP.$BEADVAR, 1 , PSHELL, 1, 10., 20.0, 70.0, YES, BOTHDRESP1, 1, MODES, FREQ,,,1PARAM POST -1

Output

Figure 8-4 shows the topography optimized result by using Patran. The first frequency has increased from

0.568HZ at the initial design to 4.78 HZ.

Figure 8-4 Topography Optimal Design of A Square

275CHAPTER 8

Optimization

Permanent Glued Contact Modeling in SOL 200

Permanent glued contact released in MD Nastran R2 and R3 is defined as a special type of contact model

which imposes the condition that there is no relative normal or tangental motion between the contacting

surfaces. In MD Nastran R3, the permanent glued contact capability is supported in all SOL 200

solutions including sizing, shape, topology, topometry, and topography optimization.

SOL 200 supports all permanent glued contacts including edge-toedge, edge-to-surface, and surface-

to-surface.

Benefits

The primary benefit of the permanent glued contact in an optimization design task is the joining of two

dissimilar meshes, with the potential to save significant modelling time.

Input

No new input. The input associated with permanent glued contact are mentioned in both the MD Nastran

R2 Release Guide and MD Nastran R3 Release Guide.

Output

None.

Guidelines and Limitations1. BCPROP (contact region by element properties) cannot reference topology and/or topometry

designed element properties.Topology and/or topometry designed element IDs can be referenced

by BSURF entries.

2. If the glue border elements are allowed in the topography optimization (BEADVAR), then the

model may fail GROUNDCHECK (see Adaptive Meshing (Ch. 2)). With the removal of those

glue border elements from topography designable regions, then the model will pass

GROUNDCHECK.

Example 4 - A Solid Beam (topoug5.dat)

The problem has two solids glued together along a transverse plane to form a cantilever. The composite

cantilever is used to demonstrate topology optimization with glued contact. The objective is to minimize

the compliance subject to mass constraint of 0.3 (70% weight reduction). The loading and boundary

conditions are shown in Figure 8-5. The structure is modeled with 1683 CHEXA elements of PSOLID=1

property and 975 CHEXA elements with PSOLID=2 property.


Permanent Glued Contact Modeling in SOL 200

276

Figure 8-5 Composite Cantilever with two solids permanently glued

Input

The input data for this example related to topology optimization model is given in Listing 8-8. Two

TOPVAR entries are used to define two topological design regions identified by PSOLID=1 and

PSOLID=2. XINIT=0.3 on the TOPVAR entries match the mass target constraint so that the initial design

is feasible. The rest of the values on the TOPVAR entry are default values for general topology

optimization applications. Type one design responses DRESP1, 2 and 10 identify fractional mass and

compliance respectively. DCONSTR = 1 specifies the mass target. DESOBJ = 10 in Case Control

command selects the DRESP1=10 entry to be used as a design objective (minimization as default) and

DESGLB selects the design constraint DCONSTR= 1 to be applied in this topology optimization task.

Case Control command BCONTACT =888 selects the Bulk Data entry BCTABLE. Value 1 in field 5 of

first line in BCTABLE entry indicates that 1 set of slave/master entries is entered. “Slave” indicates

touching body and “master” indicates touched body. Presence of BCONTACT above the Subcase and

value of 1 in field 8 (IGLUE) of “Slave” line in BCTABLE entry indicates that there is Permanent Glued

Contact between the two bodies. The first entries 1001 and 2001 in “Slave” and “Master” lines

respectively in BCTABLE entry are referenced by the two BCBODY entries with the corresponding IDs.

Field 5 in BCBODY entries contains the IDs of BSURF entries which define the deformable surfaces

identified by element IDs. In this problem deformations are small and linear.

Listing 8-8 Input File for Glued Contact Topology Optimization

DESOBJ = 10DESGLB = 1

277CHAPTER 8

Optimization

BCONTACT = 888smethod=elementANALYSIS = STATICS$ Direct Text Input for Global Case Control DataSUBCASE 1$ Subcase name : Default SUBTITLE=Default SPC = 2 LOAD = 2 DRSPAN = 1BEGIN BULK$-------2-------3-------4-------5-------6-------7-------8-------9------BCTABLE 888 1 ++ SLAVE 1001 0.1 1 ++ MASTER 2001 $$-------2-------3-------4-------5-------6-------7-------8-------9------BCBODY 1001 3D DEFORM 3 0BCBODY 2001 3D DEFORM 4 0$$DCONSTR 1 2 .3TOPVAR 1 PSOLID PSOLID .3 1TOPVAR 2 PSOLID PSOLID .3 2DRESP1 2 FRM FRMASSDRESP1 10 COMP COMP$ Direct Text Input for Bulk Data$ Elements and Element Properties for region : p1PSOLID 1 1 0BSURF 3 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129$.........................BSURF 4 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812$.........................

Output

Figure 8-6 shows the topology optimized result by using Patran without smoothing.

Figure 8-6 Glued Contact Topology Design


Randomization of an Input Data File

278

Randomization of an Input Data File

Introduction

The stochastic capability in MD Nastran is the first step toward a complete and automatic self-

randomization of a finite element model. The current capability offers the possibility to automatically

distribute tolerances and uncertainties with minimum effort. This dramatically reduces the complexity of

large-scale stochastic simulations. In fact, once the stochastic option is triggered, the entire Bulk Data

file is automatically randomized without further user intervention. The resulting model, which needs to

be incorporated in a Monte Carlo Simulation loop (there are numerous off-the-shelf products which

support this capability) possesses unprecedented levels of realism.

In order to make full use of this new capability, it is necessary to use a multi-run environment which can

spawn a certain number of independent MD Nastran executions, collect the results, and perform

statistical postprocessing. With the self-randomization capability in MD Nastran, the user need only

define the outputs to be monitored, such as stresses, Eigenfrequencies, temperatures, displacements, etc.

There is no need to define inputs, as these are defined automatically by MD Nastran. The Randomization

of an Input Data File functionality was a pre-release capability in MD Nastran R2.1. For MD Nastran R3

this is now a production capability.

Benefits

It is sometimes assumed that the inputs to an MD Nastran analysis are known exactly, and thus the

computed responses are exact. This is an invalid assumption since there will always be some uncertainty

in the input values with a corresponding variation in the results. MD Nastran R2 provides a way of

introducing this uncertainty into the analysis process by automatically randomizing user input real

numbers based on the input values and statistical quantities that characterize the variation.

Input

The randomization capability is driven by a new STOCHASTICS Case Control command, as described

in the MD Nastran Quick Reference Guide. If STOCHASTICS=ALL is used, all real quantities on

connectivity (those starting with C), material, and property Bulk Data entries, as well as any loads and

SPCD quantities, are modified based on a covariance factor of 0.05. A Gaussian distribution is used to

randomly select the perturbed quantity with the restriction than the value can be no more that a specified

number of standard deviations from the user input mean value. The default number of maximum standard

deviations is three.

Alternatively, the STOCHASTICS Case Control command can point to a STOCHAS Bulk Data entry

that provides the ability to selectively randomize different types of input quantities by means of user-

specified covariance values and user-prescribed numbers of allowed standard deviations. In this case,

only the types of input specified are randomized so that, for example, it is possible to randomize the load

inputs while leaving the property values unchanged.

279CHAPTER 8

Optimization

Output

There is no new output produced by this capability.


The randomization algorithm involves using a random number generator, a Gaussian distribution, a

prescribed covariance, and a mean value based on user input to determine a randomized value that is to

be used in the analysis. In order to avoid physically meaningless properties, the random value is

prescribed to be within m standard deviations of the input value, where m is a user input value with a

default value of 3.0.

The product of m * COV should not be greater than 1.0 to eliminate the possibility of the property

changing sign.

Any real value in the Bulk Data file will be randomized unless otherwise specified by the user. To keep

a particular field or fields from being randomized, the user must set them equal to a value of 0.0.


Random Elimination of Element Types

280

Random Elimination of Element Types

Introduction

There has been a long-standing capability in MD Nastran that allows the user to specify the random

elimination of a specified percentage of the CWELD elements contained in a bulk data file. This was

done using the PARAM CWRANDEL entry, with an additional CWDIAGP PARAM providing the

option of printing the IDs of the deleted elements. In the current release, this capability has been extended

to the CELASi, CFAST, CSEAM, and 1-D mass (CMASSi, CONM1, and CONM2) elements. In

addition, the user interface has been changed from the NASTRAN statement to the MDLPRM entry. The

Random Elimination of Element Types functionality was a pre-release capability in the MD Nastran R2.1

release. For MD Nastran R3 this is now a production capability.

Benefits

The ability to randomly delete various 1-D elements provides the user with some assessment of the

integrity of the design being modeled. For instance, if randomly deleting 20% of, say, of the CWELD

elements from a model caused a negligible change in the first ten natural frequencies, this was taken as

an indication of the robustness of the structure. Extending this approach to other element types provides

more options in this type of analysis. Placing the input on the MDLPRM entry consolidates that input so

that the user does not have to deal with the PARAM entry.

Input

The MDLPRM entry has ten new PARAMi names that support this capability. Five of these names (e.g,

DELELAS) select the element type to which the random elimination applies and the ratio to be deleted,

while an additional five names (e.g., PRTELAS) provide control as to whether the IDs of the deleted

elements are to be printed. The default is that the IDs will not be printed.

Output

There is no new output produced by this capability.


The deletion ratio is input as a real number between 0.0 and 1.0, with 0.0 indicating that no deletion is to

take place, while 1.0 eliminates all elements of the specified type.

It is possible that the elimination of a series of elements will introduce mechanisms in the structure that

will cause the analysis to fail. It is the user’s responsibility to determine whether this failure has occurred.

A likely scenario for the use of this capability would be to submit the same file multiple times and

determine the variation in the results. MSC does not offer an automated way of doing this at this time.

281CHAPTER 8

Optimization

Enhancements in SOL 200 Optimization

Introduction

Capabilities of SOL 200 have been expanded to support:

• Using properties on PCOMPG as design variables

• Using responses from exterior acoustic as design constraints

• Using responses from fluid model

• A modified objective function

Benefits

PCOMPG

The implementation provides a simple user interface to design and to track a particular ply over many

PCOMPGs which has the potential to significantly increase the productivity of engineers and designers.

Exterior Acoustics

By being able to use responses from exterior acoustic analysis in SOL 200, the automotive engineer has

the design tool to produce the optimized products which satisfy pass-by noise regulation.

Fluid Modes

Fluid modes can be utilized as design constraints in the optimization.

Objective Function Modification

Frequently, auto and aircraft manufacturers use SOL 200 to design just a tiny portion of the structure.

The mass of design portion can be 3 to 4 orders of magnitude smaller than the full structural mass.

Modifying the objective function provides a quick way avoid premature convergence.

Input

PCOMPG as Design Variables

The following KEYWORDs are added to the TYPE field of DVPREL1 Bulk Data entry.

1 2 3 4 5 6 7 8 9 10

DVPREL1 ID TYPE PID PNAME/FID

PMIN PMAX C0

DVPREL1 100 PCOMPG or GPLY

PID or GPLYID



282

For type=PCOMPG, PID field should have the ID of the PCOMPG entry and the PNAME/FID field can

have input of property name of fields or field number.

For type=GPLY, PID field should have the GPLYID on the continuation lines of PCOMPG and the

PNAME/FID field can only have T or THETA as input.

It should be noted that:

1. When DVPREL1 has TYPE=GPLY, all PCOMPG entries with GPLYID will participate in the

design. The relationship between design variable and properties are defined by the following

equation

or is the original thickness or THETA angle on PCOMPG which is determined

automatically from the PCOMPG entry and is utilized as multiplier to the design variables. This

formulation allows a ply with same GPLYID on different PCOMPG’s to change in tandem

percentage-wise.

2. For with original value equal to 0.0, is taken as 1.0 and it is recommended

to have XINIT of DVID set to 0.0.

Example

$ $ $ $ $ $ $ $ $DESVAR 1 T100000 1.00 0.01 100.0$DVPREL1 1 GPLY 100000 T 1 1.0

Exterior Acoustic Responses as Design Constraints

1 2 3 4 5 6 7 8 9 10

DRESP1 ID LABEL RTYPE PTYPE REGION ATTA ATTB ATT1

ATT2 -etc.-

Pi C0Z T0i or THETA0i( )H DVIDj COEFj⋅( )∑⋅

T0 THETA0

THETA0 THETA0

283CHAPTER 8

Optimization

Example$ $ $ $ $ $ $ $ $$ DRESP1 with new RTYPE$ ACPWR - ACoustic PoWeRdresp1 5200 APOW ACPWRdresp1 5201 APOW2 ACPWR 30.dresp1 5202 APOW3 ACPWR LFDOOR $$ ACINTS - ACoustic INTenSitydresp1 5300 AINT acints 5dresp1 5301 Aint2 acints 30. 5$$ AFPRES - Acoustic PRESsure for AFPMdresp1 5400 afprs AFPRES 100 1 194dresp1 5401 afprs2 AFPRES 100 1 30. 189$$ AFINTS - Acoustic INTenSity for AFPMdresp1 5501 afint2 AFINTS 100 1 30. 189$$ AFVELO - Acoustic VELOcity for AFPM

New Keyword Entry for

RTYPE FieldPTYPE

Response Attributes

ATTA ATTB ATTi

ACPWR – acoustic power radiated through a panel

Panel name (Blank for total)

Blank Frequency value (Blank for all forcing frequency, Real > 0.0)

Blank

ACINTS – acoustic intensity

Blank Blank Frequency value (Blank for all forcing frequency, Real > 0.0)

Grid ID of wetted surface

AFPRES – Acoustic pressure for AFPM

AFPMID – Acoustic Field Point Mesh ID (Integer > 0)

Acoustic Pressure Component (Integer = 1 or 7)

Frequency value (Blank for all forcing frequency, Real > 0.0)

Grid ID of AFPMID

AFINTS – Acoustic Intensity for AFPM

AFPMID – Acoustic Field Point Mesh ID (Integer>0)

Component Code -0-normal to AFPM, 1-x-dir2-y-dir3-z-dir


Grid ID of AFPMID

AFVLELO – Velocity for AFPM

AFPMID – Acoustic Field Point Mesh ID (Integer>0)

Component Code -11-Real/Mag in x-dir12-Real/Mag in y-dir13-Real/Mag in z-dir71-Img/Ph in x-dir72-Img/Ph in y-dir73-Img/Ph in z-dir


Grid ID of AFPMID

AFPWR – Acoustic Power for AFPM

AFPMID – Acoustic Field Point Mesh ID (Integer > 0)

Blank Frequency value (Blank for all forcing frequency, Real > 0.0)

Blank



284

dresp1 5600 afvel AFVELO 100 11 194dresp1 5601 afvel2 AFVELO 100 11 30. 189$$ AFPWR - Acoustic PRESsure for AFPMdresp1 5700 afpwr AFPWR 100dresp1 5701 afpwr2 AFPWR 100 30.

Fluid Modes as Design Constraints

With RTYPE=EIGN or FREQ, the default for PTYPE field is ‘STRUC’.


New parameter OBJMOD for DOPTPRM is implemented as a flag for objective function modification.

With DOPTPRM,OBJMOD,1, the original objective function value will be reset to 0.0. From the second

cycle onward, the objective function value represents the change of objective function with respect to the

original design.

The default value for OBJMOD is 0, meaning the total objective function value will be used.

Output

Output for the previous new features of SOL 200 is presented in the following paragraph. New features

are highlighted in BOLD characters.


A single set of DESVAR/DVPREL1 with GPLY will cover multiple PCOMPG entries which has a ply

with GPLYID. The output of comparison of analysis and design model, will then look like:

1 2 3 4 5 6 7 8 9 10

DRESP1 ID LABEL RTYPE PTYPE REGION ATTA ATTB ATT1

ATT2 -etc.-

RTYPENew Option for

PTYPE Field

Response Attributes

ATTA ATTB ATTi

EIGN or FREQ STRUC or FLUID Normal Modes Number Approximation code

----- COMPARISON BETWEEN INPUT PROPERTY VALUES FROM ANALYSIS AND DESIGN MODELS -----

----------------------------------------------------------------------------------------------------------------------------PROPERTY PROPERTY PROPERTY ANALYSIS DESIGN LOWER UPPER DIFFERENCE SPAWNING TYPE ID NAME VALUE VALUE BOUND BOUND FLAG FLAG ----------------------------------------------------------------------------------------------------------------------------GPLY 12 T 5.400000E-03 5.400000E-03 N/A N/A NONE GPLY 22 T 5.400000E-03 5.400000E-03 N/A N/A NONE GPLY 33 T 5.400000E-03 5.400000E-03 N/A N/A NONE

285CHAPTER 8

Optimization

In the previous output, the number printed under the ‘PROPERTY ID’ column is the ID of PCOMPG.

Exterior Acoustic Responses as Design Constraints

A sample of sensitivity for exterior acoustic responses is shown as follows. The output is produced via

the DSAPRT Case Control command.

Fluid Modes as Design Constraints

A sample of sensitivity for fluid mode responses is shown as follows. The output is produced via the

DSAPRT Case Control command.

**************************************************************************** * * * D E S I G N S E N S I T I V I T Y M A T R I X O U T P U T * * * * * * R E S P O N S E S E N S I T I V I T Y C O E F F I C I E N T S * * * ****************************************************************************------------------------------------------------------------------------------------------------------------------------------- DRESP1 ID= 5200 RESPONSE TYPE= ACPWR PANEL NAME= -TOTAL- SEID= 0 SUBCASE RESP VALUE FREQ/TIME DESIGN VARIABLE COEFFICIENT------------------------------------------------------------------------------------------------------------------------------- 1 6.2096E-05 3.0000E+01 1 T1 -1.5862E-05 1 6.2140E-05 3.2000E+01 1 T1 -1.6007E-05------------------------------------------------------------------------------------------------------------------------------- DRESP1 ID= 5300 RESPONSE TYPE= ACINTS GRID ID= 5 COMP NO= 0 SEID= 0 SUBCASE RESP VALUE FREQ/TIME DESIGN VARIABLE COEFFICIENT------------------------------------------------------------------------------------------------------------------------------- 1 6.1866E-05 3.0000E+01 1 T1 -1.6807E-05 1 6.1936E-05 3.2000E+01 1 T1 -1.6807E-05------------------------------------------------------------------------------------------------------------------------------- DRESP1 ID= 5501 RESPONSE TYPE= AFINTS GRID ID= 189 COMP NO= 1 SEID= 0 AFPM ID= 100 SUBCASE RESP VALUE FREQ/TIME DESIGN VARIABLE COEFFICIENT------------------------------------------------------------------------------------------------------------------------------- 1 -2.1149E-07 3.0000E+01 1 T1 8.6521E-03------------------------------------------------------------------------------------------------------------------------------- DRESP1 ID= 5600 RESPONSE TYPE= AFVELO GRID ID= 194 COMP NO= 11 SEID= 0 AFPM ID= 100 SUBCASE RESP VALUE FREQ/TIME DESIGN VARIABLE COEFFICIENT------------------------------------------------------------------------------------------------------------------------------- 1 -7.0853E-05 3.0000E+01 1 T1 2.4374E-05 1 -5.8033E-05 3.2000E+01 1 T1 2.0518E-05------------------------------------------------------------------------------------------------------------------------------- DRESP1 ID= 5700 RESPONSE TYPE= AFPWR GRID ID= 0 COMP NO= 0 SEID= 0 AFPM ID= 100 SUBCASE RESP VALUE FREQ/TIME DESIGN VARIABLE COEFFICIENT------------------------------------------------------------------------------------------------------------------------------- 1 -1.0058E-03 3.0000E+01 1 T1 6.8219E-04 1 -9.9851E-04 3.2000E+01 1 T1 6.9616E-04

**************************************************************************** * * * D E S I G N S E N S I T I V I T Y M A T R I X O U T P U T * * * * * * R E S P O N S E S E N S I T I V I T Y C O E F F I C I E N T S * * * **************************************************************************** ------------------------------------------------------------------------------------------------------------------------------- DRESP1 ID= 101 RESPONSE TYPE= FREQ MODE ID= 1 FLUID SEID= 0 SUBCASE RESP VALUE DESIGN VARIABLE COEFFICIENT------------------------------------------------------------------------------------------------------------------------------- 1 8.6023E+01 1 T 1.4641E-01 ------------------------------------------------------------------------------------------------------------------------------- DRESP1 ID= 102 RESPONSE TYPE= FREQ MODE ID= 2 FLUID SEID= 0 SUBCASE RESP VALUE DESIGN VARIABLE COEFFICIENT------------------------------------------------------------------------------------------------------------------------------- 1 2.6020E+02 1 T 4.4286E-01



286


With DOPTPRM,OBJMOD,1, objective function modification algorithm is activated. A sample of

objective function history is shown as follows. The output is available for all optimization jobs.

Guidelines• For type=GPLY, the recommended values for fields of DESVAR and DVPREL1 are

• The design model for exterior acoustic must be part of main input file which is after the ‘BEGIN

BULK’ entry. Any design model entries placed after ‘BEGIN BULK AFPM=xxxx’ are ignored.

• The effectiveness of DOPTPRM,OBJMOD,1 is not consistent. Hence, it is recommended only

for optimization problems that design just a tiny portion of the full structure.

Limitations• DVPREL2 must not be used to link design variable and properties of PCOMPG.

• Properties associated with ‘MICRO’ feature of PCOMPG are not supported in SOL 200.

Example


A simple file, d200pcg1, with multiple PCOMPG entries is utilized here to demonstrate the features

implemented for PCOMPG support in SOL 200. Some key bulk data entries are shown as follows:

$

OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY --------------------------------------------------------------------------------------------------------------- OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT --------------------------------------------------------------------------------------------------------------- >>> OBJECTIVES in COLUMN 2/3 ARE INCREMENTAL TO OBJECTIVE OF ORIGINAL DESIGN = 1.0000E+05 <<< >>> ADD INCREMENTAL OBJECTIVE TO ORIGINAL TO ARRIVE AT REAL OBJECTIVE OF EACH CYCLE <<< ---------------------------------------------------------------------------------------------------------------

INITIAL 0.000000E+00 1.249923E+00

1 8.947921E-03 7.812500E-03 1.453339E-01 9.368142E-01

2 -1.010694E-02 -7.812500E-03 -2.936888E-01 1.003581E+00

3 -1.317651E-02 -1.562500E-02 1.567034E-01 3.951643E+00

4 -1.562500E-02 -1.562500E-02 0.000000E+00 3.951643E+00 ---------------------------------------------------------------------------------------------------------------

Bulk Data Entry Field Name Recommended Value

DESVAR X0 1.0

DVPREL1 C0 0.0

DVPREL1 COEF1 1.0

287CHAPTER 8

Optimization

DESVAR 1 T100000 1.00 0.01 100.0$DVPREL1 1 GPLY 100000 T 1 1.0DVPREL1 2 PCOMPG 12 T2 1 0.0054$pcompg,12,,,5000.,hill,0.0,,,,100000, 1, .0054, 45., yes,,400000, 1, .0054, 90., yes,,500000, 1, .0054, 90., yes,,600000, 1, .0054, 0.0, yes,700000, 1, .0054,-45., yes,800000, 1, .0054, 45., yespcompg,22,,,5000.,hill,0.0,,,,100000, 1, .0054, 45., yes,,300000, 1, .0054, 0.0, yes,,400000, 1, .0054, 90., yes,,500000, 1, .0054, 90., yes,600000, 1, .0054, 0.0, yes,800000, 1, .0054, 45., yespcompg,33,,,5000.,hill,0.0,,,,100000, 1, .0054, 45., yes,,200000, 1, .0054,-45., yes,,300000, 1, .0054, 0.0, yes,,400000, 1, .0054, 90., yes,500000, 1, .0054, 90., yes,800000, 1, .0054, 45., yes$

DVPREL1,1 links the thickness of ply 100000 in PCOMPG 12, 22 and 33 to DESVAR,1 and

DVPREL1,2 connects the thickness of PLY 400000 in PCOMPG,12 to DESVAR,1. Note that

DVPREL1,2 uses the existing equation for relation between design variables and properties while

DVPREL1,1 uses the new one shown in INPUT section. PCOMPG entries corresponding to the new

design are shown as follows,



288

Exterior Acoustic as Design Constraints – TPL test file: d200exac.dat

Portions of this example are shown in the preceding Sections Input, 281 and Output, 284.

Fluid Modes as Design Constraints – TPL test file: d200fmd1.dat

The output section shows results from this file.

$ *************************************************************$ * *$ * CONTINUOUS DESIGN CYCLE NUMBER = 4 *$ * *$ *************************************************************$$$ UPDATED DESIGN MODEL DATA ENTRIES$DESVAR * 1T100000 3.37500000E+00 9.99999978E-03+D 1V*D 1V 1.00000000E+02$$ UPDATED ANALYSIS MODEL DATA ENTRIES$PCOMPG* 12 0.00000000E+00 5.00000000E+03** HILL 0.00000000E+00 0.00000000E+00 ** 100000 1 1.82250012E-02 4.50000000E+01** YES ** 400000 1 1.82250012E-02 9.00000000E+01** YES ** 500000 1 5.40000014E-03 9.00000000E+01** YES ** 600000 1 5.40000014E-03 0.00000000E+00** YES ** 700000 1 5.40000014E-03 -4.50000000E+01** YES ** 800000 1 5.40000014E-03 4.50000000E+01** YESPCOMPG* 22 0.00000000E+00 5.00000000E+03** HILL 0.00000000E+00 0.00000000E+00 ** 100000 1 1.82250012E-02 4.50000000E+01** YES ** 300000 1 5.40000014E-03 0.00000000E+00** YES ** 400000 1 5.40000014E-03 9.00000000E+01** YES ** 500000 1 5.40000014E-03 9.00000000E+01** YES ** 600000 1 5.40000014E-03 0.00000000E+00** YES ** 800000 1 5.40000014E-03 4.50000000E+01** YESPCOMPG* 33 0.00000000E+00 5.00000000E+03* * HILL 0.00000000E+00 0.00000000E+00 ** 100000 1 1.82250012E-02 4.50000000E+01* * YES * * 200000 1 5.40000014E-03 -4.50000000E+01* * YES * * 300000 1 5.40000014E-03 0.00000000E+00** YES * * 400000 1 5.40000014E-03 9.00000000E+01* * YES * * 500000 1 5.40000014E-03 9.00000000E+01* * YES ** 800000 1 5.40000014E-03 4.50000000E+01* * YES

289CHAPTER 8

Optimization


Test file, d200zobj, is used. The design model covers just a tiny portion of the structure. The original

file produced following optimization history.

From column 3 of the previous output, the change in objective function is not visible at all. The same

output from d200zobj with DOPTPRM,OBJMOD,1 is shown as follows

Column 3 of the previous table shows the change of objective function. The original objective function

value can be found on the first line bracketed by ‘>>>’ and ‘<<<’. Note that the change of objective

function is 8 orders of magnitude smaller than the original objective function value.

OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY --------------------------------------------------------------------------------------------------------------- OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT ---------------------------------------------------------------------------------------------------------------

INITIAL 1.000000E+05 1.249923E+00

1 1.000000E+05 1.000000E+05 0.000000E+00 9.361193E-01

2 1.000000E+05 1.000000E+05 0.000000E+00 1.003858E+00

3 1.000000E+05 1.000000E+05 0.000000E+00 3.077129E+00

4 1.000000E+05 1.000000E+05 0.000000E+00 3.077129E+00 ---------------------------------------------------------------------------------------------------------------

OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY --------------------------------------------------------------------------------------------------------------- OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT --------------------------------------------------------------------------------------------------------------- >>> OBJECTIVES in COLUMN 2/3 ARE INCREMENTAL TO OBJECTIVE OF ORIGINAL DESIGN = 1.0000E+05 <<< >>> ADD INCREMENTAL OBJECTIVE TO ORIGINAL TO ARRIVE AT REAL OBJECTIVE OF EACH CYCLE <<< ---------------------------------------------------------------------------------------------------------------

INITIAL 0.000000E+00 1.249923E+00

1 8.947921E-03 7.812500E-03 1.453339E-01 9.368142E-01

2 -1.010694E-02 -7.812500E-03 -2.936888E-01 1.003581E+00

3 -1.317651E-02 -1.562500E-02 1.567034E-01 3.951643E+00

4 -1.562500E-02 -1.562500E-02 0.000000E+00 3.951643E+00 ---------------------------------------------------------------------------------------------------------------


Optimization of Nonlinear Structural Responses (Pre-release)

290


Introduction

MSC Software’s SOL 200 is a gradient-based multidisciplinary design optimization capability and has

been widely used by clients in applying optimization techniques to linear structural analyses (Ref. 1.). Its

success has led to the desire to extend these techniques to nonlinear structural analyses. Studies have

been done to apply both gradient and non-gradient based approaches to the nonlinear structural analysis

problems. The gradient approach involves design sensitivity analysis of nonlinear responses and

mathematical programming. It provides accurate solutions but requires sensitivity calculations that are

either too difficult in derivation, too expensive numerically or that become problematic due to the

potential discontinuities in the responses as a function of design variables. Non-gradient based

approaches often use Response Surface Methods to construct a surrogate model and the mathematical

programming techniques are applied to the surrogate model (Refs.2.-7.). This approach is very general

but is limited in the size of the design problems. An Equivalent Static Loads (ESL) based approach has

been developed that transforms the original problem into an iterative solution of linear sub-optimization

problems (Refs. 8.-10.). The most attractive attribute of this approach is that it shares the best features in

gradient and non-gradient based approaches and avoids the disadvantages of each approach. Therefore,

it is able to solve small- or large-scale problems more efficiently. Furthermore, the approach can be

implemented with the existing highly developed nonlinear analysis (e.g., SOL 400) and linear response

optimization software systems (e.g., SOL 200). However, its limitation is that it may not support general

design statement due to limited support of nonlinear response and element types and nonlinear analysis

disciplines because it requires that any supporting nonlinear response type must have the equivalent

response type in the linear system.

The new nonlinear response optimization capability in MD Nastran R3 (ESLNRO) is based on the ESL

concept and implemented within SOL 400. This is the first attempt to introduce nonlinear response

optimization capability into MD Nastran and the new capability will be a beta release. In this release,

only nonlinear displacement and stress responses are supported. It is expected that more experience in

ESLNRO applications will lead to future enhancements.

The following describes the current status of the ESLNRO for MD Nastran R3.

What is supported:

• Analysis = NLSTATIC, RTYPE = DISP and STRESS, WEIGHT, VOLUME

• DRESP2

• Geometry nonlinear (large displacement)

• Material nonlinear

What is not supported:

• Boundary nonlinear (contact)

• Marc elements

291CHAPTER 8

Optimization

• TOPVAR, TOMVAR, BEADVAR

• DVMREL1,2 and DVCREL1,2

Benefits• Enables design optimization tasks to include structural nonlinear responses

• Leverages the existing linear multidisciplinary design optimization capability in SOL 200

• Is able to solve small- or large-scale nonlinear response optimization tasks

Theory

Basic Optimization Statement

A general nonlinear response optimization problem can be stated as follows:

ESLNRO

The ESL based approach converts the above problem into an iterative solution of linear sub-optimization

problems through use of Equivalent Static Loads (ESL). The essence of the approach can be described

in Figure 8-7:

Find: X

Minimize:

Subject to:

F X UNL,( )

g X UNL,( ) 0<

XL X XU< <



292

Figure 8-7

where subscript NL refers a nonlinear system, equivalent static loads and L a linear system.

First, a nonlinear analysis is carried out. Next, the equivalent static loads (ESL) are computed from the

nonlinear solutions. Then, the ESL is applied to a linear system and mathematical programming

techniques are carried out on this linear system. The new design from the linear optimization is used to

start a new ESLNRO loop. The process continues until the convergence criteria are satisfied. It is the ESL

that establishes a platform to perform nonlinear response optimization without actually calculating the

sensitivities of nonlinear responses.

One key ingredient in the ESLNRO is the generation of the equivalent static loads. According to Ref. 8.,

for a particular nonlinear response, a required ESL should produce an equivalent and identical linear

response at the start of the linear response optimization. The displacement-based ESL is computed by

multiplying the linear stiffness matrix and nonlinear displacement solution and satisfies the requirement.

For the stress-based ESL, Ref. 8. has used a more involved approach by solving an extra linear system

with the nonlinear stress field as the initial condition without external loading. Then, the extra

displacement solution is multiplied with the linear stiffness matrix to generate the stress-based ESL.

Furthermore, a stress ratio scheme is introduced to ensure the linear stress filed will be identical to the

nonlinear stress field. Notice that the ESLNRO in MD Nastran R3 directly uses the displacement-based

ESL as the stress-based ESL to avoid the extra linear analysis. However, the stress ratio scheme is still

applied to ensure that the linear stress responses are identical to the nonlinear stress response at the start

of the linear response optimization.

K X UNL,( )UNL PZ

Peq KLUNLZ

KL X( )UL PeqZ

F X UL,( )

KL X( )UL PeqZ

UL UAllowable

≤

σL σAllowable

≤

σDL α σL⋅Z σ σNL σL⁄Z,

Notice and at start of linear response optimizationUL UNLZ σL σNLZ

Find:

Minimize:

Subject to:

Nonlinear analysis

Transformation to ESL

Linear analysis with ESL

Linear

response

optimization

(Inner Loop)

ESLNRO

Loop

X

Peq

293CHAPTER 8

Optimization

As shown in Figure 8-7, an ESL-based nonlinear response optimization task involves two types of loops.

An inner loop (or a SOL 200 loop) is carried out in the linear response optimization and follows all the

rules in a SOL 200 job. The ESLNRO loop is the outer loop that brings the nonlinear analysis and linear

response optimization together. Like the inner loop carried out in SOL 200, the ESLNRO loop also has

its own design move limit and the convergence criteria.

Design Move Limits in ESLNRO

In the ESLNRO, the actual nonlinear response optimization is solved by iterative solutions of linear sub-

optimization problems. Although the linear responses at the beginning of the linear system optimization

are identical to the nonlinear responses, there is no guarantee that the nonlinear responses evaluated with

the proposed design are the same as those linear response evaluated with the same design. The design

proposed by a linear sub-optimization solution may be too aggressive to affect convergence negatively.

Ref. 8. has proposed a scaled-back scheme to limit the design move at each design cycle. Its main idea

is to scale back the design move proposed by a linear sub-problem solution:

where is the design variable for the k-th design cycle, is the design variable at (k-1)th design

cycle, is the proposed design from the linear optimization solution at (k-1)th design cycle and

DELXES is the fractional change allowed in each design variable during the ESLNRO loop.

An alternate to the scaled-back scheme is to limit the design move by posing more restrictive lower and

upper bounds on each design variable. The following equations are used to update the design variable

bounds. Subscript k indicates k-th design cycle, o indicates the initial design cycle, i indicates i-th design

variable, L lower bound and U upper bound. The initial design variable bounds are those specified on the

DESVAR entries and DXMIN is a DOPTPRM parameter and is the same parameter used in a SOL 200

run.

It has been found that each scheme is effective in certain applications. Therefore, a user selection is

provided.

=

=

MOVE =

Xk

*Xk 1Ó

Z Xk 1Ó

1Xk 1Ó

Ó( )H DELXESL⋅

Xk*

Xk 1Ó

Xk 1Ó

1

Xk

Lmax Xo

LXi MOVEÓ,( )

Xk

Umin Xo

UXi MOVEH,( )

max DXMIN,abs Xi( ) DELXESL⋅( )



294

Convergence Criteria in ESLNRO

An ESLNRO job will be terminated if either of the following conditions is met:

1. It reaches the maximum number of design cycle or

2. When the changes in each design variable between the current and previous design cycles must

be less than a given tolerance and the requirement will further be satisfied in two consecutive

design cycles.

Implementation

The ESLNRO capability is implemented in MD Nastran environment with nonlinear solver SOL 400, a

comprehensive and sophisticated nonlinear solution sequence that can deal with general applications

with geometric, material and boundary nonlinearities (12-14). The design logic for ESLNRO is shown

in Figure 8-8.

Note that only a single user input file is required that specifies the nonlinear analysis model as well as the

design model with its design variables and constraints. However, internally, a multiple Nastan invocation

strategy is used to bring SOL 400 and SOL 200 together to provide an integrated solution to the design

task. Specifically, a dashed frame as shown in Figure 8-8 forms the main ESLNRO loop in which the

iterative solutions of linear sub-optimization problems are obtained through SOL 200 and SOL 400. The

communication between the main driver, the SOL 400 and SOL 200 runs are established through various

intermediate files. Outputs, 298 and Guidelines and Limitations, 279 will describe them and discuss how

to manage these files.

295CHAPTER 8

Optimization

Figure 8-8 Program Flowchart

Input

In general, the required user input to perform an ESLNRO task is to add a design model definition to an

existing SOL 400 job. The detailed description will be shown in Examples, 302. Here, several new types

of input, that may be required to perform ESLNRO tasks are described.

1. Activation of ESLNRO

To invoke ESLNRO, you are required to specify a Nastran ESLOPT statement.

ΔDVi ξ?≤ i 1 ndv,Z, *

A User Submits a Single Input File (SOL 400 + Design Model)

The single file is partitioned into two files:

fn_nlsol400.dat and fn_eslsol200.dat

Launch SOL 400 to perform nonlinear analysis

Generate Equivalent Static Loads

Launch SOL 200 to perform a linear response optimization

Update Design Variable Bounds

Create design

history table and

clean up files.STOP

No, k=k+1

Yes

ESLNRO loop

k=0

k DSMXESL?>

or

* This condition must be satisfied in two consecutive design cycles.

X(new)



296

Example, to activate ESLNRO, use

Nastran ESLNRO = 1 or

Nastran system(443) = 1

2. Control parameters for ESLNRO tasks

New parameters, DELXESL and DSMXESL are added to the DOPTPRM entry. DELXESL is

used to control how much a design variable can move during a ESLNRO design cycle while

DSMXESL is the maximum allowable number of design cycles.

3. Definition of designed properties

Element property entries such as PBEAM, PROD, PSHELL and PTUBE can be specified on a

DVPRELi entry. The associated nonlinear element types are: CBEAM(94), CONROD(92),

CQUAD4(90), CQUADR(173), CROD(89), CTRIA3(88), CTRIAR(174), CTUBE(87). The

property names on these entries that can be referenced on a DVPRELi entry shown in the

following table:

DVMRELi and DVCRELi entries are not supported.

System Cell Name (Number) Function and Reference

ESLOPT (443) Flag to invoke ESLNRO concept of Equivalent Static Loads

0 – No ESLNRO, default

1 – Turn on ESLNRO

Name Description, Type, and Default Value

DELXESL Fractional change allowed in each design variable during the ESLNRO loop

(Real > 0.0, Default = 0.5)

DSMXESL Maximum number of design cycles applied to the ESLNRO loop (Integer > 0,

Default = 20).

Property Entry Property

PBEAM (A(i), I1(i), I2(i), I12(i), J(i), NSM(i), C1(i), C2(i), D1(I), D2(i), E1(i),

E2(i), F1(i), F2(i), (i=A, B, 1 ... 9)), K1, K2, S1, S2, (NSI(j), CW(j),

M1(j), M2(j), N1(j), N2(j), j=A, B)

PROD ^I=gI=`I=kpj

PSHELL T, 12I/T**3, TS/T, NSM, Z1, Z2 (The 12I/T**3 term can be designed but

must be referenced by Field ID=6 rather than by name.)

PTUBE OD, T, NSM

297CHAPTER 8

Optimization

4. New input for defining nonlinear responses with a DRESP1 Bulk Data entry

The displacement response is identified on a DRESP1 by RTYPE=DISP while the stress response

is identified by RTYPE=STRESS. The same way to define a linear displacement response on a

DRESP1 can be used to define a nonlinear displacement response. However, defining nonlinear

stress response requires specifying a nonlinear stress item code on the ATTA field of a DRESP1

entry. These stress item codes can be found in Element Stress (or Strain) Item Codes (p. 877) in

the MD Nastran Quick Reference Guide (Ref. 15.).

For this release, the stress responses from the following nonlinear elements are supported:

CONROD(92), BEAM(94), TUBE(87), QUAD4(90), TRIA3(88), QUADR(172), TRIAR(173),

HEXA(93), PENTA(91), TETRA(85). In order to ensure to support the nonlinear stress

responses that have the equivalent linear stress responses, the nonlinear element stresses are

categorized into three groups:

a. the stress having the same name and same meaning as those in the linear element stresses;

b. the stress having the different name but having the same meaning; and

c. the stress having the different name and different meaning.

Only the stresses in groups 1 and 2 can be specified on a DRESP1 entry. The following lists the

stresses from Groups 2 and 3 for supported nonlinear elements. For example, the Equivalent

Stress is a group2 stress because it is equivalent to the von Mises stress in a linear element

although their names are different. However, total strain, effective plastic strain and effective

creep strain (as shown in bold) cannot be specified on a DRESP1 entry because they do not have

linear equivalents.

Nonlinear 1D element

CONROD (92) (equivalent stress) (total strain, effective plastic strain, effective creep strain)

Beam (94) (equivalent stress), (total strain, effective plastic strain, effective creep strain)

Tube (87) (equivalent stress) (total strain, effective plastic strain, effective creep strain)

Nonlinear 2D

QUAD4 (90) (equivalent stress) (effective plastic strain, effective creep strain)

TRIA3(88) (equivalent stress) (effective plastic strain, effective creep strain)

QUADR(172) (equivalent stress) (effective plastic strain, effective creep strain)

TRIAR(173) (equivalent stress) (effective plastic strain, effective creep strain)

Nonlinear 3D

Hexa (93) (effective stress), (effective plastic strain, effective creep strain)

Penta (91) (effective stress), (effective plastic strain, effective creep strain)

Tetra (85) (effective stress), (effective plastic strain, effective creep strain)

5. New Bulk Data Parameters

Option to save ESLNRO intermediate files on disk

PARAM,ESLFSAV,character string (character, Default = NO)



298

ESLFSAV = YES requests that all the intermediate files from an ESLNRO job be saved on disk.

The destination of these files can be directed with the ‘sdir=’ option on a Nastran submittal

command line.

Selection of move limit schemes

PARAM,ESLMOVE,Integer, Default = 0

ESLMOVE = 0 selects a move limit scheme that poses restrict lower and upper bounds on design

variables during the linear response optimization. ESLMOVE = 1 selects a move limit scheme

that scales back the design move proposed from a linear response optimization.

User-supplied RC file

PARAM,ESLRCF,filename (Char*8, must be lower case). Default = blank

New Bulk Data parameter entry, PARAM,ESLRCF,filename allows the user-supplied RC file for

the internally spawned jobs where filename is a character string up to 8 characters. Only lower

case is supported.

Example:

PARAM,ESLRCF,myrc where myrc is the name of the user-supplied RC file with the following

contents:

MEM=200m

EXE=~local_path/MDNASTRAN

DEL=~local_path/SSS

The example shows a user-supplied RC file that requests each spawned SOL 200 or SOL 400 job

be run with memory allocation of 200 million words per run and with executable and delivery

database.

Option to save ESLNRO intermediate files on disk

PARAM,ESLFSAV,character string (Character, Default = NO)

ESLFSAV = YES requests that all the intermediate files from an ESLNRO job be saved on disk.

The destination of these files can be directed with the ‘sdir=’ option on a Nastran submittal

command line.

Outputs

During the ESLNRO job, in addition to the primary Nastran result files (e.g., .f06, .f04 and log), files are

generated internally for communications between the main driver and nonlinear analyses (SOL 400 run)

and linear response optimizations (SOL 200 runs). These are temporary files and will be removed at the

job’s completion by default. However, the user can use PARAM,ESLFSAV,YES to save them on the disk

if necessary.

These two types of files will be described using a user input file named deslo.dat.

299CHAPTER 8

Optimization

The Primary Nastran Result Files (deslo.f06, .f04, log, etc.)

These are regular output files from a Nastran job and follow the Nastran naming conventions such as

.f04, .f06 and log files. The .f06 file contains certain messages that are unique to an ESLNRO job. For

example, the following information messages are printed in the .f06 file for each design cycle to provide

a brief description of the ESLNRO process:

If a nonlinear analysis job is unable to converge and is terminated at design cycle 11 in the ESLNRO

loop, the following User Information Message 6464 will be printed out in the deslo.f06 file. In addition,

the deslo.f06 will also include the additional information on the lack of convergence is printed in the

regular SOL 400 .f06 file (not shown).

In addition, for initial design cycle and final design cycle, the results from nonlinear analysis tasks and

the optimization output data controlled by P1 and P2 on the DOPTPRM entry are always printed out in

the .f06 file. However, no results output are printed in the .f06 file for the intermediate design cycles.

At the end of the design cycle, a summary of design cycle history and design variable history are printed

in the .f06 file. If you are familiar with a SOL 200 job, they look very much like the design history tables

from an SOL 200 task. Here is the sample printout of the summary of design cycle history.

***************************************************** * * * E S L N R O D E S I G N C Y C L E = 11 * * * *****************************************************

^^^ A NONLINEAR ANALYSIS JOB INITIATED WITH FOLLOWING COMMAND:/nast/md20071t1/linux64/nastran /scratch/./deslo_nlsol400 scr=yes bat=no rcf=my.rc out=/scratch/./deslo_nlsol400 ^^^ A NONLINEAR ANALYSIS JOB FOR THE ESLNRO COMPLETED.

^^^ A LINEAR OPTIMIZATION JOB INITIATED WITH FOLLOWING COMMAND:/nast/md20071t1/linux64/nastran /scratch/./deslo_eslsol200 scr=yes bat=no rcf=my.rc out=/scratch/./deslo_eslsol200 ^^^ A LINEAR OPTIMIZATION JOB FOR THE ESLNRO COMPLETED.

^^^ NO HARD CONVERGENCE IS ACHIEVED IN THE ESLNRO LOOP. JOB CONTINUES

*** USER INFORMATION MESSAGE 6464 (DELSOPT) RUN TERMINATED DUE TO NONLINEAR ANALYSIS JOB UNABLE TO CONVERGE AT DESIGN CYCLE = 11.

****************************************************************** S U M M A R Y O F D E S I G N C Y C L E H I S T O R Y ******************************************************************

(HARD CONVERGENCE ACHIEVED) NUMBER OF NONLINEAR FINITE ELEMENT ANALYSES COMPLETED 38 NUMBER OF OPTIMIZATIONS W.R.T. LINEAR MODELS 37

OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY------------------------------------------------------------------------------------------------------ OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE LINEAR MODEL EXACT OF OFNUMBER OPTIMIZATION ANALYSIS LINEAR MODEL CONSTRAINT ------------------------------------------------------------------------------------------------------INITIAL 2.630691E-01 4.676274E-011 3.190933E-01 2.742739E-01 1.634111E-01 1.778786E-01



300

The Internally Spawned Files

Two user input files, one for the SOL 400 run and one for the SOL 200 run are internally generated

derived from the primary user input file: deslo_nlsol400.dat and deslo_eslsol200.dat. deslo is the name

of the primary user input file and _nlsol400 and _eslsol200 are suffixes to distinguish a SOL 400 job from

a SOL 200 job. Each has a unique Executive Control Section and a Case Control Section. Each file also

has unique Bulk Data entries and shares a portion of common Bulk Data entries.

Detailed descriptions of two user input files are as follows. Notice multiple INCLUDE entries are used

to facilitate sharing common Bulk Data entries among two jobs, updating DESVAR entries or GRID

entries for shape optimization at the end of each design cycle without the need to changing the actual

input files.

Description of a SOL 400 Input File (deslo_nlsol400.dat)

SOL 400

CEND

include '$sdir/deslo_nlsub.cas' $ = original subcase contents minus DESOBJ/DESSUB/DRSPAN

BEGIN BULK

include ‘$sdir/deslo_grid.blk' $ = all GRID entries. Original entries for initial design cycle and updated

entries for design cycle>1.

include ‘$sdir/deslo_desmod.blk' $ = all design model Bulk Data entries except DESVAR entries

include ‘$sdir/deslo_desvar.blk' $ = all DESVAR entries

include '$sdir/deslo_nlmat.blk' $ = nonlinear material entries such as MATS1, MATEP,MATF,

NLPARM

include '$sdir/deslo_loads.blk' $ = the original loading Bulk Data entries.

include ‘$sdir/deslo_model’ $ = the remaining portion of the original Bulk Data entries

ENDDATA

Description of a SOL 200 Input File (deslo_eslsol200.dat)

SOL 200

CEND

include '$sdir/deslo_eslsub.cas' $ = ESL Subcases + DESOBJ/DESSUB/DRSPAN

BEGIN BULK

include ‘$sdir/deslo_grid.blk' $ = all GRID entries. Original entries for initial design cycle and updated

entries for design cycle>1.

include '$sdir/deslo_desmod.blk' $ = all design model entries except DESVARs

include '$sdir/deslo_desvar.blk' $ = all DESVARs entries

include ‘$sdir/deslo_esl’ $ = Equivalent Static Loads Bulk Data entries

include ‘$sdir/deslo_model’ $ = the remaining portion of the original bulk data entries

All the intermediate files are stored in the same Nastran scratch directory defined by environment

variable $sdir. It could be reset on the Nastran command line with sdir=local-path-directory. If SCR

option is set to Yes, they will be removed from the directory after the ESLNRO job is complete. If SCR

is set to No, they will be saved in the directory.

301CHAPTER 8

Optimization

Descriptions of Individual Include Files

Guidelines and Limitations• The current release of the ESLNRO capability supports nonlinear analyses with geometry and

material nonlinearities but not nonlinear boundary applications such contact problems. It is

limited to static analysis with design constraints on displacements and element stresses. Both

sizing and shape design variables are supported where sizing design variables are limited to the

quantities that can be specified on a DVPRELi entry. Topology, Topometry and Topography are

not supported.

• To invoke the ESLNRO capability, set NASTRAN ESLOPT = 1 at the top of your input file.

deslo_nlsub.cas This file contains the original contents of the Case Control Section used by

a SOL 400 run.

deslo_eslsub.cas This file defines SUBCASES that reference load cases corresponding to the

same number of Equivalent Static Loads. It is generated by the SOL 400 run

and will be used by a SOL 200 job.

deslo_desmod.blk This file contains all the design entries except DESVAR entries and is used

by both a SOL 200 job and a SOL 400 job.

deslo_desvar.blk This file contains all the initial DESVAR entries for the initial design cycle.

For design cycle > 1, it contains updated DESVAR entries. The file is used

by both SOL 200 and SOL 400 runs.

deslo_grid.blk The file contains all the initial GRID entries at the initial design cycle. For

shape optimization it contains the updated GRID entries for design cycle >

1. It is used by both jobs.

deslo_loads.blk The file contains the loads Bulk data entries from the original user input

file. It is only used by a SOL 400 job.

deslo_esl.blk The file contains the loads Bulk data entries for the Equivalent Static Loads.

It is generated by a SOL 400 run at every design cycle and is only used by

a SOL 200 job.

deslo_nlmat.blk The file contains nonlinear analysis specific data such as nonlinear material

entries that are supported by this project such as MATEP, MATF, MATS1

and NLPARM and is used only by SOL 400 job.

deslo_model This file contains the remaining Bulk Data entries after the entries in

deslo_grid.blk, deslo_nlmat.blk and deslo_desmod.blk, deslo_desvar,

deslo_loads are excluded from the original Bulk Data Section and is used

by both jobs.



302

• An ESLNRO job requires a single user input file consisting of a regular SOL 400 job and a

design model definition. Various intermediate files are generated from those separate SOL 400

and SOL 200 runs that perform nonlinear analysis and linear response optimization. You can use

SDIR= option to redirect these files to your desired location. Use SCR=no if you want to keep

them on the disk at the end of the job.

• When you start an ESLNRO job, make sure the directory that will store the intermediate files

does not contain any intermediate files from the previous ESLNRO run.

• You can specify your own RC file for these internally spawned SOL 200 or SOL 400 jobs using

PARAM,ESLRCF, RC_ File_Name to allocate more memory or for other purposes.

• After an ESLNRO job is complete, a complete Bulk Data Section with updated element

properties entry or GRID and DESVAR entries for the last design cycle will be saved in the PCH

file. In addition, the history of design objective, maximum constraints and design variables are

also saved in the PCH file from which XY-Plots can be generated using spreadsheet program

such as Microsoft Excel.

• The capability is characterized as “pre-release” or “beta” because it is a new functionality that

requires considerable use and, perhaps, refinement to become a mature production tool. The

user community is invited to exercise this capability and provide MSC with feedback as to its

performance and usefulness.

Examples

10 Bar Truss (test library problem: deslo.dat)

50 GPa

200 GPa

303CHAPTER 8

Optimization

This example demonstrates an ESLNRO optimization problem involving both geometric and material

nonlinear behavior. The design task is to minimize the structural weight while maintaining nonlinear

nodal displacements and element stresses within allowable limits. It is solved using MD Nastran R3. As

stated above, SOL 400 and SOL 200 are combined in a single process for nonlinear analysis and linear

response optimization. The optimizer in SOL 200 is MSCADS, a modified version of the ADS code

(Ref. 1.). The job is terminated due to hard convergence to a feasible design. The following data compare

the results between the initial design and the final design. Although both initial nonlinear displacement

and stress constraints are violated, the final design is a feasible design.

• Max Deflection: Optimized: -99.85, Initial -146.76 (lower limit is -100.0)

• Max Axial Stress: Optimized: -218.26, Initial -283.99 (upper limit is 220.00)

Figure 8-9 shows the design history where an ESLNRO design cycle represents a nonlinear analysis

followed by a linear optimization task. Each linear optimization task typically has its own series of

design cycles as in a standard SOL 200 run. The blue line is for weight while the red line is for the

maximum constraint. It is seen that a feasible design is attained after 10 design cycles but that the weight

continues to decrease so that ultimately 37 design cycles are performed. Even for this small problem, it

should be obvious that the number of nonlinear analyses required to solve the problem are much fewer

than would be required if a response surface method approach had been used.

σj 220 MPa≤

78.5 mm2

Xi 2826.0 mm2

≤ ≤

δal l 100.0 mm≤

Find:

Minimize:

Subject to:

(both x and y directions of all nodes

(j = 1, ..., 10)

(i = 1, ..., 10)

Weight

(cross sectional areas)



304

Figure 8-9

Joined Wing

A joined-wing model is used here to demonstrate the capability. It was provided to MSC by the Air Force

Institute of Technology (Ref. 11.). The airplane has a half span of 38 meters and is operating under 11

load conditions that result in a maximum tip deflection of 20 meters.

Figure 8-10 Joined-wing configuration

305CHAPTER 8

Optimization

The optimization problem is formulated as:

This problem is solved by MD Nastran. SOL 400 is used for nonlinear analysis. Figure 8-11shows the

initial full scan displacement and the stress contour.

Figure 8-11

Find:

to minimize: Mass

subject to:

ti i 1 …2559,Z( )

σj σallowable≤ j 1 … 2559, ,Z( )

0.001016m tskin part 0.227m≤ ≤

0.000127m ttip wing part 0.227m≤ ≤

0.000254m twing spars and ribs 0.227 m≤ ≤

Initial Deflection Initial Stress Contour



306

Furthermore, a special snap over buckling behavior has been observed at approximate 50% load. See

Figure 8-12.

Figure 8-12

Again, SOL 200 is used for linear response optimization. The BIGDOT optimizer licensed from VR&D

is used here to solve large scale linear response optimization problem. The following data compares the

normalized results between the initial and final design. Figure 8-13 shows the final displacement and

stress contour plots.

• Max Deflection: Optimized: 1.0, Initial: 5.96

• Max equivalent stress: Optimized: 1., Initial: 23.30

• Snap over buckling effect is eliminated

Figure 8-13

Figure 8-14 shows the history of the joined wing design. The blue line is for weight while the red line is

for maximum constraint. The job converges at 36 design cycles with constrain value of 0.05. This is a

fairly hard problem to solve considering it includes more than 2500 design variables and 2000 plus

constraints. Here it shows that it is possible to design a joined-wing problem under large deformation

with thousands of design variables and nonlinear stress constraints, something that is impossible to solve

by the RSM approaches.

0% load 50%∼ 100% load

Optimized Deflection Optimized Stress Contour

307CHAPTER 8

Optimization

Figure 8-14

References1. MD Nastran R1 Design Sensitivity and Optimization User’s Guide, 2006.

2. Arora’s paper: Sensitivity Based Nonlinear Response Optimizations

3. G. E. P. Box and N. R. Draper, Empirical Model-Building and Response Surfaces, Wiley, New

York, 1987.

4. R. H. Myers and D. C. Montgomery, “Response Surface Methodology: Process and Product

Optimization Using Designed Experiments,” Wiley-Interscience, February 5, 2002.

5. W. J. Roux, N. Stander and R.T. Haftka, “Response Surface Approximations for Structural

Optimization,” International Journal for Numerical Methods in Engineering, 42, 517{534 (1998)

6. N. Stander et al., “LS-OPT User’s Manual Design Optimization Software for the Engineering

Analyst,” April, 2003 Version 2, Livermore Software Technology Corporation

7. H. Thomas, “NASOPT: A Flexible Optimization Capability for MSC/NASTRAN.’ Proceedings

of the MSC User Conference, 1995

8. M.K. Shin, K.J. Park and G.J. Park, “Optimization of Structures with Nonlinear Behavior Using

Equivalent Loads,” Computer Methods in Applied Mechanics and Engineering, 196 (2007)

1154–1167.

9. Y.I. Kim, G.J. Park, R.M. Kolonay, M. Blair and R.A. Canfield, “Nonlinear Response Structural

Optimization of a Joined-Wing Using Equivalent Loads,” submitted to AIAA J.

10. W.S. Choi and G.J. Park (1999), "Transformation of Dynamic Loads into Equivalent Static Loads

Based on Modal Analysis," International Journal for Numerical Methods in Engineering, August,

Vol. 46, pp. 29-43.



308

11. C.C. Rasmussen, R.A. Canfield, M. Blair, “Joined-Wing Sensor-Craft Configuration Design,”

45th AIAA/ASME/AHS/ASC Structures, Structural Dynamics and Material Conference, 2004

(AIAA 2004-1760).

12. MD Nastran R1 Release Guide, 2006.



15. MD Nastran R3 Quick Reference Guide, 2008

Chapter 9: Aeroelasticity and Rotor Dynamic Improvements MD Nastran R3 Release Guide

9 Aeroelasticity and Rotor

Dynamic Improvements

� A New Aerodynamic Interpolation Method

� External Spline Server

� Blade Vibration Analysis


A New Aerodynamic Interpolation Method

310


Introduction

Solution of the flutter equations entails interpolation to compute the aerodynamics at the exact reduced

frequency of the flutter solution as a function of the aerodynamics that have been computed explicitly

based on the ‘k’ (reduced frequency) values input on the MKAEROi entries. For many years, the

available interpolation schemes have been adaptations of the beam and surface spline methods used in

the splining of displacements and forces in aeroelasticity. Chapter 2.6 of the MSC Nastran Aeroelastic

Analysis User’s Guide documents these methods. All of these methods perform their interpolation based

only on the ‘k’ values and each term in the generalized aerodynamics matrix is weighted in the same way.

For MD Nastran R3, an alternative interpolation is provided that interpolates each term in the generalized

aerodynamic matrix individually.

Inputs

The existing FLUTTER Bulk Data entry contains an IMETH field that allows the user to select between

L (linear interpolation on k-only) and S (surface interpolation on Mach number and k) methods. Under

this enhancement, an additional option (TCUB) has been provided to invoke a termwise cubic

interpolation technique. For legacy purposes, if the FLUTTER entry has a METH field of “PK”,

“PKNL”, “PKS” or “PKNLS” and the IMETH field is blank, S or L, the linear beam spline is used to

interpolate the aerodynamics as a function of reduced frequency. If IMETH is TCUB, the termwise cubic

spline technique is employed. Any other value of IMETH results in an error. If the flutter method is “K”

or “KE”, IMETH=S selects a surface spline on Mach and reduced frequency and IMETH=L selects a

linear method on reduced frequency and using the Mach number that is closest to the Mach number

specified on the FLFACT entry. It is an error to select METH = “K” or “KE” and IMETH=”TCUB”

Outputs

There are no new outputs as a result of this implementation.


The interpolation scheme involves determining weighting coefficients using cubic spline techniques

based on the k values entered on the MKAEROi entries and the generalized aerodynamics computed at

these k’s. During the PK flutter analysis, an estimate of the k value is made. The interpolation is then

performed using:

Qi j kes t( ) Qi j k0( )Z Ci j

3Δk⋅ Ci j

2H( ) Δk⋅ Ci j

1H( )H Δk⋅

311CHAPTER 9

Aeroelasticity and Rotor Dynamic Improvements

where:

If only one value is provided for the MKAEROi input, no interpolation is performed and the

aerodynamics are invariant.

If the value falls outside the range of k’s input using the MKAEROi entries, no extrapolation is

performed. Instead, the aerodynamics at the lowest input k value are used if the desired k is lower than

the input k’s and the aerodynamics at the highest input k value are used if the desired k is higher than any

input k’s.

For sensitivity analysis, it is necessary to provide the sensitivity of the aerodynamics due to a change in

. Differentiation of the equation above gives:

If only one value is provided of if the falls outside the range of MKAEROi values, the sensitivity

is zero.

A convenient way to check interpolation using the TCUB method with the beam spline method

(IMETH=L) is to perform a flutter analysis with two subcases with the only difference being the IMETH

value. The flutter summary results should be close, but not identical. DIAG 39 can be turned on around

the FA1 module to provide debug data for the flutter analysis while DIAG 30 will print even more data.

Turning DIAG 30 and DIAG 39 on around the DSFLTE module in the FLUTSENS dmap will provide

information on the sensitivity analysis. It is cautioned that the output is particularly voluminous for the

sensitivity diagnostics.

IMETH=TCUB is only supported for the ‘PK’ method of flutter analysis and its variants, i.e., it is not

supported for the ‘K’ and ‘KE’ methods.

Examples

Two examples are available with the release demonstrating this new capability. The first is named

csint.dat and is a variation of the simple HA145A example found in the MSC Nastran Aeroelasticity

User’s Guide. An extra subcase has been provided that repeats the PK flutter analysis of the example

= A term in the generalized aerodynamic matrix. Real and imaginary terms are splined

separately

= k at which aerodynamics are required

= largest k value from the MKAEROi input that is

=

= Interpolation coefficients determined using a cubic spline (1,2,3 are superscripts, not

exponents.)

Qi j

kest

k0

kest<

k kest koÓ

Cij1 2 3, ,

k

kes t

k

dQi j kes t( )

dkJJJJJJJJJJJJJJJJJJJJJJJJJJ 3.0 C⋅ i j

3Δk⋅ 2.0 C⋅ i j

2H( ) Δk⋅ Ci j

1HZ

k kes t



312

while setting IMETH to TCUB. A comparison of the flutter summary results for the two examples show

virtually identical results.

The second example is entitled cintopt.dat and is a variation of the HA200B example from the same

User’s Guide. In this case, the flutter subcases have been converted from using the beam spline

interpolation to using the new TCUB interpolation. Again, there is virtually no change in the results.

313CHAPTER 9


External Spline Server

Introduction

The external spline evaluation capability that was introduced with MD Nastran R2.1 required that every

term in the server-generated spline matrix be stored in memory. This limited the capability since very

large, but very sparse, spline matrices would not fit into the available memory.

With this release, the API was updated to allow the spline matrix to be stored in a sparse format. The

fully-populated spline matrix format is still supported.

Inputs

No changes were made to the Nastran input file or to how the external spline server is used.

API Changes

The interface between Nastran and an external spline server was modified to support the sparse matrix

format.

Two changes were made to the calling sequence of the main spline server interface routine (sxsevd.c),

they are noted in bold and a slightly larger font:

void sxsevd ( INTEGER group_id, /* Group id */ INTEGER spline_id, /* Spline id */ INTEGER *usage, /* Usage string (stored as hollerith) */ INTEGER n_int_data, /* Number of integer data */ INTEGER *int_data, /* Integer data */ INTEGER n_real_data, /* Number of real data */ MACHINEPRECISION *real_data, /* Real data */ INTEGER n_char_data, /* Number of character data */ INTEGER *char_data, /* Character data (stored as hollerith) */ INTEGER n_dep_grid, /* Number of dependent grids */ INTEGER *dep_grid_id, /* Dependent grid ids */ MACHINEPRECISION *dep_grid_xyz, /* Dependent grid x,y,z locations */ INTEGER n_indep_grid, /* Number of independent grids */ INTEGER *indep_grid_id, /* Independent grid ids */ MACHINEPRECISION *indep_grid_xyz, /* Independent grid x,y,z locations */ INTEGER n_dep_elem, /* Number of dependent elements */ INTEGER *dep_elem, /* Dependent element table */ INTEGER n_indep_elem, /* Number of independent elements */ INTEGER *indep_elem, /* Independent element table */ char *command_line, /* Optional command line argument */ char *connect_data, /* Optional connect data */ INTEGER *ginfo, /* Output information about the spline matrix */ MACHINEPRECISION **gmat, /* The computed spline matrix */ INTEGER *error) { /* Error code */

1. A new integer parameter called ginfo is now output. This variable stores the total number of

nonzero terms in the spline matrix if it is stored in the sparse format. ginfo should have a value

of zero if the spline matrix is stored in the fully-populated format.


External Spline Server

314

2. Previous versions of Nastran allocated the memory for the spline matrix on the client (Nastran)

side of the problem. With the new version, the client does not know if the server will be storing

the spline matrix in the sparse or full formats. Therefore, it is now the server’s responsibility to

allocate the memory to store the spline matrix. As a result of this change, the gmat variable,

which was previously a pointer is now a pointer to a pointer.

Sparse Matrix Format

If the sparse format is used to store the spline matrix, then the data must be stored in gmat in triplets of

(row number, column number, value) for each nonzero term in the spline matrix:

The ginfo variable must store the number of nonzero terms (n) in the spline matrix. The sparse gmat

will store numbers total.

Upgrading an Existing Spline Server

This section provides one method for upgrading an MD Nastran R2.1 spline server to be compatible with

R3. The experienced C programmer may wish to implement the changes differently. It will be assumed

that the spline matrix will be stored in the fully-populated format.

1. Update the calling arguments of sxsevd.c to be exactly as listed above.

2. Declare a local variable to store the spline matrix:

MACHINEPRECISION *server_gmat=NULL;

3. Set the value of ginfo:

*ginfo = 0;

4. Allocate the memory to store the spline matrix.

gmat

Row number for value 1

Collumn number for value 1

Value 1

Row number of value 2

Column number for value 2

Value 2

.

.

.

Row number for value n

Column number for value n

Value n

Z

3 n×( )

315CHAPTER 9


Blade Vibration Analysis

In prior versions of Nastran; MD Nastran R2 and 2007 r1, special options were added to SOL 106 to

support blade vibration analysis but were not documented in the MD Nastran Release Guide or

MD Nastran Quick Reference Guide. The options are documented here for your convenience.

• Frequency (Forced) Response Analysis - in addition to the current normal modes analysis in

SOL 106, the user can request a frequency response analysis. Both the normal modes and

frequency response analysis are requested with a separate subcase followed by the Case Control

commands ANALYSIS=MODES (Ch. 4) and ANALYSIS=DFREQ (Ch. 4) in the MD Nastran

Quick Reference Guide.

• “Hot-to-Cold” Analysis - allows the user to input the “stressed” or “hot” (deformed) geometry

using standard Bulk Data input and then “unload” the structure to determine the “unstressed” or

“cold” shape. See the description of the Case Control command ANALYSIS=HOT2COLD

(Ch. 4) in the MD Nastran Quick Reference Guide and user parameters HTOCITS (Ch. 5),

HTOCPRT (Ch. 5), and HTOCTOL (Ch. 5) in the MD Nastran Quick Reference Guide.

• Tangential Acceleration and Coriolis Follower Forces in Frequency Response Analysis - Include

the effects of the tangential acceleration and Coriolis follower forces in the nonlinear differential

stiffness matrix to be used frequency (forced) response analysis. See the description of user

parameter CORITAN (Ch. 5) in the MD Nastran Quick Reference Guide.

These options enable the analyses of a rotating nonsymmetrical structure connected to a nonsymmetrical

stationary structure. The rotating component will be assumed to be spinning at a constant rate. The

procedure permits dynamic response calculations of the bypass fan, compressor, and turbine blades for

aerojet engines. It also allows analyses of rotating wing aircraft. The methodology can also be used for

dynamic response of the crankshaft/engine block of a reciprocating engine.


Blade Vibration Analysis

316

Chapter 10: SCA User Services MD Nastran R3 Release Guide

10 SCA User Services

� User Defined Services


SCA User Services318

User Defined Services

Introduction

This new capability in MD Nastran gives you a mechanism to utilize your own subroutines or

applications within a MD Nastran execution process. There are many benefits to this new feature, such

as embedding proprietary element formulations, or extending MD Nastran element formulations that

may not be flexible enough for a specific type of analysis. A specific case of this problem is when rotor-

dynamics users would like to provide their own formulation of Squeeze Film Dampers in MD Nastran.

In this version of MD Nastran, nonlinear force elements are equipped with an external implementation

in the form of a User Defined Service.

Example

The complete process of creating a user defined nonlinear force and incorporating it into MD Nastran is

described in the User Defined Services User’s Guide. The example presented here demonstrates how an

external implementation of a nonlinear force can be used in the same way as a built in MD Nastran

nonlinear force.

Below is a simple illustration of a MD Nastran model with the relevant information highlighted in bold.

connect service mysub 'SCA.MDSolver.Util.UDS'$id msc, rotnlt01.dat SOL senlharm$CEND$…$BEGIN BULK$…nlrsfd, 4001, 105, 205, YZ, 4.2, .95, .005, short,,1.0e-6, 1.0, 1, 10., 180., , , 201,, , ,mysub,again,1.0e3…enddata

In order to identify the service, you have to create a connection between the service name and a service

identifier. This is done through the connect statement in the FMS statement—highlighted in bold. The

connect statement above takes the service “SCA.MDSolver.Util.UDS” and gives it a service-identifier

name called “mysub”.

Next, to associate the required NLRSFD entry in the model with the service identifier, we set the

GROUP_NAME field to “mysub”. The presence of the GROUP_NAME on the NLRSFD Bulk Data

entry triggers the call to the User Defined Service.

319CHAPTER 10

SCA User Services

The new NLRSFD entry is follows:

You must of course have an implementation of the “SCA.MDSolver.Util.UDS” service based on the

interface definition given below:

To build the service, you will need MSC’s build environment which consists of a set of tools to compile

and link all necessary files. You must also obtain the appropriate compiler and compiler version on the

particular platform you are working on. The following table gives the list of appropriate compilers and

options for various MD Nastran supported platforms.

NLRSFD SID GA GB PLANE BDIA BLEN BCLR SOLN

VISCO PVAPCO NPORT PRES1 THETA1 PRES2 THETA2 NPNT

OFFFSET1 OFFSET2 GRPNAME EVALNAME

PARM1 PARM2 PARM3 PARM4 PARM5 PARM6 PARM7 PARM8

/******************************************************************************* Copyright (c) 2008, MSC.Software Corporation. All Rights Reserved. The skeleton for this file was generated by the MSC.Software SCA IDL compiler version 25.0 from 'test.sdl' This file contains the implementation for the service object 'Nlrsfd'*******************************************************************************/

#include "Nlrsfd.h"

namespace Test {

// ConstructorNlrsfd::Nlrsfd(SCAINlrsfdFactoryAccess* factoryAccess) : NlrsfdBase(factoryAccess){}

// DestructorNlrsfd::~Nlrsfd(){}

SCA::SCAResult Nlrsfd::runNlrsfd(const SCA::SCAInt32 sid,const SCA::SCAInt32 ga, const SCA::SCAInt32 gb,const SCA::SCAString plane, const SCA::SCAReal32 bdia,const SCA::SCAReal32 blen, const SCA::SCAReal32 bclr,const SCA::SCAString soln,

const SCA::SCAReal32 visco,const SCA::SCAReal32 pvapco,const SCA::SCAInt32 nport,const SCA::SCAReal32 pres1,const SCA::SCAReal32 theta1,const SCA::SCAReal32 pres2,const SCA::SCAReal32 theta2,const SCA::SCAInt32 npnt,const SCA::SCAReal32 offset1,const SCA::SCAReal32 offset2,const SCA::SCAString evalname,const SCA::SCAReal32 time,const SCA::SCAReal64 xx,const SCA::SCAReal64 yy,const SCA::SCAReal64 xdt,const SCA::SCAReal64 ydt,const SCA::SCAReal64 xb,const SCA::SCAReal64 yb,const SCA::SCAReal64 xbt,const SCA::SCAReal64 ybt,SCA::SCAReal64& fx,SCA::SCAReal64& fy,SCA::SCAInt32& fuseit,SCA::SCAInt32& bisect,SCA::SCAReal32& parm1,SCA::SCAReal32& parm2,SCA::SCAReal32& parm3,SCA::SCAReal32& parm4,SCA::SCAReal32& parm5,SCA::SCAReal32& parm6,SCA::SCAReal32& parm7,SCA::SCAReal32& parm8,const SCA::SCAReal32 omega)

{ return SCA::SCASuccess;}

}


SCA User Services320

Requirements

Platforms OS Level Compiler Compiler Versions

HP (Intel IA-64) HPUX 11.23 Fortran F90 2.8.7

C A.05.44

C++ A.06.02

aC++ A.06.02

HP (RISC PA2.0) HPUX 11.00 Fortran F90 2.9.2.

C B.11.11.16

C++ B.11.11.06

aC++ A.03.50

IBM (Power) AIX 5.1 Fortran XLF 8.1.1.4

C++ CC 6.0.0.7

Linux (Intel x86-32) RHEL 4 Fortran Intel 9.1.036

C++ Intel 9.1.043

Linux (Intel IA-64) RedHat AS 3 Fortran Intel 10.1.012

C++ Intel 10.1.012

Linux (Intel/AMD x86_64) RedHat RHEL 4.3 Fortran Intel 9.1.036

C++ Intel 9.1.043

SGI (MIPS) Irix64 6.5 Fortran F90 7.4

C++ Cc 7.3

SUN (Sparc) Solaris 10 Fortran F90 8.3

C++ CC 5.9

SUN (x86-64) Solaris 10 Fortran F90 8.3

C++ CC 5.9

Windows (Intel x86-32) Windows 2000 sp4 Fortran Intel 9.1.024

C++ Intel 9.1.022

Windows (Intel x86-64) Windows 2000 sp4 Fortran Intel 9.1.024

C++ Intel 9.1.022

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