2006 md nastran release guide

MD Nastran 2006

Release Guide

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

EuropeMSC.Software GmbHAm Moosfeld 1381829 Munich, GermanyTelephone: (49) (89) 43 19 87 0Fax: (49) (89) 43 61 71 6

Asia PacificMSC.Software Japan Ltd.Shinjuku First West 8F23-7 Nishi Shinjuku1-Chome, Shinjyku-KuTokyo 160-0023, JAPANTelephone: (03)-6911-1200Fax: (03)-6911-1201

Worldwide Webwww.mscsoftware.com

DisclaimerMSC.Software Corporation reserves the right to make changes in specifications and other information contained in this document without prior notice.

The concepts, methods, and examples presented in this text are for illustrative and educational purposes only, and are not intended to be exhaustive or to apply to any particular engineering problem or design. MSC.Software Corporation assumes no liability or responsibility to any person or company for direct or indirect damages resulting from the use of any information contained herein.

User Documentation: Copyright 2006 MSC.Software Corporation. Printed in U.S.A. All Rights Reserved.

This notice shall be marked on any reproduction of this documentation, in whole or in part. Any reproduction or distribution of this document, in whole or in part, without the prior written consent of MSC.Software Corporation is prohibited.

This software may contain certain third-party software that is protected by copyright and licensed from MSC.Software suppliers.

MSC, MSC., MD, MSC.Dytran, MSC.Marc, MSC.Nastran, MD Nastran, MSC.Patran, the MSC.Software corporate logo, and Simulating Reality are trademarks or registered trademarks of the MSC.Software Corporation in the United States and/or other countries.

NASTRAN is a registered trademark of NASA. PAMCRASH is a trademark or registered trademark of ESI Group. SAMCEF is a trademark or registered trademark of Samtech SA. LS-DYNA is a trademark or registered trademark of Livermore Software Technology Corporation. ANSYS is a registered trademark of SAS IP, Inc., a wholly owned subsidiary of ANSYS Inc. ABAQUS is a registered trademark of ABAQUS Inc. All other brand names, product names or trademarks belong to their respective owners.

MDNA:V2006:Z:Z:Z:DC-REL-PDF

C o n t e n t sMD Nastran 2006 Release Guide

MD Nastran 2006 e Guide

List of Nastran Books xii

Technical Support xiii

Internet Resources xvi

1 Overview of MD Nastran 2006

Overview 2Nonlinear Analysis 2Numerical Enhancements 2Elements 2Dynamics and Superelements 3Aeroelasticity 3Optimization 4Summary of MD Nastran Quick Reference Guide Additions 4List of MD Nastran Documents Released with MD Nastran 2006 7

2 Nonlinear Analysis

Nonlinear Transient Analysis in SOL 400 10Introduction 10Benefits 10Limitations for the Current Release 11A New Numerical Integration Method – HHT 11Nonlinear Iteration Algorithms 12Case Control Structure – SUBCASE, STEP, ANALYSIS, and NLIC 14Vector Operations and Convergence Criteria 16Nonlinear Iteration Summary Table for Nonlinear Transient Analysis in SOL 400

17Output Data Grouping: NLPACK 18Restarts 19Initial Conditions 21Transient Temperature Loads 23Boundary Condition (SPC and MPC) Changes 24Direct Matrix Input Changes 24Outputs 25

ReleasTable of Contents

MD Nastran 2006 Release Guide

iv

Error Handling 25User Interfaces 26Examples 27

MD Nastran Implicit Nonlinear - SOL 600 44Non-Supported Items 58

MD Nastran Explicit Nonlinear - SOL 700 60Introduction 60Linear and Nonlinear Analysis 60Latest Capabilities of MD Nastran Explicit Nonlinear - SOL 700 61Example: Projectile Hitting a Plate with Failure 65Example: Pickup Truck Crash Test 69Example – 3 Car Crash Simulation 70Where Can I Find More Information: 71

3 Numerical Enhancements

New Iterative Solver Option 74Introduction 74Benefits 74Method and Theory 74Inputs 75Outputs 75Guidelines and Limitations 76Demonstration Example 76Example Input Data 76Example Output 81

MDACMS Enhancements 83Background 83Summary 83New FMS Command: MEMLIST 83New Module: RESMOD 84Option P1 = ‘ATBC’ 86Option P1 = ‘MPART’ 86Option P1 = ‘LININD’ 87Option P1 = ‘LDSWEEP’ 88Option P1 = ‘USWEEP’ 89

MPYAD Method 1 Enhancement 90Example 90Problem Definition: 90Machine Resources 90

vContents

Improved Robustness in the Lanczos Method 91

MLDMP in Solution 111 (Pre-Release) 92User Interface 92Case Study 92

4 Elements

Three-Node Beam Element 96Introduction 96Benefits 96Input 96Guidelines and Limitations 97Formulation 99Output 101Example 103

CWSEAM Connector Elements 105Introduction 105Inputs 105Error Conditions for the CWELD and CWSEAM Elements 110Check the Angle and Find Next Candidate Element for CWELD and PARTPAT Format 111Check the CWSEAM Across a Cutout or Over a Corner with Elements in Plane

111Check the CWSEAM Over a Corner with Elements Out of Plane 114Example – A Symmetric Hat Profile (cwseam_hut.dat) 114

Line Interface Element 117Introduction 117User Interface 118Example and Results 123

Arbitrary Beam Cross-Section 126Introduction 126Benefits 126Inputs 126Output 128Guidelines 130Limitations 130Example 130


vi

5 Dynamics and Superelements

Efficiency Enhancements to MTRXIN Module for Handling DMIG Data 142

Enhancements to BSETi/BNDFIXi and CSETi/BNDFREEi Bulk Data Entry Processing 143

Enhancements to MATMOD Module Option 16 144Introduction 144Usage 145Example 145Enhancements to MATMOD Module 145

Enhancements to External Superelement Usage Via EXTSEOUT Case Control Command 149

Introduction 149Addition of Options to ASMBULK Keyword 149Addition of New FSCOUP Keyword 150Addition of New DMIGSFIX Keyword 150Automatic Numbering Scheme for Q-set DOFs Via AUTOQSET Usage 151Automatic Availability of Output for Boundary Points and PLOTEL Points of External Superelements in Assembly Run 152New MATDB Option As Equivalent to Current MATRIXDB Option 152

Changes to Rotordynamic for MD Nastran 2006 153Additional Damping Options for Rotors 153Squeeze Film Damper as Nonlinear Force 158Squeeze Film Damper as Nonlinear Element 159Gyroscopic Terms Added to Aero Solution Sequences 161Campbell Diagrams 161Rotor Forward and Backward Mode Identification 162Rotor Mode Tracking 165Comments 165Modified Basic Equations Used in Rotordynamics 166Frequency Response 167Complex Modes 169Nonlinear Transient Response 171

Exterior Acoustics 172Introduction 172Benefits 172Input 172Definition of Infinite Elements 172Definition of Field Point Meshes 175Example 175

viiContents

Case Control Commands 176Output 179Guidelines 179Limitations 180Example 180Input File 182Excerpt of fluid1.bdf 183Results 184

6 Aeroelasticity

Monitor Points 188Introduction 188Benefits 189Input 189Output 190Examples 193Guidelines and Limitations 193

Spline6/7 195Introduction 195Benefits 196Input 196

Combination of Controllers/User Input Loads Enhancements 197Introduction 197Benefits 197Input/Output 198Guidelines and Limitations 198Examples (aelinka.dat, aelinkb.dat,i3fusa.dat,aepload4.dat,fusae.dat) 198

Separate Rigid and Flexible Aero Meshes 199Introduction 199Benefits 199Input 199Output 199

Miscellaneous Aeroelastic Enhancements 201Revision in the Aerodynamic Splining to the Structure 201Flutter Analysis with Singular Mass Matrices 201

7 Optimization

Topology Optimization with Manufacturability Constraints 204


viii

Introduction 204Benefits 204Input 205Guidelines and Limitations 207

Example 1 – MBB Beam Baseline (topex3.dat) 209

Example 2 - MBB Beam with Minimum Member Size (topex3a.dat) 211

Example 3 - MBB Beam with Symmetric Constraints (topex3b.dat) 212

Example 4 - A Torsion Beam with Extrusion Constraints (topex5.dat) 214

Example 5 - A Torsion Beam with One Die Casting Constraints (topex5a.dat) 216

Example 6 - A Torsion Beam with Two Die Casting Constraints (topex5b.dat) 218

Revised Optimizer Options 220Introduction 220Benefits 220Input 220Output 222Guidelines and Limitations 222

Supporting Trust Region in SOL 200 for Adaptive Move Limits 223Introduction 223Benefits 223Theory 223Input 225Outputs 226Guidelines and Limitations 227Examples 227

Support of Analysis Model Value Overriding Design Model Value 230Introduction 230Benefits 230Input 230Output 230Example 230Guidelines and Limitations 231

ixContents

8 Miscellaneous Enhancements

Export of Static Loads 234Introduction 234Benefits 234Input 234Output 235Examples (TPL: exptld/imptld, sysmod/fbody, sfsw/ffsw) 235Guidelines and Limitations 236

Enhanced Participation Factor Results 237Introduction 237Theory 238Input 240Examples 240Example 241Example 241Output 242Example 243Guidelines 243Limitations 244Example 244Input Data 244

Total Strain Energy Output for Defined SETs 249Introduction 249Inputs 249Formats 249Examples 249Example 250Output Example 251

Model Checkout Procedures - Method to Vary Material Properties 252Introduction 252Benefits 252Method and Theory 252Inputs 252Outputs 253Guidelines and Limitations 253Demonstration Example 253Example Input Data 253Example Output 258


x


Preface

List of Nastran Books

Technical Support

Internet Resources


xii

List of Nastran BooksBelow is a list of some of the Nastran documents. You may order any of these documents from the MSC.Software BooksMart site at www.engineering-e.com.

Installation and Release Guides

Installation and Operations Guide

Release Guide

Reference Books

Quick Reference Guide

DMAP Programmer’s Guide

Reference Manual

User’s Guides

Getting Started

Linear Static Analysis

Basic Dynamic Analysis

Advanced Dynamic Analysis

Design Sensitivity and Optimization

Thermal Analysis

Numerical Methods

Aeroelastic Analysis

Superelement

User Modifiable

Toolkit

Implicit Nonlinear (SOL 600)

Explicit Nonlinear (SOL 700)

xiiiPreface

Technical SupportFor 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:

Web 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, available training courses, and documentation updates at the MSC.Software Training, Technical Support, and Documentation web page.


xiv

m.com

Phone and Fax

Email 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.

United StatesTelephone: (800) 732-7284Fax: (714) 784-4343

Frimley, CamberleySurrey, United KingdomTelephone: (44) (1276) 60 19 00Fax: (44) (1276) 69 11 11

Munich, GermanyTelephone: (49) (89) 43 19 87 0Fax: (49) (89) 43 61 71 6

Tokyo, JapanTelephone: (81) (03) 6911 1200Fax: (81) (03) 6911 1201

Rome, ItalyTelephone: (390) (6) 5 91 64 50Fax: (390) (6) 5 91 25 05

Paris, FranceTelephone: (33) (1) 69 36 69 36Fax: (33) (1) 69 36 45 17

Moscow, RussiaTelephone: (7) (095) 236 6177Fax: (7) (095) 236 9762

Gouda, The NetherlandsTelephone: (31) (18) 2543700Fax: (31) (18) 2543707

Madrid, SpainTelephone: (34) (91) 5560919Fax: (34) (91) 5567280

MSC.Patran SupportMSC.Nastran SupportMSC.Nastran for Windows SupportMSC.visualNastran Desktop 2D SupportMSC.visualNastran Desktop 4D SupportMSC.Dytran SupportMSC.Fatigue SupportMSC.Interactive Physics SupportMSC.Marc SupportMSC.Mvision SupportMSC.SuperForge SupportMSC Institute Course Information

[email protected]@[email protected]@mscsoftware.comvndesktop.support@mscsoftware.commscdytran.support@[email protected]@[email protected]@mscsoftware.comscsuperforge.support@[email protected]

xvPreface

TrainingThe 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 market. 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 PlaceSanta Ana, CA 92707Phone: (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.


xvi

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.

Simulation Center (simulate.engineering-e.com)

Simulate Online. The Simulation Center provides all your simulation, FEA, and other engineering tools over the Internet.

Engineering-e.com (www.engineering-e.com)

Engineering-e.com is the first virtual marketplace where clients can find engineering expertise, and engineers can find the goods and services they need to do their job

CATIASOURCE (plm.mscsoftware.com)

Your SOURCE for Total Product Lifecycle Management Solutions.

MD Nastran Release Guide

Ch. 1: Overview of MD Nastran 2006 Ch. 1: Overview of MD Nastran 2006Key Highlights for MD

Nastran 2006

1 Overview of MD Nastran 2006

Overview


2

OverviewThe MD Nastran 2006 release brings major new features for enterprise computing in the areas of high performance computing, nonlinear analysis, assembly modeling, optimization, rotor dynamics and aeroelasticity.

Nonlinear Analysis• Nonlinear Transient Analysis in SOL 400 - Nonlinear transient (SOL 400) extends the nonlinear

analysis capabilities of SOL 129. It features a new transient analysis solution (HHT method), adaptive time step control, SPC and MPC changes between Subcase/Step, improved nonlinear iteration performance, the new nonlinear squeeze film damper element for rotor dynamics, and expanded nonlinear iteration controls.

• MD Nastran Implicit Nonlinear - SOL 600 – The performance and capabilities of MD Nastran’s implicit nonlinear solution have been greatly improved over MSC.Nastran. These include more robust data exchange, faster contact (three to six-fold CPU time improvements), auto SPC and MSET, inertia relief, an improved out-of-core solver, expanded results support, automated brake squeal computations, improved fixed time stepping, and improved user subroutine support.

• MD Nastran Explicit Nonlinear - SOL 700 – With this new release capability you can perform crash and drop test analysis using existing Nastran models.

Numerical Enhancements• Iterative Solvers – There is now a new iterative solution for static analysis. Also, significant

performance improvements along with reduction in I/O requirements have been achieved in the ACMS solution.

Elements• Arbitrary Beam Cross-Section – The interface for describing arbitrary cross-section shapes for

bar and beam elements has been enhanced to include a cross-section outline display, stress data recovery and design optimization. The profiles can now be optimized using SOL 200. Stress recovery includes both torsion and shear terms.

• Line Interface Element – You can now connect dissimilar meshes along edges. A set of MPC (multipoint constraint) equations are internally generated to enforce the compatibility of displacements and rotations across the interface. This feature is particularly useful for global-local modeling, where a local fine mesh is required in a particular region due to high stress gradients.

• CWSEAM Connector ElementsCWSEAM Element - A seam element to connect surface patches is now available. This element extends the existing CWELD and CFAST connector elements. The seam weld is defined by selecting two surface patches by their property IDs and specifying the width and the thickness of

3CHAPTER 1Overview of MD Nastran 2006

the seam. Extensive error checking and user diagnostics include detection of missing connections for CWSEAMs, defined across corners and cutouts.RBE2GS Element – This element generates internal RBE2 element connecting a grid point pair closest to a user-defined search grid point. You can exclude optional grids within search radius.

• Three-Node Beam Element – A general spatial three-node beam element has been developed for linear static, modal, dynamic, and buckling analyses. The element is implemented as a curved one-dimensional Timoshenko beam element with initial curvatures and pre-twist. The cross-sectional warping effect is also included.

Dynamics and Superelements• Rotor Dynamics – In the MD Nastran release we introduce a new general displacement and

speed dependent nonlinear element for rotor bearings and a nonlinear squeeze film damper element. Also, we support the gyroscopic terms in aero solution sequences, non-linear harmonic response, and an easier Campbell diagram to identify rotor modes and track across subcases.

• Enhancements to External Superelement Usage Via EXTSEOUT Case Control Command – Several improvements have been made to external superelement (SE) usage employing the EXTSEOUT feature with a view to enhancing user convenience and flexibility. These include, the ability to: (a) specify suffixes for DMIG matrices resulting from the use of the DMIGPCH option, (b) get output for the boundary points and PLOTEL points of an external SE in the assembly run regardless of the output requests in the external SE creation run, and (c) have control over the Q-set or generalized degrees of freedom (DOFs) of an external SE in the assembly run.

Aeroelasticity• Monitor Points - We have added support for monitor points, including a MONPNT2 that selects

a specific element response for output, a MONPNT3 that outputs an integrated load on a structural subcomponent, and a MONDSP1 that provides averaged displacement components. All of these are available in SOLs 101 and 144, while SOL 146 supports MONPNT1 and MONDSP1.

• Export and Import of Loads -Two methods have been provided to extract loads from an analysis for import into another analysis. The EXPORTLD Case Control command supports the creation of a datablock that contains the external load of a user specified set of grids. Alternatively, one can export a “free-body” load based on the grid point forces of a user specified subcomponent. Both of these loads can be imported into a subsequent analysis via dblocate commands, and included in the external load specification.


4

Optimization• Topology Optimization with Manufacturability Constraints – This release supports

manufacturing constraints including casting (draw direction), extruding, and symmetry to ensure that the optimal size and shape determined for the given set of loads and boundary conditions conforms to manufacturing.

Summary of MD Nastran Quick Reference Guide AdditionsAdditions to the MD Nastran Quick Reference Guide to accommodate developments, improvements, and added functionality for MD Nastran 2006 are substantial. The following tables categorize these changes according to the section of the QRG affected.

Input Changes

Section New Modified

nastran Statement

NASTRAN

Executive Control

MODEL_CHECK SOL 600,IDSOL 700,ID


Case Control

AERCONFIGEXPORTLDFBODYLDMONITOR

PFGRIDPFMODEPFPANELSETPBCONTACT DEFAULT *ENDTIME *

ADAMSMNFBCONTACTEXTSEOUTDRSPAN

Bulk Data ACCACCMETR BCBODY BCBOX BCGRID * BCMATL BCPARA BCPROP BCSEG * BCTABLE BJOINBRKSQL# BSURF CBEAM3CBELT *CBUTT * CCRSFIL * CDAMP1D * CDAMP2D * CELAS1D * CELAS2D * CFILLET * CINTCCOMBWLD * CORD1RXCORD2RXCORD3RXCORD3R * CSPOT * CSPRCWSEAMD2R0000*D2RAUTO*D2RINER*DAMPGBL * DYCHANG*DYDELEM*DYPARAM * DYRELAX*DYRIGSW * DYTERMT*DYTIMHS *ENDDYNA*

EOSPOL * FBODYLDFBODYSBEGBAGMATD001 * MATD2AN * MATD2OR *MATD003 * MATD005MATD006 * MATD007 * MATD009MATD010 *MATD012 * MATD013 * MATD014 * MATD015 * MATD018 * MATD019 * MATD020 * MATD20M * MATD022 * MATD024 * MATD026 * MATD027 * MATD028 * MATD030 * MATD031 * MATD032 * MATD054 * MATD057 * MATD058 * MATD059 * MATD062 * MATD063 * MATD064 * MATD066 * MATD067 * MATD068 * MATD069 * MATD070 * MATD071 * MATD073 *

AEFORCEAELINKBCPROP#*BCTABLE#*BNDFIXBNDFIX1BNDFREEBNDFREE1BSETBSET1BSURF#*CELAS2DDESVARDRESP1IPSTRAIN#ISTRESS#ITERMATD126MATHED#MATORT#MBOLTUS#NLSTRAT#PBARLPCONVRESTART#*TSTEPNL

Input Changes



6

Bulk Data MATD074 * MATD076 * MATD077 * MATD080 * MATD081 * MATD083 * MATD087 * MATD093 * MATD094 * MATD095 * MATD097 * MATD100 * MATD119 * MATD121 * MATD126 * MATD127 * MATD181 * MATDB01 * MATDS01MATDS02MATDS03 * MATDS04 * MATDS05 * MATDS06 * MATDS07 * MATDS08 * MATDS13 * MATDS14 * MATDS15 * MATF MATRIGMONDSP1MONPNT1MONPNT2MONPNT3PBEAM3PBEAM71 * +PBEAMDPBELTD * PCOMPA * PELAS1*

PLOADB3PSHELL1 * PSHELLDPSOLIDD * PSPRMATPWSEAMRBE2ARBE2DRBE2F * RBE3D * RBJOINT * RCONN * RESTART SBPRET * SBRETR * SBSENSR * SBSLPR * SPCD2 * SPLINE6SPLINE7SUPORT6#SWLDPRMTABLEDR * TEMPB3TICD *TIC3 * TMPSETTODYNA*TTEMPUSRSUB6#WALL * WALLGEO

Input Changes



List of MD Nastran Documents Released with MD Nastran 2006Along with this Guide, the following documents are updated for the MD Nastran 2006 release.

MD Nastran 2006 Quick Reference Guide

MD Nastran 2006 Installation and Operation’s Guide

MD Nastran 2006 Implicit Nonlinear (SOL 600) User’s Guide

MD Nastran 2006 Explicit Nonlinear (SOL 700) User’s Guide

Input Changes


Parameters CWLDIGNR*DYDTOUT,DT*DYDYLOAD*DYELAS1C,*DYELAS1F,*DYELAS1R,*DYELPLET,*DYELPLFL,*DYELPLSY,*DYSTEPFCT,,#HEATCMD#MARCBATCH#MARCBUSH#MARCITER#

MARCCBAR#*MARCRCID#MARGPFOR#MEXTRNOD#MLSTRAIN#MRBEPARM,#MRCOMPOS#MRCONVER#MRPSHELL#MSPEEDOU#SCALEMAS,*STEPFCT*

MARCAUTO#MARCOTIM#MARCPINN#MARCPOST#MARCRBE3#MARCSAME#MARCSLHT#

MARCSOLV#MARCUSUB#MRESTALL#MRMAXMEM#MRSPAWN2#MRSPEEDSE#MRTABLS2#MRTABLS1#

Items with a pound sign (#) next to them are only available for MD Nastran Implicit Nonlinear (SOL 600). Items with an asterisk (*) sign next to them are only available for MD Nastran Explicit Nonlinear (SOL 700). See the individual parameter for further details. + PBEAM71 has three alternates, please see the MD Nastran Quick Reference Guide for more information.


8


+ Ch. : h0title Ch. 2: Nonlinear Analysis Ch. 2: Nonlinear Analysis

2 Nonlinear Analysis

Nonlinear Transient Analysis in SOL 400, 10

MD Nastran Implicit Nonlinear - SOL 600, 44

MD Nastran Explicit Nonlinear - SOL 700, 60


10

Nonlinear Transient Analysis in SOL 400

IntroductionNonlinear transient analysis in SOL 400 improves the general nonlinear solution procedure in MD Nastran. It allows most linear files to be run in a nonlinear analysis environment, and includes the nonlinear solution types:

• SOL 106, nonlinear static analysis (Prerelease)

• SOL 129, nonlinear transient analysis

• Rotor Dynamics

It will eventually include:

• SOL 153, steady heat transfer

• SOL 159, nonlinear heat transfer

• Nonlinear normal modes analysis

• Nonlinear buckling analysis

Different types of nonlinear analysis can now talk to each other in a meaningful physical sequence.

For the MD Nastran 2006 release, nonlinear transient analysis is now considered a product release for SOL 400. However, the nonlinear static analysis still remains a pre-release.

In this release guide, all items pertaining to the nonlinear transient analysis are discussed. For nonlinear static analysis, only items pertaining to the transient analysis are discussed. These include the SUBCASE and STEP Case Control command and the static pre-loads.

BenefitsThe benefits of the nonlinear transient analysis in SOL 400 are discussed in this section. Some of the benefits may be subject to the limitation discussed in next section. The benefits are:

• A new transient solution integration method, the HHT (Hilbert-Hughes-Taylor) method, to give stable transient solution.

• Improved nonlinear iteration algorithms to make the solution easier and faster to converge. These includes ADAPT, AUTO, ITER, and SEMI methods.

• A new SUBCASE and STEP case control structure allows flexible loading and solution sequences. Different nonlinear analysis types can now communicate with each other in a meaningful physical sequence in a SUBCASE.

• A new comprehensive nonlinear summary table for the transient analysis.

• Support of the initial conditions (IC).

• A new control command NLIC allows any previous converged nonlinear static solution as the preload for the first nonlinear transient step.

11CHAPTER 2Nonlinear Analysis

• The boundary conditions SPC and MPC can change between load steps.

• Direct matrix input, such as K2PP, M2PP, B2PP, and TFL, can change between load steps.

• Support for “grid based reordering” for a faster version of decomposition for time step size change and stiffness update in the nonlinear iterations.

• Support the nonlinear thermal loads in the transient analysis. Two new Bulk Data entries, TTEMP and TMPSET, have been added for this new feature in the nonlinear transient analysis.

• Support for rotor dynamics in the nonlinear transient analysis.

• A user-friendly restart procedure introduced earlier is available to nonlinear transient analysis.

• A more flexible output method for the nonlinear transient analysis. You can use a new parameter NLPACK to control the output and restart time steps.

• Solution output at requested time points. Also, allows the simulation of the same output logic and format of SOL 129 by specifying a negative NO on the TSTEPNL Bulk Data entry.

• Supports linear superelements.

• Supports the XDB database for communicating with a post processor, such as MSC.Patran.

• The OTIME output request is supported (except NLSTRESS).

Limitations for the Current ReleaseThe following are limitations for the current release of the nonlinear transient analysis.

• RFORCE – RFORCE was supported in old SOL 99. In SOL 129, the RFORCE must be used in conjunction with an old SOL 99 iteration method. In this release of SOL 400, RFORCE is not supported.

• Omitted degrees-of-freedom (o-set).

• Slide line contacts.

• The XDB database is not supported for restarts. XDB can be used only for non-restart cases in SOL 400 to communicate with post-processors such as MSC.Patran. For restart cases, use OP2 instead.

• For SOL 400 nonlinear transient analysis, the Case Control command RIGID=LINEAR is set automatically by MD Nastran.

These limitations will be addressed in a future release.

A New Numerical Integration Method – HHTTo solve the equation of motion for a nonlinear transient analysis, two aspects must be resolved. The first is how to integrate the equation of motion for the transient analysis and second is how to obtain an equilibrium solution for the nonlinear analysis. This section discusses the numerical integration of the equation of motion and the next section will discuss the nonlinear iteration methods for obtaining the balanced solution.


12

For numerical integration, the second order HHT (Hilbert-Hughes-Taylor) method is used in nonlinear transient analysis in SOL 400. It provides a user-definable parameter α, which defines a numerical damping associated with higher frequency modes, but also maintains the accuracy in the essential lower frequency modes. Since it is a key feature of the HHT method, it is sometimes called the HHT-α method.

When , numerical damping is introduced into the system. This leads to an unconditionally stable integration time scheme when it is in the following range

When comparing with other numerical damping methods even at (the maximum numerical damping value), the HHT method still introduces less damping. Therefore, the solution is more accurate theoretically. Note that when , this method is equivalent to the central finite difference method.

The numerical damping, , can be specified using parameter NDAMP (default is -0.05 in SOL 400).

Parameter NDAMP is used in Example 1 and Example 7.

Nonlinear Iteration AlgorithmsThis section discusses the nonlinear iteration algorithm used in SOL 400 to obtain an equilibrium solution for the nonlinear transient analysis.

In SOL 400, the equilibrium solution is achieved by a combination of the following methods:

• Time step size adjustment – At the beginning of a SUBCASE or at the convergence of a time step, the time step size is adjusted based on the estimated current natural frequency of the structural model or the input loads.

• Load iteration – At each time step, the quasi Newton method and line search technique are employed repeatedly to obtain the balance of internal forces and external loads. This is called the load iteration or simply the iteration. The time step is converged when the balance of internal forces and external loads is obtained. You can deselect the quasi Newton method or the line search by using parameter in the TSTEPNL Bulk Data entry. When the quasi Newton method is deselected, the solution scheme becomes the modified Newton method.

• Stiffness update – In many situations, the load iteration will not be able to achieve equilibrium at a time step. In this situation, the stiffness matrix can be recomputed using the current geometric and material state of the structure model to facilitate convergence. This is called the stiffness update. Consecutive stiffness updates without load iteration is called the full Newton method.

• Bisection – When the program reads that it is impossible for the solution to converge, a procedure called divergence processing is employed. One technique used in this procedure is bisection. Bisection means cutting the time step size or load increment size by half. Divergence processing uses a combination of stiffness updates and bisections to facilitate convergence.

Externally, bisection and time step adjustment are similar. However, they are initiated due to different reasons. Time step adjustment is based on the requirement of the natural frequency of the structure, which may or may not be nonlinear. Bisection is, on the other hand, due to large nonlinearity in the solution.

α 0<

13---– α 0≤ ≤

α 1 3⁄–=

α 0=

α


Another difference is that the time step adjustment is performed at the beginning of a SUBCASE or at a converged time step. Bisection is performed during a time step when the program determines that the solution is diverging.

When the program determines that the large nonlinearity is gone and the solution is stabilized toward convergence, reversal of the bisection is performed in order to maintain the time step size required by the time step adjustment method given above.

The METHOD field on the TSTEPNL Bulk Data entry selects the nonlinear iteration method. There are four options available.

• ADAPT – The convergence of a time step is obtained chiefly by the time step adjustment and the load iteration. No stiffness update is performed during the normal iteration. Stiffness updates are performed only for divergent processing and at solution convergence of a time step with number of iterations greater than 3*MAXITR. MAXITR is the maximum number of iterations given on the TSTEPNL Bulk Data entry. Even for divergence processing, the main method to correct the divergence is bisection.

• AUTO – The convergence of a time step is achieved by automatically selecting the load iterations and the stiffness updates, in combination with the ADAPT method. The ADAPT method can be deselected by setting ADJUST=0 on the TSTEPNL Bulk Data entry. This is the default method. For divergence processing, the divergence is corrected by a combination of stiffness updates and bisections. The AUTO method always tries to maintain the time step size required by the time step adjustment method.

• ITER – The convergence of a time step is achieved by performing a stiffness update at every KSTEP load iterations, in combination with the ADAPT method. Again, the ADAPT method can be deselected by setting ADJUST=0. When KSTEP=1, this is the full Newton method. The divergence processing is the same as that of the AUTO method.

• SEMI – Same as the AUTO method, except that a stiffness update is performed at first iteration of a new time step.

A stiffness update is always performed at convergence of a STEP, irrespective of the option selected.

AUTO and ADAPT are two major methods in SOL 400. The AUTO method tries to maintain the time step size required by the time adjustment method or the user time step. The ADAPT method usually converges with a time step size smaller than the time step required by the time step adjustment method or the user time step. For most problems, AUTO method gives better solutions; therefore, it is selected as the default method. However, if the time step estimated by the time step adjustment method or the user time step is too large, the ADAPT method gives a better solution. A better solution here means that the solution converges faster or does not diverge.

The DT and NO fields on the TSTEPNL Bulk Data entry need more explanation here. The DT field defines the user time step size. NO, which may be positive or negative, defines that, at every |NO| time steps, the results are saved for output. Since both time step size adjustment and bisection may modify the time step size, options are given to select whether to output at user time step size DT or at internally computed time step size, as shown in the following:


14

If NO > 0, the output will be at the user time step size or multiples of the user time step size. Also, the time step size computed by the time step adjustment will never be greater than the user time step size DT. For default, NO = 1.

If NO < 0, the output will be at the internally computed time step size, which may or may not be at the user time point determined by DT. Also, the time step size computed by the time step adjustment can be either greater or less than the use time step size DT.

Case Control Structure – SUBCASE, STEP, ANALYSIS, and NLICThe STEP command has been expanded to support nonlinear transient analysis for SOL 400 only. You can specify the type of analysis for each SUBCASE and STEP by using the Case Control command ANALYSIS. ANALYSIS supports three keywords for SOL 400. LNSTATIC, NLSTATIC (the default), and NLTRAN. A new Case Control command, NLIC is also introduced in this version. It selects the initial condition from a previous static analysis. The combination of SUBCASE, STEP, ANALYSIS, and NLIC commands provide a mechanism for defining the multiple load steps, running multiple independent cases, and specifying multiple (and mixed) types of analyses in one job.

The following examples illustrate the manner in which the SUBCASE, STEP, and ANALYSIS commands are used.

• With one SUBCASE and multiple steps, each step defines the total new 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 omittedANALYSIS = NLTRAN

TSTEPNL = 200STEP 10

DLOAD = 10STEP 20

DLOAD = 20STEP 30

DLOAD = 30

• Multiple SUBCASEs may be executed in one job where the types of analysis, loads and boundary conditions can be changed. All SUBCASEs are independent of each other, i.e., no load history information is transmitted from one SUBCASE to the next. At the start of each SUBCASE, the deflections, stresses and strains throughout the model are zero. For example:

SUBCASE 1ANALYSIS = NLSTAT $ This line can be omittedNLPARM = 100STEP 110

LOAD = 110STEP 120

LOAD = 120


SUBCASE 2ANALYSIS = NLTRANTSTEPNL = 200STEP 210

DLOAD = 210STEP 220

DLOAD = 220

• In the above example, the solutions of SUBCASE 1 and SUBCASE 2 are independent of each other. If solution divergence is detected in a step, MD Nastran will terminate the solution of the current subcase and jump to the next subcase if it exits.

• A case control command placed below the step level allows that command to vary from one step to another. If it is placed above the step level, the command remains constant 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.

• The SOL 400 uses an enhanced dynamic solution algorithm that makes the linear static solution and the nonlinear static solution special cases of the general nonlinear solution procedure. For example:

SUBCASE 10STEP 1

ANALYSIS = LNSTATICLOAD = 10

STEP 2ANALYSIS = NLSTATICLOAD = 20NLPARM = 20

In above example, SUBCASE 10 has two steps. The first step requests a linear static analysis and the second step requests a nonlinear static analysis.

• In the MD Nastran release, NLSTATIC and NLTRAN analyses can be mixed in a single SUBCASE. For example:

SUBCASE 10STEP 1

ANALYSIS = NLSTATLOAD = 10NLAPRM = 110

STEP 2ANALYSIS = NLSTATLOAD = 20NLPARM = 120

STEP 3ANALYSIS = NLTRANDLOAD = 30TSTEPNL = 130


16

In the above example, SUBCASE 10 has three steps. The first two request a nonlinear static analysis and the third requests a nonlinear transient analysis. Since there is no NLIC request in the third step, the final result of the second step automatically becomes the initial condition of the third step. Note that in one SUBCASE, all steps of NLSTAT must come before the STEPs of NLTRAN.

• The meaning of multiple SUBCASEs without STEP is dependent on the system cell NASTRAN SYSTEM (366), as follows:

• 0 - The solutions of all SUBCASE are independent of each other. This is consistent with the new SOL 400 procedure. MD Nastran will keep all SUBCASE commands in the Case Control file and insert internally a “STEP 1” for each SUBCASE.

• 1 - The solution of each SUBCASE is a continuation of the previous SUBCASE. This is similar to the solution sequence SOL 129 procedure. MD Nastran will convert internally all the SUBCASE identification number to STEP identification number and insert a “SUBCASE 1” before the first STEP.

The default is 0.

Both SUBCASE and STEP are used in Examples 1, 2, 3, 4, 5, 7, and 8. SUBCASE only is used in Example 9. No SUBCASE and no STEP are used in Example 6.

Vector Operations and Convergence CriteriaThe convergence criteria are specified using the Bulk Data entry TSTEPNL in the nonlinear transient analysis. In performing the convergence tests, three error factors are computed: the displacement, the load, and the work (energy) error factors, which are printed in the Nonlinear Iteration Summary Table. These three error factors must satisfy the error tolerance rules specified by CONV, EPSU, EPSP, and EPSW on the Bulk Date entry TSTEPNL.

In computing the error factors, SOL 129 used the d-set vectors for displacements and forces. By using this method, the effect of SPC loads and MPC constraints are accounted for only indirectly. Also, there are difficulties to account for the effect of Lagrange multipliers for the Lagrange rigid elements. For these reasons, in SOL 400, whenever possible, the matrix and vector operations, which include the computations of error factors, are performed in p-set (the physical set). For MD Nastran set definition, refer to the Degree-of-Freedom Set Definitions (p. 940) in the MD Nastran Quick Reference Guide.

Another major modification is the computation of the work error. In SOL 129, the work error is based on the multiplication of the residual force and the displacement change. During iteration, both the residual force and the displacement change become smaller; therefore, the convergence rate of this value is proportional to the square of the convergence rate of the solution. Thus it becomes very small near convergence. Also, it does not have a counter part in the physical world. In SOL 400, the total work done to the structure model is computed at each iteration and the work error is estimated based on the total work. In this way, the work error gives an estimation of the error in the actual work done to the structural model. The total work for each iteration is printed on the Nonlinear Iteration Summary Table. Please note that this total work is only an approximation.


Nonlinear Iteration Summary Table for Nonlinear Transient Analysis in SOL 400In order to track the solution sequence during the nonlinear iteration, a detailed Nonlinear Iteration Summary Table is output. A line for each iteration is output on the F06 file. Printing of the average and the maximum displacements allows you to know the solution status before the end of the job. This is useful for large nonlinear problems. Even for small problems, you will be able to know approximately how the analysis of a structural model is performing by examining this table. An example of this table is given below.

0 N O N - L I N E A R I T E R A T I O N M O D U L E O U T P U T

STIFFNESS UPDATE TIME 0.01 SECONDS SUBCASE 1 STEP 1 ITERATION TIME 0.00 SECONDS

- TIME STEP - - - ERROR FACTORS - - CONV ITR MAT AVG TOTL - - - - - DISP - - - - - - NO. TOT TOT TIME NO. BIS ADJUST ITR DISP LOAD WORK RATE DIV DIV R_FORCE WORK AVG MAX AT GRID C QNV KUD ITR

1.10800E-02 1108 0 1.0000 2 8.58E-07 3.52E-03 2.40E-08 0.01 0 1 6.6E+01 3.451E+00 1.61E-03 -8.120E-03 103 3 7 0 2202 1.10900E-02 1109 0 1.0000 2 8.81E-07 3.65E-03 2.25E-08 0.01 0 1 6.8E+01 3.462E+00 1.61E-03 -8.134E-03 103 3 7 0 2204 1.11000E-02 1110 0 1.0000 2 9.02E-07 3.77E-03 2.07E-08 0.01 0 1 7.0E+01 3.473E+00 1.61E-03 -8.147E-03 103 3 7 0 2206 1.11100E-02 1111 0 1.0000 2 9.21E-07 3.89E-03 1.88E-08 0.01 0 1 7.2E+01 3.484E+00 1.61E-03 -8.160E-03 103 3 7 0 2208 1.11200E-02 1112 0 1.0000 2 9.40E-07 4.01E-03 1.66E-08 0.01 0 1 7.4E+01 3.495E+00 1.62E-03 -8.173E-03 103 3 7 0 2210

Table 2-1 Information in Nonlinear Iteration Summary Table

TIME The Current Time. Starts from 0.0 at the beginning of the 1st STEP and accumulate the value until at the end of the last STEP.For each STEP, the total time is determined by NDT and DT on TSTEPNL Bulk Data entry.

TIME STEP NO Number of time step, including bisection. Initialized to 0 in the beginning of each STEP.

TIME STEP BIS Number of bisections performed.

TIME STEP ADJUST The ratio of the current time increment to the original DT on TSTEPNL Bulk Data entry.

ITR Number of iteration at each time increment.

ERROR FACTORS:DISPLOADWORK

There are three error factors: displacement, load, and works. In order for an increment to converge, these factors must satisfy the error tolerance rules specified by CONV, EPSU, EPSP, and EPSP on the TSTEPNL Bulk Data entry.

CONV RATE Converge rate, which denote how fast the solution converges for the current increment. A value of 0.0 means fast converges and a value > 1.0 means that the solution will never converge.

ITR DIV Number of iteration divergences. Action to correction solution divergence will be taken if ITRDIV > MAXDIV.


18

For a large problem, TIME STEP NO,l TOT KUD, and TOT ITR in this table may be too large to be printed in the allocated fields, resulting in print overflow. If any of these values overflows, an additional line is printed to show the offsets of these values. In the table below, TOT ITR of the first line is 111764. The offset of TOT ITR is shown as TOT ITR= 110000+XXX, where XXX is the number shown under the TOT ITR column.

Output Data Grouping: NLPACKFor the nonlinear transient analysis of a large problem with short time steps, the amount of data to be stored in the database will be huge if we do not devise some schemes to group the output data. Data grouping will save CPU time, IO time, and disk space to store the database. Another advantage is that, for a large problem, if an accident happens in the middle of a run, you can salvage the data for later restart.

There are two types of data required to be saved - output and restart data

• Output data – these are displacements, stresses, and strains, etc. at each output time step to be printed on the f06 file or plotted by the post processors. They are controlled by the NO field on the TSTEPNL Bulk Data entry. For this type of data, we output them as requested by the user.

MAT DIV Number of material divergence + 1, i.e., it will be 1 if there is no material divergence. Material divergence is due to bad creep strain or excessive sub-increments in plasticity.

AVG R_FORCE Average residual force. In order for a time step to converge, this value must become very small.

TOTAL WORK Accumulated total work done to the structure model. This value is only an approximation.

DISPAVGMAX AT GRID C

The average displacement, the maximum displacement and its grid point identification number and component number.

NO. QNV Number Quasi Newton vectors stored and used.

TOT KUD Total number of stiffness updates performed.

TOT ITER Total number of iterations performed, including the number of stiffness updates and time steps.

Table 2-1 Information in Nonlinear Iteration Summary Table

0 N O N - L I N E A R I T E R A T I O N M O D U L E O U T P U T

STIFFNESS UPDATE TIME 0.01 SECONDS SUBCASE 1 STEP 1 ITERATION TIME 0.00 SECONDS TIME STEP NO.= 20000 TOT KUD= 0 TOT ITR= 110000

- TIME STEP - - - ERROR FACTORS - - CONV ITR MAT AVG TOTL - - - - - DISP - - - - - - NO. TOT TOT TIME NO. BIS ADJUST ITR DISP LOAD WORK RATE DIV DIV R_FORCE WORK AVG MAX AT GRID C QNV KUD ITR

2.99820E-01 9982 0 1.0000 4 3.99E-08 5.61E-04 2.24E-09 0.03 0 1 6.0E2.386E 7.32E-02 -1.860E-01 101 3 10 0 1764 2.99830E-01 9983 0 1.0000 4 4.04E-08 5.77E-04 2.25E-09 0.03 0 1 6.1E2.386E 7.32E-02 -1.861E-01 101 3 10 0 1768 2.99840E-01 9984 0 1.0000 4 4.10E-08 5.93E-04 2.26E-09 0.03 0 1 6.3E2.385E 7.32E-02 -1.862E-01 101 3 10 0 1772 2.99850E-01 9985 0 1.0000 4 4.15E-08 6.09E-04 2.27E-09 0.03 0 1 6.4E2.385E 7.32E-02 -1.863E-01 101 3 10 0 1776 2.99860E-01 9986 0 1.0000 4 4.20E-08 6.26E-04 2.27E-09 0.03 0 1 6.6E2.385E 7.32E-02 -1.865E-01 101 3 10 0 1780


• Restart data – these are used to described the material and geometric state of the structure model. We use them to reconstruct the stiffness, the mass, the damping matrices and other tables required in later usage. Restart data are usually much larger than the output data if the structural model is large. This type of data can be saved selectively without degrading the effectiveness of the transient analysis.

For this purpose, in the current release, a user modifiable parameter: ‘PARAM, NLPACK,N’ is available. N means that SOL 400 will pack output data for N output time steps and restart data for the last time step as a single data package. For example, if N = 100 (the default), then one data package has output data for 100 output time steps and restart data for the last time step. Later usage, such as restart or initial condition for later step, can be performed only at NLPACK data group boundaries.

Some N’s have special meaning

• N = -1, all output data for a STEP and restart data for the end of the STEP are grouped into a single package. This is the SOL 129 grouping method. In this case, the restart can be performed only at STEP boundaries.

• N = 0, this is illegal.

• N = 1, each package of data on the database includes the output data for one output time step and restart data. This is the NLSTATIC grouping method. Therefore, for the nonlinear static analysis, the restart can be performed at each user output load increment, which is controlled by INTOUT on the NLPARM Bulk Data entry.

NLPACK is used in Example 1.

RestartsA nonlinear restart allows you to use the material or the geometrical properties of a previously converged solution as a new starting point to continue the analysis. This is useful when you want to change your loading sequence, the solution criteria, or to extend the analysis.

For SOL 400, a user-friendly restart procedure for the nonlinear static pre-release is available. For nonlinear transient analysis, the following principles are noted.

• The restart must be continued at a previous converged solution point in a nonlinear transient analysis or a static analysis by specifying a SUBCASE, STEP, and/or TIME (LOADFAC). This is accomplished by using the Case Control command NLRESTART. Refer to the Case Control Command Descriptions (p. 196) in the MD Nastran Quick Reference Guide.

• When the cold start is ANALYSIS=NLSTAT, it can be restarted at any user-specified output load increment (controlled by NOUT in NLPARM Bulk Data entry).

• When the cold start is ANALYSIS=NLTRAN, it must be restarted from a saved or check-pointed time step. The checkpoint times are dependent on DT and NO values on the TESTEPNL Bulk Data entry, and PARAM, NLPACK of the cold start run. The checkpoint times are integer multiples of (DT x NO) x NLPACK. For example, if DT=0.001 second, NO=10, and NLPACK=100, the possible times that can be used for restart are at 1.0, 2.0, etc... If a requested restart time does not match a checkpoint time, the closest checkpoint time will be used


20

• The geometry and the initial material properties of the structural model cannot be modified. This is obvious because any modification to the geometry or the initial material properties would invalidate the previous analysis and require the nonlinear solution to start from the very beginning. In such cases, it is simpler to initiate another cold start.

Performing a restart is described in the following sub-sections.

File Management Commands

For a restart, the data of the cold start must be made available by using the File Management commands. For nonlinear restart, two commands are needed: ASSIGN and RESTART. These two commands are existing commands and no special requirements are needed for SOL 400.

There are many methods to retrieve data for a restart. One method is given in the example below. For other methods, refer to the File Management Statement Descriptions (p. 37) in the MD Nastran Quick Reference Guide or Chapter 12 of the MD Nastran Reference Manual.

Case Control Modifications

The presence of a Case Control command NLRESTART indicates that the current run is a restart execution. The Case Control file contains both subcases and steps, which have been executed in the cold start, and those that are to be executed in the restart. The first subcase, step and/or load factor to be executed in the restart is indicated by the options on the NLRESTART command. This is shown in the following example.

NLRESTART SUBCASE 1, STEP 2, TIME 0.3SUBCASE 1

STEP 1LOAD = 10

STEP 2LOAD = 20

STEP 3LOAD = 30

In the above example, the first STEP through time 0.3 of the second STEP has been previously executed. The restart execution begins with time 0.3 of the second STEP, and continues through the end of the third STEP. If time 0.3 is not a restart point saved by NLPACK on the cold start, SOL 400 will search for the nearest restart point on the data base and use that point to begin the restart. For restart, the Case Control file structure for SUBCASE and STEP commands must be the same as the cold start up to the restart point. After the restart point, you may modify the Case Control file structure for SUBCASE and STEP commands. For example, in above example, STEPs 1 and 2 must exist in the cold start. However, STEP 3 may or may not exist in the cold start.

The following Case Control commands may be modified in a nonlinear restart:

• Boundary conditions such as MPC and SPC.

• Nonlinear solution control, NLPARM.

• The LOAD requests.

• Output request such as DISP and NLSTRESS.


• The analysis type ANALYSIS.

Depending on the option selected with the NLRESTART command, the nonlinear restart may be logically divided into three types: a case restart, a step restart, or a time restart:

The case restart begins the execution with a SUBCASE. All five types of modification described above are legal for a case restart.

The step restart begins the execution with a STEP, which may be a new step or a previously executed step. Although boundary condition and analysis type modifications are allowed, you have the responsibility to determine whether they are meaningful. Special attention should be given to the analysis type modification; it may not be meaningful in many situations and could lead to erroneous results.

The time restart begins execution with a user-specified TIME. For a time restart, you should not modify the analysis type, boundary conditions, or load requests. You need to exercise discretion when attempting other types of modification at this level. Also, in order to perform this type of restart, the specified TIME must be at the NLPACK data group boundary. If it is not, SOL 400 will search for the nearest data boundary and use this boundary as the restart point.

Bulk Data Modifications

The Bulk Data file for a nonlinear restart contains only those entries that are to be added to the cold start. The deletion Bulk Data entry “/” cannot be used. This is to serve as a reminder that the geometry and the initial properties cannot be modified. You may make modifications to the Bulk Data file by introducing new entries, which may be copies of the original entries with appropriate changes and new identification numbers. The following list of entries can be added in a restart.

• Load entries such as LOAD, FORCE, PLOAD4, and SPCD.

• NLPARM entries.

• Boundary condition entries such as SPC, SPC1, and MPC.

Examples for cold start and restart are given in Example 4 and Example 5.

Initial ConditionsIn SOL 400, the traditional way of requesting initial conditions by using the Case Control command, IC, and its associated Bulk Data entry, TIC, to assign initial displacements and velocities is supported.

In the current release, a user-friendly interface to define initial condition is implemented. This is the new Case Control command NLIC. It allows users to assign the result of any previous STEP of NLSTAT analysis as the initial condition for the first STEP of NLTRAN analysis in a SUBCASE. The following is an example:

SUBCASE 10STEP 1

ANALYSIS = NLSTATLOAD = 10NLAPRM = 110


22

STEP 2ANALYSIS = NLSTATLOAD = 20NLPARM = 120

STEP 3ANALYSIS = NLTRANNLIC STEP 1 LOADFAC 0.5DLOAD = 30TSTEPNL = 130

Now, the 3rd STEP will use the result of the 1st STEP at 50% load increment as the initial condition. Please note that the NLIC can only be defined at a load increment whose output flag is on - an available restart point in static analysis. Otherwise, a fatal error message will be issued and job will be terminated. Here, SOL 400 will not search for the nearest available restart point, because we want you to know the precise restart point.

In above example, if ‘LOADFAC 0.5’ is left out, then STEP 3 will take last state of STEP 1 as its initial condition. In this case, the job will always run because the last state of a step is always a restart point.

For NLIC, there are some rules and limitations:

• SOL 400 requires that all STEPs’ of NLSTAT must be located before all STEPs’ of NLTRAN. In other words, analysis change can only occur once between NLSTAT and NLTRAN in one SUBCASE.

• In one SUBCASE, the beginning time of a transient STEP will be reset to 0.0 when the analysis type is changed from a static STEP to transient STEP (or NLIC Case Control command is detected).

• If you do not specify a NLIC entry when the analysis type changes from NLSTAT to NLTRAN, the final result of the last STEP of NLSTAT will be picked up as the initial condition.

• The NLIC (or IC) can only appear in the first transient analysis STEP (ANALYSIS=NLTRAN) in a SUBCASE. Otherwise, it will be ignored.

• The new Case Control command NLIC can only specify restart-able NLSTAT location as the initial condition. (Please read the Restart section for the definition of “Restart-able”.)

• It is not allowed to use NLIC to select the initial condition from any previous STEP of NLTRAN, SOL 400 will issue a fatal error message and you should run a restart job instead.

• In the same STEP, the NLIC cannot appear together with an IC. A fatal error message will be issue when NLIC and IC appear in the same STEP.

• The NLIC can only be used in SOL 400 (NONLIN).

Parameter ICOPT is used with the NLIC and IC Case Control commands. At the beginning of a NLTRAN step, the user input loads may or may not be in equilibrium with the results of the previous preload step. When ICOPT = 0, SOL 400 will compute the initial acceleration based on your’s inputs. Otherwise, it will be assumed that the initial acceleration is null. In other words, when ICOPT = 1 (the default), it is assumed that the whole structure is in equilibrium automatically. Theoretically, ICOPT = 0 gives better performance in the iteration algorithm since it guarantees the equilibrium in the beginning to avoid a suddenly jump of loads or displacements. The drawback of ICOPT = 0 comes from the


characteristics of the mass matrix itself, whose inverse matrix is required when computing the initial acceleration. The mass matrix is usually highly singular for a ‘lumped’ mass matrix or for a model with only solid 3D elements, a large amount of CPU times may be required and the accuracy of the result may be in doubt.

An alternative way to resolve the problem of ICOPT = 1 with a suddenly large jump of loads or displacements is to insert a NLTRAN step in between the analysis step and its previous preload step. This step will have very short time duration in comparison with the analysis step and will provide a transition between the preload step and the analysis step.

NLIC is used in Example 4 and Example 5. ICOPT is also used in these two examples.

Transient Temperature LoadsA new capability, which has never been supported in the original nonlinear transient analysis (SOL 129), is added into SOL 400 when ANALYSIS=NLTRAN. It is the time-dependent dynamic thermal effect, which is applied to all the nonlinear elements in the residual.

The time-dependent thermal-elastic equation can be written as follows

(2-1)

where

For all nonlinear elements, the temperature effect, in both static and transient, is directly handled as thermal strain in SOL 400 when computing the element forces.

To support the thermal effect in nonlinear transient analysis, two new bulk data entries have been created in the MD Nastran release. They are TTEMP and TMPSET. Basically, TTEMP is to define a time-dependent dynamic thermal field, , which includes a spatial temperature distribution (TMPSET) and a time function (TABLEDi), in the same form as TLOAD1. TMPSET defines the spatial distribution by referencing a set of grid points. The temperatures of these grid points are defined by TEMPD,

TEMP, TEMPP1, or TEMPRB in the normal way. Please see the Bulk Data Entry Descriptions (Ch. 8) in the MD Nastran Quick Reference Guide, for the details of these two new bulk data entries. By using TTEMP and TMPSET, the whole model can be separated into finite sub-regions and each sub-region can have its own temperature distribution pattern. If it is necessary, you can also make every grid point as an independent sub-region or make the whole model as a single sub-region.

= The thermal strain,

= The current temperature is defined in the following equation

is the temperature field and is the time function,

Tref = The reference temperature,

T0 = The stress free temperature (initial temperature), and

= The coefficient of thermal expansion.

εT t( ) α T t( )( )= T t( ) Tref–( )⋅ α T0( )– T0 Tref–( )⋅

εT t( )

T t( )T t( ) Tp f t( )=

Tp f t( )

α T( )

T t( )

Tp( )


24

As in nonlinear static analysis, TEMP(INIT) and TEMP(LOAD) commands are used in the Case Control file to define the temperature input in nonlinear transient analysis. The SID of TEMP(LOAD) can refer to TTEMP to define the transient temperature load for a STEP. The spatial temperature distribution defined by TEMP, TEMPD, etc., must have the same SID as that of the associated TTEMP. If TEMP(INIT) refers to TTEMP entry, only the spatial temperature distribution of the entry is used and the time function is ignored.

The Case Control command TEMP(LOAD) can also refers to a spatial distribution (TEMP, etc.) directly without TTEMP. In this case, the temperature time functions are linearly interpolated for the current step by using the last values of the previous step and the values of the spatial distribution referenced by the TEMP(LOAD) command. For the first step of a subcase, the interpolation is performed between the TEMP(INIT) temperature and the current temperature.

The thermal effects computed by the above method depend on the current material state and geometric shape of the structural model. Therefore, they are called the ‘nonlinear’ transient temperature loads.

For all upper stream superelements and all linear elements in the residual, the thermal effects are computed using the conventional method – you can use the DLOAD Bulk Data entry to combine multiple TLOAD1 and TLAOD2’s, whose EXCITE_ID reference thermal loads. The DLOAD Bulk Data entry must be referenced by a DLOAD Case Control command to be selected for analysis. The transient temperature loads computed by this method depend on the initial stiffness matrix only and are called the ‘linear’ transient temperature load. The TEMP(LOAD) and all its corresponding temperature related bulk data entries introduced above can only describe the thermal effect for the nonlinear elements in the residual. If there is no DLAOD Case Control command to select the temperature load for the linear temperature load, the temperature effect for the linear part of the structure will be lost.

An example for the temperature load is given in Example 3.

Boundary Condition (SPC and MPC) ChangesIn SOL 400, the SPC and MPC are allowed to change from one step to next. This is accomplished by placing the SPC or MPC case control command below step level.

However, it should be noted that SPC or MPC change requested below step level affect only the delta (incremental) displacements for the specific step. For example, if we add a SPC request on a grid point in STEP 2 of a subcase, the displacements of this grid will be kept constant in STEP 2 and equal to the final displacements of STEP 1. This means that the delta displacements of the grid for STEP 2 are zero because the SPC request in STEP 2, and the total displacements of STEP 2 is equal to the final displacements of STEP 1. The same principle is also applied to MPC requests below step level.

An example for boundary condition changes is given in Example 8.

Direct Matrix Input ChangesIn SOL 400, the direct input matrices, K2PP, M2PP, B2PP and TFL, are allowed to change between steps. This is accomplished by the placing these case control commands below step level.


An example for the direct matrix changes is given in Example 7.

OutputsThe outputs are requested by using the Case Control commands. All existing output Case Control commands such DISPLACEMENT, VELOCITY, ACCELERATION, STRESS, NLSTRESS, OLOAD, SPCFORCE, etc., are also allowed in the nonlinear transient analysis in SOL 400.

Two special outputs, “Nonlinear Iteration Summary Table” and “PARAM, PH2OUT”, are available for nonlinear transient analysis in SOL 400. In addition, a new output control, “PARAM, NLPACK”, is added for the current release for nonlinear transient analysis only.

This new parameter, NLPACK (=100 is the default), is used to control the packed output in SOL 400. The value of NLPACK represents the total number of output time steps in one output package. SOL 400 will process the output procedure only after collecting all "NLPACK" output time steps or at the end of each STEP. For details, please see Output Data Grouping: NLPACK, 18.

Because the matrix and table trailers output volume may be extremely high, the diagnostic output requests of DIAG 8 and DIAG 15 have been turned off automatically when preparing the output data in the solver of SOL 400 if NLPACK 1. This action can reduce the .F04 file output size tremendously, especially, when there is a large output time steps requested. You can force them on by setting DIAG 56 but it is not recommended.

Error HandlingIn SOL 400, there are three types of fatal errors:

• User or system fatal errors.

• Fatal errors due to solution divergence

• Fatal errors due to lack of CPU time.

For user or system fatal errors, if error occurs before the solution iteration phase, the run will terminate immediately without output the stored data. If the error occurs during the solution iteration phase, SOL will try to output all stored data for the current subcase and terminate the run. The solution will not continue into next subcase if there are multiple subcases.

For fatal error due to solution divergence, SOL 400 will try to output all stored data for the current subcase and terminate the subcase. The solution sequence will jump to perform the next subcase if there are multiple subcases.

For fatal error due to not enough CPU time, SOL 400 will try to output all stored data and terminate the run.

≠


26

User InterfacesThe user interfaces, which are important or new to the nonlinear transient analyses in SOL 400, are summarized in this section. For detail, please refer to the MD Nastran Quick Reference Guide.

Nastran System Cells• STPFLG (SYSTEM (366)) – Selects the SUBCASE or STEP layout when there are a number of

SUBCASE commands and no STEP command in a Case Control file.

• TZEROMAX(SYSTEM (373)) – Controls initial time step adjustment in nonlinear transient analysis.

File Management Commands

The following File Management commands are required for restarts. Please refer to the File Management Statement Descriptions (Ch. 2) in the MD Nastran Quick Reference Guide or Chapter 12 of the MD Nastran Reference Manual for details.

• ASSIGN – Assigns physical file names to database files that are used by a Nastran data file to run a job.

• RESTART – Requests that data stored in a previous run be used in the current run.

Executive Control Command• SOL 400 or SOL NONLIN – Requests the SOL 400 general nonlinear solution sequence

Parameters• PARAM, LGDISP – Requests a geometric nonlinear analysis. The default is 0, no geometric

nonlinear effect.

• PARAM, FOLLOWK – Requests whether the follower force stiffness will be used in a geometric nonlinear analysis. The default is YES.

• PARMA, FKSYMFAC – Controls whether the symmetrical follower force stiffness will be used in a geometric nonlinear analysis. Default = 0.24.

• PARAM, MAXLP – Specifies maximum number of iterations for element relaxation and material point sub-increment process. Default = 10.

• PARAM, NLAYERS – Specifies the number of layer for through thickness integration in the material nonlinear analysis. Default = 5.

• PARAM, NLTOL – Selects defaults for CONV, EPSU, EPSP, and EPSW for the Bulk Data entries NLPARM and TSTEPNL. Default = 2.

• PARAM, PH2OUT – Requests phase II outputs for a nonlinear analysis. Default = 0, phase III output only.

• PARAM, NLPACK – Control the total output time step in one output package; see section Output Data Grouping above. Default = 100.


• PARAM, NDAMP – Specifies the α values when the HHT-α method using in SOL 400, see section A New Numerical Integration Method above. Default = -0.05.

• PARAM, ICOPT – Select how to handle the equilibrium when dealing with the initial condition, see section Initial Conditions above.

Case Control Commands• ANALYSIS – Selects solution method for an analysis step, see section Case Control Structure

above.

• NLRESTART – Requests a restart execution at a specific solution point for SOL 400, see section Restarts above.

• NLSTRESS – Requests the form and type of the nonlinear element stress output.

• STEP – Delimits and identifies an analysis step, see section Case Control Structure above.

• NLIC – Select the initial condition from any static analysis for the nonlinear transient analysis

Bulk Data Entries• MATHP- Specifies the hyperelastic material properties for an element.

• MATS1 – Specifies the stress-dependent material properties for an element.

• TSTEPNL – Defines a set of parameters for the nonlinear transient analysis iteration strategy.

• TTEMP – Defines a time-dependent temperature distribution for use in the nonlinear transient response.

• TMPSET – Defines a spatial temperature distribution for use in the TTEMP Bulk Data entry.

ExamplesThe following nine examples show the inputs and capabilities of the nonlinear transient analysis. The intention of these examples is to show the input structure for SOL 400. The model itself and the detailed entries in the Bulk Data file are not important.

Example 1

Example one, EX01, is a simplified version of the standard QA file, NLTSUB02. This model only has QUAD4 elements. It has both material nonlinearity (MATS1) and geometrical nonlinearity (PARAM,

LGDISP, 1). The 1st STEP will process the output data at every 5 output time steps and the 2nd STEP do it only once because of the settings of the parameter NLPACK. All bold-font statements are entries pertaining to the nonlinear analysis.

ID MSC, EX01 $TIME 150 $SOL 400 $CENDTITLE=ISOTROPIC MATERIAL & MATS1, ELLIPTIC CYLINDER UNDER EX01SUBTITLE =SPC CHANGE IN EACH STEP, NLPACK’sSET 10 = 10000,11200


28

SET 20 = 101 SEALL = ALL DISPL = ALL STRESS = 20$SUBCASE 100 ANALYSIS=NLTRANSTEP 10 PARAM,NLPACK,5 DLOAD = 100 SPC = 200 TSTEPNL = 310STEP 20 PARAM,NLPACK,-1 DLOAD = 100 SPC = 400 TSTEPNL = 320$BEGIN BULKPARAM NDMAP -0.05PARAM LGDISP 1TSTEPNL 310 100 0.01 10 AUTOTSTEPNL 320 100 0.01 10 AUTO$PLOAD4 510 101 5. THRU 112$TLOAD1 100 510 0 0 120TABLED1 120 +TBD1+TBD1 0. 0. 5. 1. 16. 1. ENDTMAT1 100 3.+7 0.3 .283-2MAT1 101 3.+7 0.3 .283-2MATS1 100 PLASTIC 3.+5 500000.$GRID 10000 100. 0.0 10. 345GRID 10001 100. 0.0 0.0 345GRID 10100 99.3625 3.30491 10. 345GRID 10101 99.3625 3.30491 0.0 345GRID 10200 96.8149 6.51543 10. 345GRID 10201 96.8149 6.51543 0.0 345GRID 10300 92.5105 9.59323 10. 345GRID 10301 92.5105 9.59323 0.0 345GRID 10400 86.6025 12.5 10. 345GRID 10401 86.6025 12.5 0.0 345GRID 10500 79.2443 15.1974 10. 345GRID 10501 79.2443 15.1974 0.0 345GRID 10600 70.5889 17.6472 10. 345GRID 10601 70.5889 17.6472 0.0 345GRID 10700 60.7898 19.8111 10. 345GRID 10701 60.7898 19.8111 0.0 345GRID 10800 50. 21.6506 10. 345GRID 10801 50. 21.6506 0.0 345GRID 10900 38.3729 23.1276 10. 345GRID 10901 38.3729 23.1276 0.0 345GRID 11000 26.0617 24.2037 10. 345GRID 11001 26.0617 24.2037 0.0 345GRID 11100 13.2197 24.8406 10. 345GRID 11101 13.2197 24.8406 0.0 345GRID 11200 0.0 25. 10. 345GRID 11201 0.0 25. 0.0 345$


CQUAD4 101 100 10000 10001 10101 10100CQUAD4 102 100 10100 10101 10201 10200CQUAD4 103 100 10200 10201 10301 10300CQUAD4 104 100 10300 10301 10401 10400CQUAD4 105 100 10400 10401 10501 10500CQUAD4 106 100 10500 10501 10601 10600CQUAD4 107 100 10600 10601 10701 10700CQUAD4 108 100 10700 10701 10801 10800CQUAD4 109 100 10800 10801 10901 10900CQUAD4 110 100 10900 10901 11001 11000CQUAD4 111 100 11000 11001 11101 11100CQUAD4 112 100 11100 11101 11201 11200$PSHELL 100 100 0.10 100 101$SPC1 200 16 11200 11201SPC1 200 26 10000 10001$SPC1 400 16 11200 11201SPC1 400 26 10000 10001SPC1 400 1 10700SPC1 400 2 10701$ENDDATA

Example 2

Example two, EX02, is modified version of the standard QA file, NLTSUB02. It shows two different types of analyses in the same job. This model is similar to the Example one except for adding some static loads and the required NLPARM’s. All bold-font statements are entries that show the difference in the two different analysis types.

ID MSC, EX02 $TIME 150 $SOL 400 $CENDTITLE=TEST MIXED ANALYSES - NLSTAT AND NLTRAN EX02SUBTITLE =SPC CHANGE IN THE STEPS IN EACH SUBCASE SET 10 = 10000,11200SET 20 = 101 SEALL = ALL DISPL = ALL STRESS = 20$SUBCASE 100 ANALYSIS=NLSTATSTEP 10 LOAD = 800 SPC = 200 NLPARM = 110STEP 20 LOAD = 900 SPC = 400 NLPARM = 120$SUBCASE 200 ANALYSIS=NLTRANSTEP 10


30

DLOAD = 100 SPC = 200 TSTEPNL = 310STEP 20 DLOAD = 100 SPC = 400 TSTEPNL = 320$BEGIN BULKNLPARM 110 10 AUTO YESNLPARM 120 10 AUTO YES$LOAD 800 0.01 1.0 510LOAD 900 0.05 1.0 510(.. The rest is the same as what is in the Bulk Data file in the first example....)ENDDATA

Example 3

Example three, EX03, is modified form of the standard QA file, NLTTL002. This model only has 1 QUAD4 element and 2 TRAI3 elements. Its major purpose is to show the various combinations of TTEMP and TMPSET inputs in nonlinear transient analysis for the thermal effect. All the bold-font statements are entries related to the temperature related inputs.

ID MSC, EX03 $SOL 400 DIAG 8,15TIME 60CEND SEALL = ALL SUPER = ALL TITLE = THERMAL LOAD TEST FOR NONLINEAR TRANSIENT ANALYSIS EX03SUBTITLE = Q4/T3 MODEL, TTEMP AND TMPSET$ECHO = NONE MAXLINES = 999999999 $TEMPERATURE(INITIAL) = 1 SUBCASE 1 analysis=NLTRANstep 1 TSTEPNL= 1 SPC = 2 TEMPERATURE(LOAD) = 3 DISPLACEMENT(SORT1,REAL)=ALL nlstress = all stress = allstep 2 TSTEPNL= 1 SPC = 2 TEMPERATURE(LOAD) = 4 DISPLACEMENT(SORT1,REAL)=ALL nlstress = all stress = allSUBCASE 2analysis=NLTRANstep 3 TSTEPNL= 1 SPC = 2


TEMPERATURE(LOAD) = 5 DISPLACEMENT(SORT1,REAL)=ALL nlstress = all stress = allstep 4 TSTEPNL= 1 SPC = 2 TEMPERATURE(LOAD) = 6 DISPLACEMENT(SORT1,REAL)=ALL nlstress = all stress = allSUBCASE 3analysis=NLTRANstep 5 TSTEPNL= 1 SPC = 2 TEMPERATURE(LOAD) = 7 DISPLACEMENT(SORT1,REAL)=ALL nlstress = all stress = allstep 6 TSTEPNL= 1 SPC = 2 TEMPERATURE(LOAD) = 8 DISPLACEMENT(SORT1,REAL)=ALL nlstress = all stress = allSUBCASE 4analysis=NLTRANstep 7 TSTEPNL= 1 SPC = 2 TEMPERATURE(LOAD) = 9 DISPLACEMENT(SORT1,REAL)=ALL nlstress = all stress = allstep 8 TSTEPNL= 1 SPC = 2 TEMPERATURE(LOAD) = 10 DISPLACEMENT(SORT1,REAL)=ALL nlstress = all stress = all$BEGIN BULK PARAM POST -1 PARAM COUPMASS 1 PARAM LGDISP 1 PARAM K6ROT 100. PARAM,NOCOMPS,-1 PARAM PRTMAXIM YES PARAM,COMPMATT,YES PARAM,EPSILONT,INTEGRAL PARAM NLTOL 0 TSTEPNL,1,4,0.25,1,AUTO$PCOMP 1 79. 0. * 1 .04875 0. YES $MAT8 1 7.15+6 2.9+6 .29 1.4+6 1.9-4


32

2.9-6 6.-6 79.MATT8 1 3 5 4 6 1 2$TABLEM1 1 + CR+ CR 60. 2.9-6 70. 2.9-6 80. 3.24-6 100. 3.86-6 + CS+ CS 120. 4.01-6 140. 3.89-6 150. 3.78-6 160. 3.68-6 + CT+ CT 180. 3.52-6 200. 3.47-6 220. 3.55-6 240. 3.76-6 + CU+ CU 250. 3.87-6 260. 3.99-6 280. 4.12-6 300. 4.24-6 + CV+ CV 320. 4.24-6 ENDT $TABLEM1 2 + CW+ CW 60. 6.-6 70. 6.-6 80. 7.67-6 100. 1.168-5+ CX+ CX 120. 1.341-5 140. 1.37-5 150. 1.349-5 160. 1.328-5+ CY+ CY 180. 1.266-5 200. 1.222-5 220. 1.218-5 240. 1.259-5+ CZ+ CZ 250. 1.296-5 260. 1.334-5 280. 1.415-5 300. 1.46-5 + DA+ DA 320. 1.46-5 ENDT $TABLEM1 3 + BX+ BX 60. 7.15+6 70. 7.15+6 80. 7.15+6 100. 7.13+6 + BY+ BY 120. 7.11+6 140. 7.08+6 150. 7.07+6 160. 7.07+6 + BZ+ BZ 180. 7.06+6 200. 7.05+6 220. 7.05+6 240. 7.04+6 + CA+ CA 250. 7.04+6 260. 7.05+6 280. 7.06+6 300. 7.08+6 + CB+ CB 320. 7.08+6 ENDT $TABLEM1 4 + CM+ CM 60. .29 70. .29 80. .29 100. .29 + CN+ CN 120. .29 140. .29 150. .29 160. .29 + CO+ CO 180. .29 200. .29 220. .29 240. .29 + CP+ CP 250. .29 260. .29 280. .29 300. .29 + CQ+ CQ 320. .29 ENDT $TABLEM1 5 + CC+ CC 60. 2.9+6 70. 2.9+6 80. 2.9+6 100. 2.82+6 + CD+ CD 120. 2.75+6 140. 2.68+6 150. 2.64+6 160. 2.58+6 + CE+ CE 180. 2.47+6 200. 2.35+6 220. 2.22+6 240. 2.09+6 + CF+ CF 250. 2.03+6 260. 1.95+6 280. 1.8+6 300. 1.65+6 + CG+ CG 320. 1.65+6 ENDT $TABLEM1 6 + CH+ CH 60. 1.4+6 70. 1.4+6 80. 1.4+6 100. 1.34+6 + CI+ CI 120. 1.29+6 140. 1.24+6 150. 1.22+6 160. 1.2+6 + CJ+ CJ 180. 1.15+6 200. 1.1+6 220. 980000. 240. 870000.+ CK+ CK 250. 810000. 260. 750000. 280. 620000. 300. 500000.+ CL+ CL 320. 500000. ENDT $cquad4,1,1,1,2,5,4ctria3,2,1,1,2,4ctria3,3,1,2,5,4$GRID 1 0.00000 0.00000 0.00000GRID 2 1.00000 0.00000 0.00000GRID 4 0.00000 1.00000 0.00000GRID 5 1.00000 1.00000 0.10000$SPCADD 2 1


SPC1 1 123456 1 2spc1 1 123456 4$TTEMP,3,111,300TMPSET,111,4,5TTEMP,3,101,310TMPSET,101,1,2$TTEMP,4,102,400TMPSET,102,1,2,4,5$TTEMP,5,201,500TMPSET,201,1,2,4,5$TTEMP,6,-1,400$TTEMP,7,202,700TMPSET,202,1,2$TTEMP,8,204,800TMPSET,204,1,2$TTEMP,9,402,900TMPSET,402,1,2,4,5$ TEMP 1 1 79.TEMP 1 2 79.TEMP 1 4 79.TEMP 1 5 79.$TEMP 3 1 80.TEMP 3 2 80.TEMP 3 4 80.TEMP 3 5 80.TABLED1 300 0.0 .9875 1.0 1.0 ENDTTABLED1 310 0.0 .9875 1.0 1.0 ENDT$TEMP 4 1 81.TEMP 4 2 81.TEMP 4 4 81.TEMP 4 5 81.TABLED1 400 1.0 .9876542 2.0 1.0 ENDT$TEMP 5 1 80.TEMP 5 2 80.TEMP 5 4 80.TEMP 5 5 80.TABLED1 500 0.0 .9875 1.0 1.0 ENDT$TEMP 6 1 81.TEMP 6 2 81.TEMP 6 4 81.TEMP 6 5 81.$$TEMP 7 1 80.


34

TEMP 7 2 80.TEMP 7 4 80.TEMP 7 5 80.TABLED1 700 0.0 .9875 1.0 1.0 ENDT$TEMP 8 1 81.TEMP 8 2 81.TEMP 8 4 81.TEMP 8 5 81.TABLED1 800 1.0 .9876542 2.0 1.0 ENDT$TEMP 9 1 80.TEMP 9 2 80.TEMP 9 4 80.TEMP 9 5 80.TABLED1 900 0.0 .9875 1.0 1.0 ENDT$TEMP 10 1 81.TEMP 10 2 81.TEMP 10 4 81.TEMP 10 5 81.ENDDATA

Example 4

Example four, EX04, is modified from the standard QA file, NLTIC19. This model only has 1 HEXA element. Its purpose is to shows two different types of analyses in the same SUBCASE, the model itself is not important. All the bold-font statements are entries that show the difference between those analyses and how to set the initial condition for the nonlinear transient analysis after static analysis. Note that the nonlinear transient analysis does not use the final results of the closest static analysis as the initial

condition; instead, it asks the results of the 50% load increment in the 1st STEP to be the initial condition. Also, parameter ICPOT=0 is selected, which will compute the initial acceleration at the beginning (t=0.0) of the transient analysis when it is not in balance.

ID MSC, EX04 $DIAG 8,15TIME 60SOL 400 $CENDTITLE= ELASTIC-PLASTIC STATIC & TRANSIENT RESPONSE, EX04SUBTI= INITIAL ACCELERATION COMPUTED - PARAM,ICOPT,0SET 1 = 1111SET 2 = 100 DISP = 1 VELO = 1 ACCE = 1 OLOAD = 1$ STRESS(PLOT) = 2SUBCASE 1130 step 1 LABEL=UNIAXIAL TENSION (LOADING) ANALYSIS=NLSTAT SPC=100 LOAD=1130


NLPARM = 1 step 2 LABEL=UNIAXIAL TENSION (UNLOADING) ANALYSIS=NLSTAT SPC=100 NLPARM = 1 step 10 LABEL=I.C. FROM THE FIRST NLSTAT STEP(50%) - UNBALANCED CASE (NLIC) ANALYSIS=NLTRAN NLIC STEP 1 LOADFAC 0.5 SPC=100 DLOAD=2130 TSTEPNL=10 param,icopt,0BEGIN BULKPARAM,LANGLE,3PARAm,LGDISP,1PARAM,W4,1.0$NLPARM 1 4 AUTO ALL 1.-6TSTEPNL 10 2000 0.001 AUTO $MAT1 1 30.0+6 11.5+6 0.3 7.332-2 0.01PSOLID 1 1$SPC1 100 123456 1000SPC1 100 1 1010SPC1 100 2 1001SPC1 100 3 1100GRDSET 456$TLOAD1 2130 2130 0 500TABLED1 500 +TAB1+TAB1 0. 0. 1. -1. 1.2 0. 10. 0. +TAB2+TAB2 ENDT$LOAD 1130 -1.6 2. 121LOAD 2130 -1.6 1. 121$GRID 1000 0. 0. 0.GRID 1100 1. 0. 0.GRID 1110 1. 1. 0.GRID 1010 0. 1. 0.GRID 1001 0. 0. 1.GRID 1101 1. 0. 1.GRID 1111 1. 1. 1.GRID 1011 0. 1. 1.$CHEXA 100 1 1000 1100 1110 1010 1001 1101 +HX100+HX100 1111 1011$PLOAD4 121 100 36.+3 1100 1111PLOAD4 121 100 36.+3 1000 1011ENDDATA


36

Example 5

Example five, EX05, is a modified version of the standard QA file, NLTIC19R. This model is a restart run of the Example four, EX04. Since there is no structure change in the SUBCASE 1130 and there is

no parameter in NLRESTART command, this restart job will start from the 2nd SUBCASE. Its purpose is to shows how the Case Control commands NLRESTART and NLIC can work together. All bold-font statements are entries that show the key Case Control commands in this example. Note that the nonlinear

transient analysis in the 2nd SUBCASE asks the final results in the 1st STEP of the 1st SUBCASE to be the initial condition. Also, parameter ICPOT=1 (the default) is selected, which will NOT compute the initial acceleration but loads in the beginning (t=0.0) of the transient analysis, that assumes the whole model is in equilibrium automatically when initial conditions are applied.

ASSIGN RSFILE=’DBSDIR:ex04.MASTER’ $RESTART LOGICAL=RSFILE $$ID MSC, EX05 $DIAG 8,15TIME 60SOL 400 $CENDTITLE= ELASTIC-PLASTIC STATIC & TRANSIENT RESPONSE, EX05SUBTI= NO INITIAL ACCELERATION COMPUTED - PARAM,ICOPT1SET 1 = 1111SET 2 = 100 DISP = 1 VELO = 1 ACCE = 1 OLOAD = 1$ STRESS = 2NLRESTARTSUBCASE 1130 step 1 LABEL=UNIAXIAL TENSION (LOADING) ANALYSIS=NLSTAT SPC=100 LOAD=1130 NLPARM = 1 step 2 LABEL=UNIAXIAL TENSION (UNLOADING) ANALYSIS=NLSTAT SPC=100 NLPARM = 1 step 10 LABEL=I.C. FROM THE FIRST NLSTAT STEP - UNBALANCED CASE (NLIC) ANALYSIS=NLTRAN NLIC STEP 1 LOADFAC 0.5 SPC=100 DLOAD=2130 TSTEPNL=10 param,icopt,0SUBCASE 1131 LABEL=I.C. FROM THE 1st NLSTAT STEP OF PREVIOUS SUBCASE (NLIC) ANALYSIS=NLTRAN NLIC SUBCASE 1130 STEP 1 SPC=100 DLOAD=2130 TSTEPNL=10


param,icopt,1BEGIN BULKENDDATA

Example 6

Example six, EX06, is modified from the standard QA file, NLTROT01. This model simply shows how to run Rotor Dynamics in SOL 400. All bold-font statements are the basic entries that may be required in rotor dynamic analysis.

ID MSC, EX06 $SOL 400DIAG 8, 15 CEND$ANALYSIS=NLTRANRIGID=LINEAR$RGYRO= 100 TSTEP= 100SET 99= 101disp= 99$BEGIN BULK$UNBALNC, 100, 2.0, 101, 0., 1., 0.,, 1.0, 0.0, 0.0, 0.0, 1000., none$TSTEPNL, 100, 5000, 3.0E-4, 10$ROTORG 10 101 THRU 103$RSPINT 10 101 102 FREQ 100 0.01TABLED1, 100,, 0.0, 22.5, 100.0, 22.5, endt$$ ROTOR 1$GRID, 101, , 0., 0., 0.GRID, 102, , 1., 0., 0., , 14GRID, 103, , 2., 0., 0. GRID, 104, , 0., 0., 0.GRID, 105, , 2., 0., 0.$RBE2, 1001, 102, 123456, 101, 103RBE2, 1002, 101, 123456, 104RBE2, 1003, 103, 123456, 105$CONM2, 1004, 102, , 50.,, 5.0, , 15.0, , , 15.0$CELAS1, 1005, 1000, 104, 2CELAS1, 1006, 1000, 104, 3CELAS1, 1007, 1000, 105, 2CELAS1, 1008, 1000, 105, 3PELAS, 1000, 1.0E+5, 0.0$param, g, 0.05


38

param, w3, 141.3$enddata

Example 7

Example seven, EX07, is modified from the standard QA file, NLTK2PP1. This model shows how to

apply K2PP in SOL 400, such as using different sets of K2PP in different STEP. For example, the 1st

STEP requests the K2MAT matrix as a K2PP input and the 2nd STEP requests the combination of K2MAT and K3MAT matrices as a K2PP input. All the bold-font statements are the entries that are required in this kind of analysis.

ID MSC, EX07 $SOL 400 $DIAG 8,15TIME 50CEND$SEALL=ALLMPC = 20SPC = 10analysis=NLTRANTITLE = LINEAR TRANSIENT RESP. (DIRECT METHOD) TEST EX07SUBTITLE = COULOMB FRICTION LESS F3(0),F4(0)$ ECHO = NONE SET 10= 1,7 DISP=10$SUBCASE 1 STEP 1 DLOAD = 12 K2PP = K2MAT TSTEPNL = 10 STEP 2 DLOAD = 12 K2PP = K2MAT, K3MAT TSTEPNL = 10$BEGIN BULKparam,ndamp,-0.055$CORD2R 1 0 0. 0. 0. 0. 0. 1. +CORD+CORD 1. 0. 0.$GRDSET 1 1 1246GRID 1 -460. 0. 0.GRID 3 -460. 0. 100.GRID 5 -460. 0. 200.GRID 2 290. 0. 0.GRID 4 290. 0. 100.GRID 6 290. 0. 200.GRID 7 0. 0. 200.$CONM2 3 3 1 0.6867CONM2 4 4 1 1.2735CONM2 7 7 1 15.445 +CONM+CONM 3.0E5$


CELAS2 1 2200. 1 3 3 3CDAMP2 1 3.2 1 3 3 3CELAS2 2 4200. 2 3 4 3CDAMP2 2 6.2 2 3 4 3CELAS2 3 550. 3 3 5 3CDAMP2 3 13.3 3 3 5 3CELAS2 4 2000. 4 3 6 3CDAMP2 4 0. 4 3 6 3$MPC 10 7 3 750. 5 3 -290. +MPC10+MPC10 6 3 -460.MPC 11 7 5 750. 5 3 -1. +MPC11+MPC11 6 3 1.MPCADD 20 10 11$SPC1 10 5 1 THRU 6$TABLED1 12 +TBLD11+TBLD11 -100. 0. 0. 0. 0.005 3. 100. 3. +TBLD12+TBLD12 ENDT$EPOINT 101$DMIG K2MAT 0 1 1 1DMIG K2MAT 1 3 101 2.DMIG K2MAT 101 1 3 -2.$DMIG K3MAT 0 1 1 1DMIG K3MAT 1 3 101 3.DMIG K3MAT 101 1 3 -3.$DAREA 12 101 1.DELAY 12 101 0.$EPOINT 202$DMIG K2MAT 2 3 202 2.DMIG K2MAT 202 2 3 -2.$DMIG K3MAT 2 3 202 3.DMIG K3MAT 202 2 3 -3.$DAREA 12 202 1.DELAY 12 202 0.54$TLOAD1 12 12 12 12$TSTEPNL 10 1000 0.002 1 AUTO 10000ENDDATA

Example 8

Example eight, EX08, is modified from the standard QA file, NLTSTP06. This model shows the example of the SPC-Set change between STEP’s. All the bold-font statements are the entries that are required.

ID MSC, EX08 $TIME 150 $SOL 400 $


40

DIAG 8,15 $CENDTITLE=ANISOTROPIC MATERIAL & MATS1, ELLIPTIC CYLINDER UNDER EX08SUBTITLE = TWO STEP’S TEST, SPC SET CHANGE AND SAME DTSET 10 = 10000,11200SET 20 = 101 SEALL = ALL DISPL = ALL STRESS = 20 SPCF = ALL OLOAD = ALL$SUBCASE 100 ANALYSIS=NLTRANSTEP 10 DLOAD = 100 SPC = 200 TSTEPNL = 310STEP 20 DLOAD = 100 SPC = 400 TSTEPNL = 320$BEGIN BULKPARAM LGDISP 1TSTEPNL 310 100 0.01 10 AUTO +TS11TSTEPNL 320 100 0.01 10 AUTO +TS21$PLOAD4 510 101 5. THRU 112$TLOAD1 100 510 0 0 120TABLED1 120 +TBD1+TBD1 0. 0. 5. 1. 16. 1. ENDTMAT2 100 3.2967+79.8901+60. 3.2967+70. 1.1538+70.283-2MAT2 101 3.2967+79.8901+60. 3.2967+70. 0.283-2MATS1 100 PLASTIC 3.+5 500000.$GRID 10000 100. 0.0 10. 345GRID 10001 100. 0.0 0.0 345GRID 10100 99.3625 3.30491 10. 345GRID 10101 99.3625 3.30491 0.0 345GRID 10200 96.8149 6.51543 10. 345GRID 10201 96.8149 6.51543 0.0 345GRID 10300 92.5105 9.59323 10. 345GRID 10301 92.5105 9.59323 0.0 345GRID 10400 86.6025 12.5 10. 345GRID 10401 86.6025 12.5 0.0 345GRID 10500 79.2443 15.1974 10. 345GRID 10501 79.2443 15.1974 0.0 345GRID 10600 70.5889 17.6472 10. 345GRID 10601 70.5889 17.6472 0.0 345GRID 10700 60.7898 19.8111 10. 345GRID 10701 60.7898 19.8111 0.0 345GRID 10800 50. 21.6506 10. 345GRID 10801 50. 21.6506 0.0 345GRID 10900 38.3729 23.1276 10. 345GRID 10901 38.3729 23.1276 0.0 345GRID 11000 26.0617 24.2037 10. 345GRID 11001 26.0617 24.2037 0.0 345GRID 11100 13.2197 24.8406 10. 345


GRID 11101 13.2197 24.8406 0.0 345GRID 11200 0.0 25. 10. 345GRID 11201 0.0 25. 0.0 345$GRID 20000 0. 0. 0. 123456$GRID 20001 100. 0. 0. 123456$GRID 20100 0. 100. 0. 123456$CQUAD4 101 100 10000 10001 10101 10100CQUAD4 102 100 10100 10101 10201 10200CQUAD4 103 100 10200 10201 10301 10300CQUAD4 104 100 10300 10301 10401 10400CQUAD4 105 100 10400 10401 10501 10500CQUAD4 106 100 10500 10501 10601 10600CQUAD4 107 100 10600 10601 10701 10700CQUAD4 108 100 10700 10701 10801 10800CQUAD4 109 100 10800 10801 10901 10900CQUAD4 110 100 10900 10901 11001 11000CQUAD4 111 100 11000 11001 11101 11100CQUAD4 112 100 11100 11101 11201 11200$PSHELL 100 100 0.10 100 101$SPC1 200 16 11200 11201SPC1 200 26 10000 10001$SPC1 400 16 11200 11201SPC1 400 26 10000 10001SPC1 400 1 10700SPC1 400 2 10701$ENDDATA

Example 9

Example nine, EX09, is modified from the standard QA file, NLTSTP07. This model shows that the upper stream superelement can have output requests that are different from the residual. Also, a case control command OTIME is used here to select a subset of all output time steps, which is selected by the TSTEPNL Bulk Data entry. It can reduce the output data dramatically. For example, in the following file, TSTEPNL asks output at time=0.0, 0.1,…, 1.0 second but OTIME overwrites this request and only makes output at time=0.5 second. All the bold-font statements are the entries that are required to complete all above requests in this example.

ID MSC, EX09 $TIME 150 $SOL 400 $DIAG 8,15 $CENDTITLE=Test For Upperstream Superelement Output Request EX09SUBTITLE = OTIME Output RequestSET 1 = 0.5SET 10 = 11200SET 20 = 101LOADSET = 500DISPL = 10OTIME = 1$SUBCASE 10


42

SUPER=10 METHOD=10 SET 10001 = 10001 DISP =10001SUBCASE 100 ANALYSIS=NLTRAN DLOAD = 100 SPC = 200 TSTEPNL = 310$BEGIN BULKPARAM LGDISP 1$SESET,10,10000,thru,10301SEQSET1 10 0 10500 THRU 11001EIGRL 10$TSTEPNL 310 100 0.01 10 AUTO +TS11$+TS11 1.E-2LSEQ 500 110 510PLOAD4 510 101 5. THRU 112$TLOAD1 100 110 0 0 120TABLED1 120 +TBD1+TBD1 0. 0. 5. 1. 16. 1. ENDT$MAT1 100 3.+7 0.3 .283-2MAT2 100 3.2967+79.8901+60. 3.2967+70. 1.1538+70.283-2MAT2 101 3.2967+79.8901+60. 3.2967+70. 0.283-2MATS1 100 PLASTIC 3.+5 500000.$GRID 10000 100. 0.0 10. 345GRID 10001 100. 0.0 0.0 345GRID 10100 99.3625 3.30491 10. 345GRID 10101 99.3625 3.30491 0.0 345GRID 10200 96.8149 6.51543 10. 345GRID 10201 96.8149 6.51543 0.0 345GRID 10300 92.5105 9.59323 10. 345GRID 10301 92.5105 9.59323 0.0 345GRID 10400 86.6025 12.5 10. 345GRID 10401 86.6025 12.5 0.0 345GRID 10500 79.2443 15.1974 10. 345GRID 10501 79.2443 15.1974 0.0 345GRID 10600 70.5889 17.6472 10. 345GRID 10601 70.5889 17.6472 0.0 345GRID 10700 60.7898 19.8111 10. 345GRID 10701 60.7898 19.8111 0.0 345GRID 10800 50. 21.6506 10. 345GRID 10801 50. 21.6506 0.0 345GRID 10900 38.3729 23.1276 10. 345GRID 10901 38.3729 23.1276 0.0 345GRID 11000 26.0617 24.2037 10. 345GRID 11001 26.0617 24.2037 0.0 345GRID 11100 13.2197 24.8406 10. 345GRID 11101 13.2197 24.8406 0.0 345GRID 11200 0.0 25. 10. 345GRID 11201 0.0 25. 0.0 345$CQUAD4 101 100 10000 10001 10101 10100CQUAD4 102 100 10100 10101 10201 10200CQUAD4 103 100 10200 10201 10301 10300


CQUAD4 104 100 10300 10301 10401 10400CQUAD4 105 100 10400 10401 10501 10500CQUAD4 106 100 10500 10501 10601 10600CQUAD4 107 100 10600 10601 10701 10700CQUAD4 108 100 10700 10701 10801 10800CQUAD4 109 100 10800 10801 10901 10900CQUAD4 110 100 10900 10901 11001 11000CQUAD4 111 100 11000 11001 11101 11100CQUAD4 112 100 11100 11101 11201 11200$PSHELL 100 100 0.10 100 101$SPC1 200 16 11200 11201SPC1 200 26 10000 10001$SPC1 400 16 11200 11201SPC1 400 26 10000 10001SPC1 400 1 10700SPC1 400 2 10701$ENDDATA


44

MD Nastran Implicit Nonlinear - SOL 600This section documents the additions to SOL 600 for MD Nastran 2006. The following new capabilities have been added:

• Reduced memory for many SOL 600 analyses is triggered by PARAM,MARCOOCC. There are two effects when selecting this parameter:

• The memory used for decomposition is used for other purposes as well, which reduces memory required, but may result in an increase in I/O time.

• When using SOLVER type 8, the minimal amount of memory will be used.

• Reduced memory for analyses when composites or multiple element types are used.

The storage of element data quantities like stresses and strains has been modified. Previously, the amount of memory allocated per element was the maximum required for any element type. Thus there was a memory overhead in cases with different element types, or shells with different number of layers. In this release, the element data is dynamically allocated based upon element groups, where an element group contains one unique element type and material type.

The amount of memory saved with the new element data storage is model dependent. There is no savings in memory if a homogeneous model with one element type is used. Extreme cases would be when there are only a few elements that require a large amount of memory, for example a model with a few 20-grid point CHEXA with the remainder of the mesh being 4-grid point CTETRA.

In one example with a combination of 10,000 composite CHEXA and 80,000 CTETRA, which had several composite groups, with a maximum of 30 layers, the memory required for element storage was reduced from 11.9 Gbytes to 0.75 Gbytes. An engine model that had a total of 310,000 elements containing a combination of 20-node CEXA, 8-node CHEXA, 10-node CTETRA, 4-node CTETRA and CQUAD4 has achieved a memory reduction from the prior 3.76 GBytes to 0.86 Gbytes.

No new input is required.

• The amount of memory has been reduced when a large number of MPC, RBE2, and RBE3 are in the model. The memory usage was especially acute when some RBEs have a large number of grid points. Furthermore the computational time associated with the application of the MPCs has been reduced.

• Improvements have been made to reduce the amount of memory used by SOL 600 when spawned from MSC.Nastran and in the Nastran translator. For advanced users, parameters were added to override the automatic memory variables and control each memory request. These are all documented in the MD Nastran 2006 Quick Reference Guide.

• The value on the memory given on the PARAM,MARCMEM,value is no longer used in the

same way as in previous versions. Instead of setting the 2nd field of the SIZING entry, it now sets –ml value on the command line where the integer value entered is in Mbytes. For most analyses, the value entered can be smaller than what was needed for previous versions.


• There are two new parameters for allocating the memory use, the first PARAM,MRALLOCG,value; allocates the initial amount of General memory. The value specified is in megabytes. In this release General memory is used for material property data, boundary condition data, overhead, and the assembly of the global stiffness matrix (except CASI solver). The General memory is also used for Solver 0 and Solver 4 (NLSTRAT,ISOLVER). The second parameter PARAM,MRALLOCS,value’ allocates the initial memory for the decomposition of the global stiffness matrix for Solver 8 (multifrontal direct solver). This is often useful to avoid reallocation of memory which occurs in deformable-deformable contact. For parallel processing the amount specified is the total for the job. It is divided by the number of domains used for each domain.

• The CASI iterative solver was added; which can be activated by the NLSTRAT ISOLVER entry. Currently, two preconditioner are available, a primal and standard preconditioned, types 0 and 1, respectively. The primal preconditioner is the default and is recommended for ill-conditioned problems. If a non-positive definite matrix is encountered (such as in a buckling analysis), the solver automatically switches to a direct solver. In this release this solver may not be used for Herrmann elements, where the Lagrange multiplier is at the corner node, such as the higher order elements or the triangular and tetrahedral elements. This solver should also not be used with the gap element.

As an example of the improved performance with this solver an engine block with 2.2 million degrees of freedom was analyzed with the following normalized results.

• The computational times associated with running jobs in parallel has been reduced. This reduction is both in the time associated with creating the domains in during the solution process. For poorly conditioned models, the improvements have been as large as a factor of two.

• MD Nastran 2006 PC versions are released using the Intel version of MSC.Marc as the default. The Digital Visual Fortran (DVF) version is available on the MD Nastran CD, but is no longer fully supported by SOL 600. If you prefer to use the DVF version, the OUTR options (op2, punch, xdb, f06) are no longer available and if attempted will generate an error.

Memory has been reduced for analyses run in parallel.

• The number of contact bodies has been increased from 99 to 999

• We have made improvements to MD Nastran so more problems with MPC's, RBE2, RBAR, and RTRPLT will run to completion. For the 2006 release, AUTOMSET (param,automset,yes) has been added. Most analyses will not require AUTOMSET and since it takes additional computing time, MPC-CHECK,3 (param,marmpchk,3) should usually be used instead for models with complex rigid systems.

Solver TypeNormalized

Solution Time

2 0.785

8 1.0

9 0.174


46

• MPC's and rigid elements combined with contact and/or the same node in more than one contact body can sometimes cause the solver portion of SOL 600 to fail. There is a new feature in MSC.Marc known as optimized contact that can frequently help these types of models to run correctly. For version MSC.Marc 2005 r3, optimized contact is not the default either in MSC.Marc (stand-alone) or MD Nastran SOL 600. If MSC.Marc exit 2011 or convergence problems are encountered with such models, you should try optimized contact. To invoke optimized contact from MD Nastran, set field 6 of each BCBODY entry with flexible contact to 2. In addition, set field 3 of each "SLAVE" continuation line (the next line after all lines with SLAVE) to 2. In turn, this sets MSC.Marc's CONTACT entry 4th datablock, 3rd field to 2 and each CONTACT TABLE 3rd datablock 8th entry to 2 respectively. Detailed discussions and an example of optimized are provided in Chapter 8 of the MSC.Marc Theory and Information Manual (Volume A of the MSC.Marc documentation) - see text before and after figure 8-4.

• For most bulk data entries, SOL 600 does not make the distinction between zero and a blank. Thus, if a zero is entered and the default is some other value, the default will normally be used. If you wish to use zero, enter a small number such as 1.0E-12 instead.

• Not all MD Nastran Case Control or Bulk Data entries are supported in SOL 600. Please consult the MD Nastran Version 2006 QRG (SOL 600 Executive Control entry) for a list of items that are not supported.

• Inertia Relief has been added. The SOL 600 capability exceeds that available in other MD Nastran solution sequences using new Bulk Data entry, SUPORT6.

• The “support” method may be used to specify which degrees of freedom should be “supported” for each body. This is an extension of the PARAM,INREL,1 method and may use fewer computer resources than the eigenvalue method for some models.

Inertia Relief may be employed on a subcase-by-subcase basis and can be removed if all previously unsupported bodies merge into the main body (which is supported) either all at once or gradually.

• PSHELL with the same bending-membrane coupling as in other solution sequences has been added into the 2006 release. This will allow you to analyze composite structures using the smeared approach (such as done in other MD Nastran solution sequences) or through-the-thickness integration (which is more accurate and presently the only way to analyze composite structures) will be offered. If material nonlinearity occurs in the element, then the PSHELL smeared approach should not be used. The choice is activated by using PARAM,MRPSHELL,1.

• Post-buckling responses using the single-file parallel option sometimes do not agree with the responses using a single processor for the 2006 version. It is recommended that post-buckling analyses use a single processor.

• A new option named DMIG-OUT is available in the 2006 release. This capability will allow the stiffness, differential stiffness and mass matrices (assembled or element-by-element) to be output for selected output times or at the end of each nonlinear subcase for use in other analyses. This is a less expensive procedure, than using the Bulk Data entry, MDMIOUT (which creates a superelement), but results in a much larger matrix.

• We have made the following improvements to the OP2 file produced by SOL 600 for MD Nastran 2006:


• Contact forces are now included on the OP2 file in the “slide line” block.

• GPFORCE is available starting with the 2006 release

• MPC forces are now included on the OP2 file.

• In the 2006 release, Case Control MUST be used to create an OP2 file. This is consistent with other Nastran solution sequences, but is a change in behavior from previous releases.

• For the 2006 release, you must include Case Control requests such as DISP=ALL in order to obtain output in op2, xdb, punch or f06 files. In addition, OUTR requests on the SOL 600 entry must be made (for example OUTR=OP2,F06). The applicable Case Control requests for SOL 600 are DISP, STRESS, STRAIN, SPCFORCE, MPCFORCE, GPFORCE and BOUTPUT. BOUTPUT maps 3D contact to the older 2D Slideline Contact datablock (see item codes for contact in section 6 of the 2006 Quick Reference Guide). At present, MSC.Patran cannot process 2D slideline or 3D contact from the op2 or xdb.

• The output interval for the t16 file (and thus the OP2 file) is controlled by either the NLPARAM bulk data or PARAM,MARCOTIM, which is documented in the MD Nastran 2006 Quick Reference Guide.

• A preliminary version of Grid Force Balance is available. The output is available in the op2, xdb, f06 and punch files and is triggered by Case Control GPFORCE( )=ALL as well as PARAM,MARGPFOR

• A simplified procedure is available for activating large displacement – large strain analysis, by using the PARAM,MLSTRAIN. This option will automatically select the best formulation based upon the individual element type and material model. It effectively replaces the use of PARAM,LGDISP; PARAM, MRUPDATE; PARAM, MRFINITE and PARAM,MARCDILT for most simulations. Internally the following formulations are used.

• The Gent and Arruda Boyce models may now be used with plane stress, shell and membrane elements

Large Strain Option

element type / material model

1-d plane stress or membranes or shell elements

plane strain or axisymmetric, or 3-d, displacement form.

plane strain or axisymmetric, or 3-d, Herrmann form

conventional elastic-plastic

Updated Lagrange Additive Plasticity No Finite Strain

Updated Lagrange Additive Plasticity Includes Finite Strain

Updated Lagrange Additive Plasticity Includes Finite Strain Utilized Constant Strain

Updated Lagrange Multiplicative Plasticity Includes Finite Strain

Mooney, Ogden, Gent or Arruda-Boyce

Total Lagrange Total Lagrange Updated Lagrange Updated Lagrange

Foam Total Lagrange Total Lagrange Updated Lagrange Updated Lagrange, Incompressibility Neglected


48

• The NLELAST option on the MATS1 is now supported in SOL 600 as in the other solution sequences (106, 129, and 400). It is more general in that it may be used will all structural element types (except the shear panel).

• A new higher order tetrahedral element is available which has improved behavior in bending. To activate this element, use the PARAM,MRALIAS,127184 to switch the element formulation from SOL 600 element type 127 to 184.

• The method for updating the thickness of shells and plane stress elements has changed if the PARAM,MRFINITE or PARAM,MLSTRAIN. This is activated using: PARAM,MRV09V11,1

• The in-plane shear behavior of the CQUAD 4 element using reduced integration has been improved. This element technology is invoked by using PARAM,075140. This is activated using: PARAM,MRV09V11,1

• Dissimilar meshes of shell elements may now be “glued” together using fully moment carrying capability of the contact glue option. This is activated using the BCTABLE option.

• A new parameter has been added when using SOL 600 analysis. When relevant, this generally results in improved behavior, but will lead to some differences in results with the previous release. This is activated using PARAM,MRV09V11,value, where

Note that the above features are only used for certain problems. Even though all are included with the default option, they have no effect for problems that do not use them. For example, feature,5801 has no effect on models that do not use SOL 600 element type 140, feature 601 has no effect on models that do not have contact.

• The speed of the t16op2 results translator has been increased by a factor of 4 or more for large models. The speed increase is triggered using PARAM,MSPEEDOU,1

• Translation speed has increased for beam and shell type elements (in addition to the previous speed enhancements for solid elements) by using PARAM,MSPEEDSE,2 (or 3). The speed increase varies from model to model but can be as great as a factor of 4-10 for some models.

-1 Do not add the features

1 Add the following features (default):

feature,4703 to speed up DDM jobs (for 1-processor jobs, it has no effect).

feature,5701 to disable old rigid rotation checking which was too stringent

feature,601 to improve contact

feature,5301 to improve deformable-deformable contact

feature,3201 to improve contact friction types 6 and 7

feature,5601 to improve thickness updating when the updated Lagrange method is used

feature,5801 to improve in-plane bending of SOL 600 element type 140

feature,6001 to improve concrete cracking analysis


• A new Bulk Data entry for brake squeal named BRKSQL is available which replaces several parameters and MARCIN entries previously used. With the entry, new capabilities are also introduced. It is now possible to determine the unstable brake squeal roots using MD Nastran’s complex eigenvalue solver and unsymmetric friction stiffness matrices for an undeformed structure or after a nonlinear subcase. Brake squeal analysis for SOL 600 is accomplished by starting a primary MD Nastran job (as usual) which spawns SOL 600 to calculate the unsymmetric friction stiffness matrices either at the beginning or end of a nonlinear subcase, then spawning a second MD Nastran job to calculate the complex eigenvalues. Unstable roots indicate potential brake squeal. They are designated by positive real roots and negative damping in the f06 output file. See the BRQSQL entry from more details and the attached example.

• A new fixed-time stepping approach has been added which avoids some convergence problems with AUTO LOAD particularly for multiple subcases. AUTO LOAD is still available but the new approach is recommended particularly for multiple subcases. The available methods are selected using PARAM,MARCITER,N where N is the number of fixed time steps desired.

• MD Nastran SOL 600 now uses the same compilers on all systems. This allows user subroutines to be employed on all systems. For Windows and Linux, the Intel compiler is now used. Previously, the Digital Visual Fortran and PFG Fortran compilers, respectively, were used. Only the Intel versions are delivered with MD Nastran.

• User subroutine support has been added through Bulk Data entry, USRSUB6

• The SOL 600,ID executive control statement has been revised to add some clarifying remarks

• TEMP(INIT) does not work properly using Updated Lagrange (param,mvarupdat,1). If TEMP(INIT) is required in the model, please use the Total Lagrange formulation (param,marupdat,-1). If all initial temperatures are zero, TEMP(INIT) may be omitted and Updated Lagrange may be used.

• The Case Control BCTABLE text has been clarified

• The NDDL description for some SOL 600 bulk data entries is not up to date. These entries are intercepted and placed on a special database used by the SOL 600 translators. Another aspect of the NDDL not being up to date is that the 3D contact Bulk Data entries are only valid for SOL 600. They must be removed from the input deck for other solution sequences for MD Nastran 2006. It is anticipated that this will be corrected in the next MD Nastran release.

• The following new Bulk Data entries have been added for SOL 600 (see next section for a description of each new entry):

• BRKSQL (Brake Squeal)

• SUPORT6 (Inertia Relief for SOL 600)

• USRSUB6 (User subroutines for SOL 600)

• The following Bulk Data entries have been revised or additional capabilities added:

• RESTART (Shared with SOL 700, items for SOL 700 were added)

• NLSTRAT (CASI solver, rigid rotation control added)

• IPSTRAIN (text clarified)

• IPSTRESS (text clarified)


50

• BCPROP (text clarified)

• MBOLTUS (Extraneous variables removed)

• MATHED (text clarified)

• MATORT (defaults change to zero)

• The following parameters have been added

• MARCITER

• HEATCMD

• MSPEEDOU

• MRCONVER

• MEXTRNOD

• MARCBUSH

• MRCOMPOS

• MRBEPARM

• MARBATCH

• MARCCBAR

• MARCRACC

• MARCRCID

• MRPSHELL

• MARGPFOR

• MLSTRAIN

• MARCRADD

• MRV09V11

• The following parameters have been revised to add options, clarify text or change defaults

• MARCSOLV

• MARCRBE3

• MARCOTIM

• MARCSLHT

• MARCPOST

• MARCAUTO

• MARCGAUS

• MRMAXMEM

• MRTABLS1

• MRTABLS2

• MARCUSUB


• MRSPAWN2

• MARCPINN

• MRESTALL

• MARCOPP2

• MSPEEDSE

• MARCSAME

• The following parameter has been removed:

• MARNOT16

• Detailed Descriptions of each new Bulk Data entry:


52

Specifies data for brake squeal calculations using SOL 600.

Format:

Example:

BRKSQL Specifies data for Brake Squeal Calculations using SOL 600

1 2 3 4 5 6 7 8 9 10BRKSQL METH AVSTIF FACT1 GLUE ICORD

R1 R2 R3 X Y Z

NASCMD

RCFILE

BRKSQL 1 5.34E6 1.0 1.0

0.0 0.0 1.0 2.0 3.0 4.0

tran

nastb

Field Contents

METH Method flag corresponding to the type of brake squeal calculations to be performed. (Integer, Default = 1)

0 = Perform brake squeal calculations before any nonlinear analysis has taken place.

1 = Perform brake squeal calculations after all nonlinear load cases.

AVSTIF Approximate average stiffness per unit area between the pads and disk. This value is also known as the initial friction stiffness in the MSC.Marc Volume C documentation. AVSTIF can be obtained by either experiment or numerical simulation. A larger value of AVSTIF corresponds to a higher contact pressure, which usually results in more unstable modes. (Real; no Default; required field)

FACT1 Factor to scale friction stiffness values; see Remark 3. (Real; Default = 1.0)

GLUE Flag specifying whether MPC for non-pad/disk surfaces with glued contact are used or ignored (Integer, Default = 0). A value of 0 means ignore the MPC; a value of 1 means include the MPCs (see Remark 6).

ICORD Flag indicating whether coordinates are updated or not. A value of 0 means coordinates are not updated. A value of 1 means coordinates are updated using the formula Cnew=Corig+Defl, where Cnew are unpdated coordinates, Corig are original coordinates, and Defl are the final displacements. (Integer; Default = 0)


Remarks:1. This entry is used to calculate complex eigenvalues for brake squeal using unsymmetric stiffness

friction matrice. Options exist to obtain the unsymmetric stiffness matrices using the undeformed geometry (initial contact) or after all specified nonlinear subcases.

2. SOL 600 performs brake squeal calculations. The main (original) MD Nastran job with input file jid.dat or jid.bdf spawns the SOL 600 job. MD Nastran SOL 600 calculates unsymmetric friction stiffness matrices that1 are saved on a file (jid.marc.bde with associated file jid.marc.ccc). The primary MD Nastran job then creates input data for a second MD Nastran job (jid.nast.dat) to use the unsymmetric stiffness matrices in an complex eigenvalue extraction. The primary MD Nastran job spawns a second MD Nastran job to calculate the complex eigenvalues. The complex eigenvalues and eigenvectors are found in jid.nast.f06, jid.nast.op2, etc.

NASCMD is the name of the command used to execute the secondary MD Nastran job. NASCMD can be up to 64 characters long and must be left justified in field 2. The sting as entered will be used as is -- except that it will be converted to lower case regardless of whether it is entered in upper or lower case.

R1 X direction cosine (basic coord system) of axis of rotation; corresponds to ROTATION A second datablock. (Real; no Default. Required field)

R2 Y direction cosine (basic coord system) of axis of rotation; corresponds to ROTATION A second datablock.

R3 Z direction cosine (basic coord system); corresponds to ROTATION A second datablock. (Real; no Default. Required field)

X X coordinate in basic coord system of a point on the axis of rotation; corresponds to ROTATION A third datablock. (Real; no Default. Required field)

Y Y coordinate in basic coord system of a point on the axis of rotation; corresponds to ROTATION A third datablock. (Real; no Default. Required field)

Z Z coordinate in basic coord system of a point on the axis of rotation; corresponds to ROTATION A third datablock. (Real; no Default. Required field)

NASCMD Name of a command to run MD Nastran (limited to 64 characters) -- used in conjunction with the CONTINUE options on the SOL 600 entry. The full path of the command to execute MD Nastran should be entered. The string will be converted to lower case. See Remark 2. (Character; Default = nastran)

RCFILE Name of an RC file to be used with a secondary MD Nastran job (limited to 8 characters) -- used in conjunction with the CONTINUE options on the SOL 600 entry. An extension of “.rc” will automatically be added. See Remark 2. (Character; Default = nastb.rc)

Field Contents


54

RCFILE is the name of an RC file to be used for the secondary MD Nastran job. It should be similar to the RC file used for the primary run except that additional memory will usually be necessary to calculate the complex eigenvalues and batch=no should also be specified. RCFILE is limited to 8 characters and an extension of “.rc” will be added automatically. This entry will be converted to upper case in MD Nastran but will be converted to lower case before spawning the complex eigenvalue run. This RC file must be located in the same directory as the MD Nastran input file. This entry is the same as specifying PARAM,MRRCFILE. One or the other should be used.

3. MPC are produced for contact surfaces with glued contact. DMIGs are produced for contact surfaces without glued contact. The brakes and drums should not use glued contact; other regions of the structure can used glued contact.

4. The continuation lines may be omitted if defaults are appropriate.

5. When a BRKSQL entry is used, PARAM,MRMTXNAM and PARAM,MARCFIL1 should not be entered.

6. When brake squeal matrices are output, unsymmetric friction stiffness matrices are output for non-glued contact surfaces. For surfaces with glued contact, MPCs are output. The GLUE flag signals SOL 600 to look for these MPCs and combine them with other MPCs that might be in the model using MPCADD, or if no MPCs were originally used, to add the MCPs due to glued contact. Glued contact surfaces may not be used for the disk-rotor interface. If GLUE is zero or blank, the MPC for glued contact in the brake squeal bde file, if present, will be ignored. Sometimes MD Nastran puts out MPCs with only one degree-of-freedom defined. Such MPCs will be ignored; otherwise, MD Nastran will generate a fatal error.

7. If ICORD=1, an MD Nastran t19 file will be automatic.


Defines inertia relief for SOL 600.

Format:

Examples:

SUPORT6 Inertia Relief for SOL 600 - Used in MD Nastran Implicit Nonlinear - SOL 600 only

1 2 3 4 5 6 7 8 9 10

SUPORT6 SID METH IREMOV GID CDOF CID IDS1

MODES FMAX FSHIFT

SUPORT6 2 1 3000 123456 0

SUPORT6 3 2

6 0.6 -10.0

SUPORT6 0 3 1 101

SUPORT6 4 3 -2


56

Field Contents

SID Set ID corresponding to a Case Control SUPORT1 command or zero (Integer, Default = 0)0 = if this is the only SUPORT6 entry, use this SUPORT6 entry for all subcases. If there are multiple SUPORT6 entries, use the one with SID=0 for increment zero.N = Use this SUPORT6 entry for the subcase specified by Case Control SUPORT1=NDifferent SUPORT6 entries can be used for each subcase if desired and different subcases can use different methods.If there is only one SUPORT6 entry (with SID=0) no Case Control SUPORT1 commands are necessary.

METH Method to use (Integer, Default = 0)0 = Inertia relief is not active for this subcase 1 = Use the “Kinematic” method – do not enter continuation line. Input will come from fields 5-7 of this entry2 = Use the “Eigenvalue” method – Input data from the 2nd line must is used and fields 5-7 of the primary line must be blank (any SUPORT/SUPORT1 Bulk Data entries are ignored).3 = Use the “Support Method”, usually specified using param,inrel,-1 for other solution sequences (see Remark 3). Do not enter the continuation line. Input will come from all SUPORT entries and those SUPORT1 entries with ID=SID.

IREMOV Method to retain or remove inertia relief from a previous subcase (Integer, Default = 1)1 = Retain inertia relief conditions from previous subcase1 = Remove inertia relief loads immediately2 = Remove inertia relief loads graduallyIREMOV should be blank or 1 unless METH is 0

GID Reference Grid ID for kinematic method (Integer, Default = 0)=0 Use the origin=N Use grid ID N(Used for METH=1 ONLY)

CDOF Degrees of freedom for which inertia relief loads will be applied (Integer, no Default). Enter a string of values identifying the degrees of freedom for the model. For 3D models, usually 123456 is entered. For 2D models two or three degrees of freedom as applicable may be entered. The limit is 6 degrees of freedom for 3D models (see Remark 2).(Used for METH=1 ONLY)

CID Coordinate system flag designating how to apply inertia relief loads (Integer, Default = 0) 0= Basic coordinate systemN=Apply loads in coordinate system designated by field 7 of the GRID entry for grid id N.(Used for METH=1 ONLY)


Remarks:1. The continuation entry is required only if the eigenvalue method (METH=2) is used. Fields 5-7

must be blank if the eigenvalue method is to be used. The continuation option must be omitted if the kinematic method is to be used. The kinematic method is similar to param,inrel,-2 for other solution sequences except that the inertia relief loads are updated at each iteration.

2. For the kinematic method, a maximum of 6 degrees of freedom are allowed for 3D structures (2 or 3 dof for 2D structures). You are responsible for knowing how many rigid body modes need to be “constrained” with inertia relief. For multiple contact bodies which are unsupported at the beginning of an analysis but eventually contact, there are usually 6 dof per flexible body. This situation requires the use of the eigenvalue method with MODES set to 6 times the number of unsupported flexible bodies. If some flexible bodies are supported in some directions but not in others, the number will be less than 6 per body. It is suggested that a preliminary SOL 103 eigenvalue extraction be performed to assess the number of rigid body modes.

3. The parameter INREL is ignored by SOL 600.

IDS1 ID of SUPORT1 entries to be used if METH=3 and SID=0 (Integer, no Default) For METH=3, only SUPORT1 entries with ID=IDS1 will be used in increment zero. All SUPORT entries will be used(Used for METH=3 when SID=0 ONLY)

MODES Number of modes to use in the Eigenvalue method (Integer, no Default)(Used for METH=2 ONLY)

FMAX Rigid body modes frequency cutoff (Hz) (Real, Default =1.0 Hz)(Used for METH=2 ONLY)

FSHIFT Shift frequency used in Lanczos eigenvalue extraction (Hz) (Real, Default = -1.0 Hz)(Used for METH=2 ONLY)

Field Contents


58

Defines user subroutines for SOL 600

Format:

Examples:

Remarks:1. All user subroutines must reside in the directory where the MD Nastran input file resides.

2. All names must be in lower case and have the extension .f

3. SOL 600 combines all user subroutines into one large subroutine named u600.f and u600.f is passed to the command line when spawned from MD Nastran.\

Non-Supported ItemsOf the remaining non-supported items, the most important are listed below. If your model requires the use of these items, you should use SOL 106 or 129 instead.

• CGAP is only partially supported and its use with SOL 600 is discouraged

• Most MD Nastran superelements types are not available yet except for external superelements. SOL 600 may be used to create a superelement and write out a DMIG that may be used in a subsequent MD Nastran analysis.

• Certain Case Control entries such as STATSUB are not available

USRSUB6 Defines User Subroutines for SOL 600 - Used in MD Nastran Implicit Nonlinear - SOL 600 only

1 2 3 4 5 6 7 8 9 10

USRSUB6 U1 U2 U3 U4 U5 U6 U7 U8

U9 U10

USRSUB6 UDAMAG UVOID TENSOF

USRSUB6* SEPFORBBC

Field Contents

Ui Name of user subroutine to be included (Character, no Default) See MSC.Marc Volume D for list of available User subroutines


• MSC.Marc 2005 r3 is installed with MD Nastran 2006. Appropriate licenses are needed to use SOL 600. For most computer systems, installation is automatic. However, for some systems, particularly IBM AIX systems, the MSC.Marc Installation Manual found in the MSC Combined Documentation CD should be consulted. For certain IBM AIX systems, the include file in the tools directory must be changed and the ~/marc2005/lib/lib_extra directory might need to be renamed to ~/marc2005/lib/lib_shared if a compiler is not available. MSC technical support personnel can assist with these issues.

• For MD Nastran 2006 it is still recommended that postprocessing be accomplished using the t16 file particularly if contact output or multiple type of stress or strain tensor information is desired. MSC.Patran and certain other programs can postprocess all t16 data.


60

MD Nastran Explicit Nonlinear - SOL 700

IntroductionSOL 700 is the first release of powerful Explicit Nonlinear Solution available in MD Nastran 2006 and offers unprecedented new 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.

MD Nastran SOL 700 is being developed in phases. The first phase, available in MD Nastran 2006 r1 is intended to solve highly nonlinear transient structural applications such as crash simulations, drop test, crush and impact problems. Although Phase 1 primarily addresses crash and impact loading, usually described by initial velocity input, other types of dynamic loading are also supported. Special crash features such as seat belts and occupant dummies are also supported. Future releases of MD Nastran will also support fluid structure interaction (FSI) capability and allows users to simulate applications such as airbags, sloshing and blast problems.

SOL 700 is based on the well-known LS-DYNA solver, which is well integrated inside MD Nastran. The MD Nastran style of input data is processed within the IFP (Input File Processor) for user input errors and then filtered and mapped directly to the LS-DYNA memory by means of LS-DYNA style structured file. There are no translations between Nastran “.bdf” input file to LS-DYNA “.key” input file format. LS-DYNA then continues with computations to produce output results for highly nonlinear problems.

Native LS-DYNA results files such as d3plot and d3thdt are available for post processing. In the MD Nastran 2006 r1 release, standard Nastran output such as op2, xdb and punch are not available but may be supported in future releases.

The MD Nastran input can contain as many subcases as desired; however only one may be selected for use in any particular SOL 700 analysis. This is done using the Case Control commands, SKIP ON or OFF, to pick the desired subcase.

Linear and Nonlinear AnalysisSOL 700 is an explicit dynamic analysis program that can perform linear transient analyses (such as SOL 109) as well as nonlinear transient analyses (such as SOL 129).

It is also set up to perform linear or nonlinear static analyses (such as SOL 101 and SOL 106). Because of the numerical integration approach used within LS-DYNA, very small time steps are required to maintain accuracy and solution stability. The penalty for taking small time steps is partially offset by not having to decompose a stiffness matrix. See the MD Nastran Explicit Nonlinear User’s Guide for further theoretical details. The small time step requirements do not create a large problem when simulating events that occur quickly, such as impact or crash. However, for longer events such as low frequency


dynamics or static analysis, the run time sometimes becomes too large for explicit methods and implicit analyses need to be employed.

New entries have been added to MD Nastran to make it easier to describe crash and impact. Examples are the new TICD entry that adds a from-thru-by grid ID description so that initial velocity input can be described by one line rather than a TIC entry for each grid. This allows an existing input file to be edited and quickly changed to a crash analysis.

For those familiar with the LS-DYNA material descriptions, about 70 of the most commonly used LS-DYNA material models are supported in SOL 700. Contact is described using the same style as MD Nastran Implicit Nonlinear Solution (SOL 600); however, a new entry called “WALL” is added to facilitate the modeling of rigid and flat barriers commonly used during crash and impact simulations.

During explicit simulations, the structure will usually undergo very large deformations. As elements are distorted severely, the smallest element dimension will control the simulation timestep and therefore the runtime.

When the time step for explicit analysis decreases to very small values or reaches zero, the job will hung. To alleviate the small time step problem, an initial and minimum time step using PARAM*,DYINISTEP and PARAM*DYMINSTEP should be defined. Default values of 1.0E-6 and 1.0E-9 have been defined respectively if these parameters are not entered. If different values are desired, you can enter them (both) in the Bulk Data or in an RC file. RC files do not allow wide-field parameters, therefore if they are to be entered in an RC file, they must be truncated to 8 characters. For example, param,dyinistep,1.0E-4 and param,dyminstep,1.0E-8 are both valid entries.

Latest Capabilities of MD Nastran Explicit Nonlinear - SOL 700MD Nastran 2006 is the first official release of Explicit Nonlinear SOL 700 and it has been dramatically enhanced. The following additions including thirty NEW material models have been added:

• MATD032 – Auto glass

• MATD058 – Composites and fabrics

• MATD067 – Nonlinear Elastic Discrete Beam

• MATD068 – Nonlinear Plastic Discrete Beam

• MATD069 – SID Damper Discrete Beam

• MATD070 – Hydraulic Gas Damper Discrete Beam

• MATD071 – Cable Discrete Beam

• MATD073 – Urethane foam

• MATD074 – Elastic Spring Discrete Beam

• MATD076 – Viscoelastic

• MATD083 – Low and medium density foams

• MATD087 – Cellular Rubber

• MATD093 – Elastic 6DOF Spring Discrete Beam


62

• MATD094 – Inelastic Spring Discrete Beam

• MATD095 – Inelastic 6DOF Spring Discrete Beam

• MATD097 – General Joint Discrete Beam

• MATD119 – General Nonlinear 6DOF Discrete Beam

• MATD121 – General Nonlinear 1DOF Discrete Beam

• MATD126 – Modified Honeycomb

• MATDB01 – Seatbelt Material

• MATDHP – Hyperelastic - Mooney Rivlin

• MATDS03 – Elastoplastic Spring Material

• MATDS04 – Nonlinear Elastic Spring Material

• MATDS05 – Nonlinear Viscous Damper Material

• MATDS06 – General Nonlinear Spring Material

• MATDS07 – Maxwell Viscoelastic Spring Material

• MATDS08 – Inelastic Spring Material

• MATDS13 – Tri-Linear Degrading Material

• MATDS14 – Squat Shear wall Material

• MATDS15 – Muscle Material

The scripts used to execute the explicit solution were improved for parallel runs when different computers are involved. It is recommended that only the same type of computers running the same O/S be used with the exception that different O/S’s may be used in certain cases for Linux systems and different versions of Windows may be used with PC’s. For such systems, a hostlist needs to be setup with the format:

Hostname1 #cpus1 workdir1 exe1



etc.

• If exe3 is blank, it is assumed that the exe on node 3 is at the same location as node 1

• workdir(i) is not used but is added for compatibility with SOL 600 and other MSC products. A dummy entry needs to be made if exe(i) is required

• Multiple CPU runs using a machine with several cpu’s in the same box do not require a hostlist

• See the SOL 700,ID (p. 175) in the MD Nastran Quick Reference Guide for more details

• Two ways of specifying dynamic loads are available using PARAM,DYDYLOAD. The first method is to translate the loads in MD Nastran. The second method is to pass the loads directly to the explicit solution which has improved capabilities to handle these loads. A description of this parameter follows:

PARAM,DYDYLOAD,IFLAG (Integer, Default = 1)


Determines if MD Nastran dynamic loads are passed directly to the explicit solution or translated by the internal translator in MD Nastran.

1. Dynamic loads are translated by the internal translator in MD Nastran.

2. Dynamic loads are passed directly to the explicit solution. For this option to work properly, if loads other than what is listed below are used, the job may fail or obtain the wrong results.

Case Control

DLOAD

LOADSET

LOAD (dynamic relaxation only)

Bulk Data

LSEQ

DLOAD

DELAY

LOAD (dynamic relaxation only)

DAREA

TLOAD1

TABLED1, TABLED2, TABLED3

FORCE

FORCE2

MOMENT

MOMENT2

GRAV

PLOAD

PLOAD4

RFORCE (CID, METHOD, RACC, MB fields are not available)

SPCD

Note:

1. This parameter may be placed in rc files.

Error diagnostics have been improved. You should examine files jid.dytr_prep.d3hsp, jid.dytr_prep.out and jid.dytr.d3hsp for the string “Error” as well as the standard files jid.f06 (search for FATAL and Severe Warning”) and jid.log (look for anything unusual) should a job not run to completion.

The following new Bulk Data entries have been added:

• ACCMETR – Define seat belt an accelerometer

• BCGRID – Define grid points to be included as slave body contact entity


64

• BCSEG – Define grid points which are part of an element to be used in contact analyses

• CBELT – Define a Seatbelt Element

• DYDELEM – Delete failed elements and continue analysis

• DYTERMT – Terminate the job depending on user-specified conditions (such as failed elements)

• DYRELAX – Dynamic relaxation specifications for restart runs

• DYCHANG – Boundary changes for restart runs

• D2R0000 – Switch standard materials to rigid materials

• D2RINER – Define inertial properties for materials switch to rigid materials

• PBELTD - Define section properties for the seat belt elements

• R2RAUTO – Switch parts to rigid materials

• RBE2F – Define nodal constraint sets for translational motion in global coordinates

• RCONN – Defines a rigid connection between the different parts of Lagrangian meshes

• SBPRET – Defines a seat belt pretensioner

• SBRETR – Defines a seat belt retractorBSENSR – Defines a seat belt sensor

• SBSLPR – Define seat belt slip ring

• SPCD2 – Define an imposed nodal motion on a node or a set of nodes.

The following Bulk Data entries have been changed or additions have been made

• CELAS2D

• PBARL (now available for SOL 700)

• RESTART (new options added)

• DYPST1, DYPST2, DYPST3, DYPST4, DYPST5 (Bulk Data entries for d3plot to op2).

• WALLGEO – Defines a geometric rigid wall

The following SOL 700 parameters have been added or revised:

• CWLDIGNR

• SCALEMASS

• STEPFCT

• DYELPLSY

• DYELPLET

• DYELPLFL

• DYELAS1C

• DYELAS1F

• DYELAS1R

• DYDTOUT


• DYDYLOAD

• DYPARAM,ELDLTH

• DYPARAM,LSDYNA,BINARY

• DYPARAM,LSDYNA,DB-EXTENT

• DYPARAM,LSDYNA,HOURGLASS

• DYPARAM,LSDYNA,OUTPUT

• DYPARAM,LSDYNA,RELAX

Example: Projectile Hitting a Plate with FailureOne typical example of SOL 700 Phase 1 is a projectile hitting a plate at an oblique angle. The initial velocity of the projectile is large enough that over time various elements in the plate fail. Depending on the postprocessor used, if it can account for failed elements, the failed elements are removed from the model.

This model involves contact between the projectile and the plate. SOL 600-style contact is used. It also involves the use of LS-DYNA material MATD024 (elastoplastic material with arbitrary stress- strain curves and strain-rate dependency). This model with close to 8000 grid points requires about 20 minutes to run on a 2.4 GHz PC.

The following plots show the evolution of the effective stress and damage with time:


66


Portions the MD Nastran input file named projtl.dat are shown and discussed below:

SOL 700,NLTRAN path=1 stop=1TIME 10000CENDECHO = NONEDISPLACEMENT(SORT1,print,PLOT) = ALLStress(SORT1,PLOT) = ALLStrain(SORT1,PLOT) = ALLaccel(print,plot)= ALLvelocity(print,plot)= ALLecho=bothSPC = 2IC=1TSTEPNL = 20BCONTACT = 1weightcheck=yespageBEGIN BULKTSTEPNL 20 10 11 1 5 10 ++ +


68

+ 0PARAM,DYDTOUT,5PARAM*,DYCONSLSFAC,1.0PARAM,OGEOM,NOPARAM,AUTOSPC,YESPARAM,GRDPNT,0param,dyendtim,1param,dymats1,1param,dyldknd,0$BCTABLE 1 4SLAVE 3+YESMASTER 4$BCBODY 3 3 DEFORM 3 0BCBODY 4 3 DEFORM 4 0$BCPROP 3 2BCPROP 4 1$$$ ========== PROPERTY SETS ==========$$ * projectile *$PSOLID 1 1$$ * plate *$PSOLID 2 2$$$ ========= MATERIAL DEFINITIONS ==========$$$$ -------- Material MAT_PLASTIC_KINE.2 id =2MATD024 1 18.62 1.17 .22 0.0179 0.8$ -------- Material MAT_PLASTIC_KINE.1 id =1MATD024 2 7.896 2.1 .284 0.01 0.8$$$$ ======== Load Cases ========================$$$ ------- Initial Velocity BC ini -----$TICD 1 1 1 0.1246 2586 1TICD 1 1 3 -0.03339 2586 1...ENDDATA

All of the previous input data are described in the MD Nastran Quick Reference Guide and summarized above. Note that it was only necessary to add BCONTACT=1 to the Case Control, a few new Bulk Data


parameters and a few contact entries to the Bulk Data to an existing file that would be used in MD Nastran SOL 101, 106, 109 or 129 analyses.

Example: Pickup Truck Crash TestAnother example involves crash testing of a pickup truck against a rigid wall. The input data file for this example is quite large and can be provided on request. It is a typical example of what can be done using a full car or truck model, developed originally for NVH analysis and subsequently used for SOL 700 for crash simulation.


70

Example – 3 Car Crash SimulationThis is an example of a large model simulating the 3 car crash scenario. The model was taken from topcrunch.org –site (http://www.topcrunch.org/benchmark_results.sfe). The original model was in LS-DYNA key-file which was translated to MD Nastran format to be run by SOL 700. The original model was corrected to include the contact definition between the front and rear cars and the road. The model size information and results are shown below:

http://www.topcrunch.org/benchmark_results.sfe


Where Can I Find More Information:MD Nastran Explicit Nonlinear Analysis, SOL 700, is documented in the following manuals and guides:

• MD Nastran Quick Reference Guide

• MD Nastran Explicit Nonlinear User’s Guide

• MSC.Patran User’s Guide

• MSC.Patran – MD Nastran and MSC.Dytran Preference Guides

• LS-DYNA Keyword User’s Manual, Version 970 (available from LSTC)

• LS-DYNA Theoretical Manual (available from LSTC)


72


Ch. :

3 Numerical Enhancements

New Iterative Solver Option, 74

MDACMS Enhancements, 83

MPYAD Method 1 Enhancement, 90

Improved Robustness in the Lanczos Method, 91

MLDMP in Solution 111 (Pre-Release), 92


74

New Iterative Solver Option

IntroductionStatic structural analyses of very large solid element models pose difficult computational challenges for the solvers available in MD Nastran. For most modeling situations, the sparse direct solver is the solver of choice because it is usually the most efficient. However, as the number of degrees of freedom grows ever larger, iterative solution methods become more attractive since they tend to produce results faster than the direct method. For this reason, both solution techniques are available in MD Nastran.

In order to increase performance even more in the iterative method, the solver offered by Computational Applications and System Integration, Inc. (CASI) is being introduced into MD Nastran.

BenefitsThe introduction of the element-based iterative solver option allows users to run larger jobs faster and with fewer resources (memory and disk) than could be done before. It is anticipated that most jobs will run at least twice as fast when the element-based solver option is specified compared to jobs run with any of the existing MD Nastran iterative solver pre-conditioner choices. For very large jobs, the performance could be up to ten times better.

Method and TheoryUntil now, the iterative solution technique in MD Nastran has been matrix-based, meaning that the process does not use any element topology information to assist in the solution. The iterative solver operates on the same matrices that are processed by the direct solver. The element-based iterative solver on the other hand, uses finite element topology and element stiffness matrices directly to obtain the solution. Using this information generally results in smaller pre-conditioners that take less time to factor and that have more model – specific “information”, as a result, fewer conjugate gradient iterations are required to arrive at a converged solution compared to matrix-based techniques.

Convergence for the element-based iterative solver is achieved when the value of one of four norms falls below the specified convergence tolerance (the default value is 1.0e-04) and the values of all four norms have fallen below a slightly looser tolerance. To define the norms, let

• b be the original right-hand-side

• A be the global system matrix

• M be the pre-conditioner

• x be the solution at the current step

• r be the current residual

• || || denote 2-norm

• | | denote infinity norm

• ∆x denote the change in current solution x at a particular step.

75CHAPTER 3Numerical Enhancements

Then, the four norms are defined as follows:

1. Reduction in 2-norm of residual

2. Reduction in infinity norm of residual

3. Reduction in preconditioned norm of residual

4. Estimate of normalized energy norm of error in solution

InputsThe SMETHOD Case Control command must be used to select the iterative solver. The SMETHOD command has been enhanced to allow selection of either the existing matrix-based technique or the new element-based technique directly, accepting all default options. This is accomplished by specifying SMETHOD=MATRIX to invoke the existing matrix-based iterative solution technique and SMETHOD=ELEMENT to invoke the new element-based iterative solution technique. The SMETHOD command also accepts the specification of an integer value representing the ID of an ITER Bulk Data entry. In this way, default options can be changed. The PRECOND field of the ITER Bulk Data entry accepts the keyword “CASI” to indicate that the element-based solver is to be used.

OutputsThere is no new MD Nastran output produced by the element-based iterative solver. The intermediate convergence parameter output produced by the MSGFLG=YES option of the ITER Bulk Data entry contains the values of the four convergence norms at each iteration. A summary file is produced by the element-based iterative solver that contains various statistics about the solution process. The file name uses the Job ID (jid.PCS), where jid is the name of the input data file.

N1rb

--------=

N2rb

------=

N3 rT

M1–r b

TM

1–b⁄=

N4 ∆xT

A∆x( ) xT

Ax( )⁄=


76

Guidelines and LimitationsThe element-based iterative solver is intended for very large static structural analysis models composed mainly of 10 node CTETRA elements. It generally out-performs the direct solver when the problem size exceeds one million degrees of freedom and will out-perform the matrix-based iterative solver when the problem size reaches approximately three million degrees of freedom. The element-based solver is intended for a very specific set of model characteristics. As such, the following limitations apply:

• Available in linear static structural analysis (SOL 101) only

• No GENEL elements allowed

• No K2GG direct input matrix selection allowed

• No ASET/OMIT reduction allowed

• No SUPORTi allowed

• No SCALAR points (explicitly or implicitly defined) allowed

• No heat transfer allowed

• No p-elements allowed

• Only BAR, BEAM, BUSH, ROD, CONROD, ELAS1, ELAS2, SHEAR, QUAD4, QUAD8, QUADR, TRIA3, TRIA6, TRIAR, TETRA, PENTA and HEXA elements are allowed

Demonstration ExampleA simple example is presented that demonstrates the use of the element-based iterative solver. The ITER Case Control command is used to specify the element-based iterative solver. The example problem is used for demonstration purposes only and is not representative of anything in particular. The model data consists of a simple solid brick structure subject to an end load.

Example Input Data

ID CASI,DEMOSOL 101TIME 10000CENDECHO = NONEDISPLACEMENT = ALLsmethod = elementSUBCASE = 1SPC = 1LOAD = 1BEGIN BULKiter,1000,,,,,,,,+it1+it1 precond=casiPARAM,AUTOSPC,YESGRID, 1,, 0.00,0.00,0.00GRID, 2,, 0.00,1.00,0.00GRID, 3,, 0.00,0.00,0.50GRID, 4,, 0.00,1.00,0.50GRID, 5,, 1.25,0.00,0.00


GRID, 6,, 1.25,1.00,0.00GRID, 7,, 1.25,0.00,0.50GRID, 8,, 1.25,1.00,0.50GRID, 9,, 2.50,0.00,0.00GRID, 10,, 2.50,1.00,0.00GRID, 11,, 2.50,0.00,0.50GRID, 12,, 2.50,1.00,0.50GRID, 13,, 3.75,0.00,0.00GRID, 14,, 3.75,1.00,0.00GRID, 15,, 3.75,0.00,0.50GRID, 16,, 3.75,1.00,0.50GRID, 17,, 5.00,0.00,0.00GRID, 18,, 5.00,1.00,0.00GRID, 19,, 5.00,0.00,0.50GRID, 20,, 5.00,1.00,0.50GRID, 21,, 6.25,0.00,0.00GRID, 22,, 6.25,1.00,0.00GRID, 23,, 6.25,0.00,0.50GRID, 24,, 6.25,1.00,0.50GRID, 25,, 7.50,0.00,0.00GRID, 26,, 7.50,1.00,0.00GRID, 27,, 7.50,0.00,0.50GRID, 28,, 7.50,1.00,0.50GRID, 29,, 8.75,0.00,0.00GRID, 30,, 8.75,1.00,0.00GRID, 31,, 8.75,0.00,0.50GRID, 32,, 8.75,1.00,0.50GRID, 33,,10.00,0.00,0.00GRID, 34,,10.00,1.00,0.00GRID, 35,,10.00,0.00,0.50GRID, 36,,10.00,1.00,0.50GRID, 37,, 0.00,0.50,0.00GRID, 38,, 0.00,0.50,0.50GRID, 39,, 1.25,0.50,0.00GRID, 40,, 1.25,0.50,0.50GRID, 41,, 2.50,0.50,0.00GRID, 42,, 2.50,0.50,0.50GRID, 43,, 3.75,0.50,0.00GRID, 44,, 3.75,0.50,0.50GRID, 45,, 5.00,0.50,0.00GRID, 46,, 5.00,0.50,0.50GRID, 47,, 6.25,0.50,0.00GRID, 48,, 6.25,0.50,0.50GRID, 49,, 7.50,0.50,0.00GRID, 50,, 7.50,0.50,0.50GRID, 51,, 8.75,0.50,0.00GRID, 52,, 8.75,0.50,0.50GRID, 53,,10.00,0.50,0.00GRID, 54,,10.00,0.50,0.50GRID, 55,, 0.00,0.00,0.25GRID, 56,, 0.00,1.00,0.25GRID, 57,, 1.25,0.00,0.25GRID, 58,, 1.25,1.00,0.25GRID, 59,, 2.50,0.00,0.25GRID, 60,, 2.50,1.00,0.25GRID, 61,, 3.75,0.00,0.25GRID, 62,, 3.75,1.00,0.25GRID, 63,, 5.00,0.00,0.25GRID, 64,, 5.00,1.00,0.25GRID, 65,, 6.25,0.00,0.25


78

GRID, 66,, 6.25,1.00,0.25GRID, 67,, 7.50,0.00,0.25GRID, 68,, 7.50,1.00,0.25GRID, 69,, 8.75,0.00,0.25GRID, 70,, 8.75,1.00,0.25GRID, 71,,10.00,0.00,0.25GRID, 72,,10.00,1.00,0.25GRID, 73,, 0.625,0.00,0.00GRID, 74,, 0.625,1.00,0.00GRID, 75,, 0.625,0.00,0.50GRID, 76,, 0.625,1.00,0.50GRID, 77,, 1.875,0.00,0.00GRID, 78,, 1.875,1.00,0.00GRID, 79,, 1.875,0.00,0.50GRID, 80,, 1.875,1.00,0.50GRID, 81,, 3.125,0.00,0.00GRID, 82,, 3.125,1.00,0.00GRID, 83,, 3.125,0.00,0.50GRID, 84,, 3.125,1.00,0.50GRID, 85,, 4.375,0.00,0.00GRID, 86,, 4.375,1.00,0.00GRID, 87,, 4.375,0.00,0.50GRID, 88,, 4.375,1.00,0.50GRID, 89,, 5.625,0.00,0.00GRID, 90,, 5.625,1.00,0.00GRID, 91,, 5.625,0.00,0.50GRID, 92,, 5.625,1.00,0.50GRID, 93,, 6.875,0.00,0.00GRID, 94,, 6.875,1.00,0.00GRID, 95,, 6.875,0.00,0.50GRID, 96,, 6.875,1.00,0.50GRID, 97,, 8.125,0.00,0.00GRID, 98,, 8.125,1.00,0.00GRID, 99,, 8.125,0.00,0.50GRID,100,, 8.125,1.00,0.50GRID,101,, 9.375,0.00,0.00GRID,102,, 9.375,1.00,0.00GRID,103,, 9.375,0.00,0.50GRID,104,, 9.375,1.00,0.50GRID,105,, 0.625,0.00,0.25GRID,106,, 0.625,1.00,0.25GRID,107,, 1.875,0.00,0.25GRID,108,, 1.875,1.00,0.25GRID,109,, 3.125,0.00,0.25GRID,110,, 3.125,1.00,0.25GRID,111,, 4.375,0.00,0.25GRID,112,, 4.375,1.00,0.25GRID,113,, 5.625,0.00,0.25GRID,114,, 5.625,1.00,0.25GRID,115,, 6.875,0.00,0.25GRID,116,, 6.875,1.00,0.25GRID,117,, 8.125,0.00,0.25GRID,118,, 8.125,1.00,0.25GRID,119,, 9.375,0.00,0.25GRID,120,, 9.375,1.00,0.25GRID,121,, 0.625,0.50,0.00GRID,122,, 0.625,0.50,0.50GRID,123,, 1.875,0.50,0.00GRID,124,, 1.875,0.50,0.50GRID,125,, 3.125,0.50,0.00


GRID,126,, 3.125,0.50,0.50GRID,127,, 4.375,0.50,0.00GRID,128,, 4.375,0.50,0.50GRID,129,, 5.625,0.50,0.00GRID,130,, 5.625,0.50,0.50GRID,131,, 6.875,0.50,0.00GRID,132,, 6.875,0.50,0.50GRID,133,, 8.125,0.50,0.00GRID,134,, 8.125,0.50,0.50GRID,135,, 9.375,0.50,0.00GRID,136,, 9.375,0.50,0.50GRID,137,, 0.000,0.50,0.25GRID,138,, 1.250,0.50,0.25GRID,139,, 2.500,0.50,0.25GRID,140,, 3.750,0.50,0.25GRID,141,, 5.000,0.50,0.25GRID,142,, 6.250,0.50,0.25GRID,143,, 7.500,0.50,0.25GRID,144,, 8.750,0.50,0.25GRID,145,,10.000,0.50,0.25GRID,146,, 0.625,0.50,0.25GRID,147,, 1.875,0.50,0.25GRID,148,, 3.125,0.50,0.25GRID,149,, 4.375,0.50,0.25GRID,150,, 5.625,0.50,0.25GRID,151,, 6.875,0.50,0.25GRID,152,, 8.125,0.50,0.25GRID,153,, 9.375,0.50,0.25CTETRA 1 1 1 4 3 7 137 38 55 105 122 75CTETRA 2 1 1 4 7 5 137 122 105 73 146 57CTETRA 3 1 4 7 5 8 122 57 146 76 40 138CTETRA 4 1 1 2 4 5 37 56 137 73 121 146CTETRA 5 1 2 4 5 8 56 146 121 106 76 138CTETRA 6 1 2 8 5 6 106 138 121 74 58 39CTETRA 7 1 5 8 7 11 138 40 57 107 124 79CTETRA 8 1 5 8 11 9 138 124 107 77 147 59CTETRA 9 1 8 11 9 12 124 59 147 80 42 139CTETRA 10 1 5 6 8 9 39 58 138 77 123 147CTETRA 11 1 6 8 9 12 58 147 123 108 80 139CTETRA 12 1 6 12 9 10 108 139 123 78 60 41CTETRA 13 1 9 12 11 15 139 42 59 109 126 83CTETRA 14 1 9 12 15 13 139 126 109 81 148 61CTETRA 15 1 12 15 13 16 126 61 148 84 44 140CTETRA 16 1 9 10 12 13 41 60 139 81 125 148


80

CTETRA 17 1 10 12 13 16 60 148 125 110 84 140CTETRA 18 1 10 16 13 14 110 140 125 82 62 43CTETRA 19 1 13 16 15 19 140 44 61 111 128 87CTETRA 20 1 13 16 19 17 140 128 111 85 149 63CTETRA 21 1 16 19 17 20 128 63 149 88 46 141CTETRA 22 1 13 14 16 17 43 62 140 85 127 149CTETRA 23 1 14 16 17 20 62 149 127 112 88 141CTETRA 24 1 14 20 17 18 112 141 127 86 64 45CTETRA 25 1 17 20 19 23 141 46 63 113 130 91CTETRA 26 1 17 20 23 21 141 130 113 89 150 65CTETRA 27 1 20 23 21 24 130 65 150 92 48 142CTETRA 28 1 17 18 20 21 45 64 141 89 129 150CTETRA 29 1 18 20 21 24 64 150 129 114 92 142CTETRA 30 1 18 24 21 22 114 142 129 90 66 47CTETRA 31 1 21 24 23 27 142 48 65 115 132 95CTETRA 32 1 21 24 27 25 142 132 115 93 151 67CTETRA 33 1 24 27 25 28 132 67 151 96 50 143CTETRA 34 1 21 22 24 25 47 66 142 93 131 151CTETRA 35 1 22 24 25 28 66 151 131 116 96 143CTETRA 36 1 22 28 25 26 116 143 131 94 68 49CTETRA 37 1 25 28 27 31 143 50 67 117 134 99CTETRA 38 1 25 28 31 29 143 134 117 97 152 69CTETRA 39 1 28 31 29 32 134 69 152 100 52 144CTETRA 40 1 25 26 28 29 49 68 143 97 133 152CTETRA 41 1 26 28 29 32 68 152 133 118 100 144CTETRA 42 1 26 32 29 30 118 144 133 98 70 51CTETRA 43 1 29 32 31 35 144 52 69 119 136 103CTETRA 44 1 29 32 35 33 144 136 119 101 153 71CTETRA 45 1 32 35 33 36 136 71 153 104 54 145CTETRA 46 1 29 30 32 33 51 70 144 101 135 153


CTETRA 47 1 30 32 33 36 70 153 135 120 104 145CTETRA 48 1 30 36 33 34 120 145 135 102 72 53PSOLID 1 1 0MAT1,1,1.0SPC1,1,456,1,THRU,153SPC 1 1 123 0.SPC 1 2 123 0.SPC 1 3 123 0.SPC 1 4 123 0.SPC 1 55 123 0.SPC 1 56 123 0.SPC 1 37 123 0.SPC 1 38 123 0.SPC 1 137 123 0.PLOAD4* 1 48 1.000000000E+00 1.000000000E+00** 1.000000000E+00 1.000000000E+00 33 30** 0 1.000000000E+00 0.000000000E+00 0.000000000E+00** PLOAD4* 1 45 1.000000000E+00 1.000000000E+00** 1.000000000E+00 1.000000000E+00 33 32** 0 1.000000000E+00 0.000000000E+00 0.000000000E+00** ENDDATA

Example OutputThe output generated consists of the usual MD Nastran output as well as an output file generated by the element-based iterative solver. The contents of this file summarize various statistics about the solution process. Some of the statistics include the number of terms in the various matrices, number of degrees of freedom, number of iterations taken and convergence parameter values. The file will have a suffix of .PCS and appear in the same location as other output files produced by the job. The contents of the .PCS file for the example problem are shown here for reference.

******************************************************************************(C) Copyright 1992-2004Computational Applications and System Integration Inc.All rights Reserved.******************************************************************************

Job:./v2006rgat:Wed Oct 12 10:30:35 2005

******************************************************************************

ESTIMATED MEMORY (MB): 0.094738Preallocated Virtual Memory : 27.3828 MBVirtual Memory Used : 1.96344 MB

************************************************************************************************************************************************************


82

(C) Copyright 1992-2004Computational Applications and System Integration Inc.All rights Reserved.******************************************************************************

Job:./v2006rgat:Wed Oct 12 10:30:36 2005

Degrees of Freedom: 459DOF Constraints: 27Elements: 48Assembled: 0Implicit: 48Nodes: 153Number of Load Cases: 1

Nonzeros in Upper Triangular part of Global Stiffness Matrix : 0Nonzeros in Preconditioner: 8298*** Precond Reorder: MLD ***Nonzeros in V: 2160Nonzeros in factor: 5220*** Primal Preconditioner Activated ***VTAeV:uTime:0 Sec:sTime:0 Sec

Total Operation Count: 851878Total Iterations In PCG: 8Average Iterations Per Load Case: 8.000000Input PCG Error Tolerance: 1e-04Achieved PCG Error Tolerance: 5.81869e-05

DETAILS OF SOLVER CP TIME(secs)User SystemAssembly0 0Preconditioner Construction0 0Preconditioner Factoring0 0Preconditioned CG0 0******************************************************************************Total PCG Solver CP Time: User: 0 secs: System: 0 secs******************************************************************************Available Physical Memory (RAM) : 0 MBEstimate of Memory Usage In CG : 0.080898 MBEstimate of Disk Usage : 0.09228 MBPreallocated Virtual Memory : 27.3828 MBVirtual Memory Used : 4.16164 MB*** Implicit Matrix Multiplication Activated : Mode 3 *********************************************************************************Multiply with A time in decisecs 0Precond solve time in decisecs 0******************************************************************************Total Elapsed Time (Secs): 1******************************************************************************


MDACMS Enhancements

BackgroundMatrix Domain Automated Component Modal Synthesis (MDACMS) is now the default ACMS method. The older Geometric Domain approach (GDACMS) remains available but is not the recommended ACMS method. The PARTOPT keyword on the DOMAINSOLVER Executive System command is used to choose between the Geometric and Matrix (or DOF) domains: PARTOPT=DOF is now the default for ACMS.

SummaryThe primary goal of development of MD Nastran 2006 MDACMS is to improve performance by reducing disk I/O and Executive System overhead. Generally, this is achieved by allowing Nastran to utilize memory more effectively than in the past. In addition, several subDMAPs have been consolidated into a single new DMAP module.

Specific enhancements to the MDACMS capability include the following:

• The ability to specify key scratch datablocks for Scratch Memory (SMEM) residence via a new FMS command: MEMLIST.

• Introduction of a new module to perform functions in support of residual vector calculations: the RESMOD module.

• Enhancements to matrix multiply-and-add (MPYAD module) Method 1.

New FMS Command: MEMLISTThe File Management Section (FMS) has been enhanced to include a new MEMLIST command, described below. The purpose of the MEMLIST command is to limit the use of Scratch Memory (SMEM) to a subset of Nastran scratch datablocks. In this way, the effectiveness of SMEM increases to the extent that the user knows which scratch datablocks are likely to be accessed most often.

A pre-defined MEMLIST command has been created and is available in the form of an INCLUDE file. This file is delivered in the SSSALTERDIR directory, which is available when a full Nastran installation has been performed. In order to access this file, specify the following INCLUDE command in the FMS Section of the input file:

INCLUDE ‘SSSALTERDIR:memlist.acms’

This file lists scratch datablocks that will reduce the disk I/O by a significant amount, provided that enough Scratch Memory has been specified.

The following is the MD Nastran Quick Reference Guide description of the MEMLIST command.


84

Specify a list of scratch datablocks that may reside in scratch memory (SMEM).

Format:MEMLIST DATABLK = (DBname1, DBname2, ..., DBnamei)

Remarks:1. Only NDDL and local scratch datablocks may be included in MEMLIST specification.

2. Datablocks specified will reside in SMEM on a first come, first served basis.

3. Datablocks not specified by this command will not reside in SMEM.

4. Database directories for the SCRATCH DBset reside in SMEM and are not affected by any MEMLIST specification.

5. Continuation lines are allowed.

6. Multiple MEMLIST commands are honored.

7. Scratch I/O activity is reported in the F04 file by including DIAG 42 in the Executive Section.

Example:MEMLIST DATABLK = (KOO, MOO, KQQ, MQQ)

If generated, datablocks KOO, MOO, KQQ, and MQQ will reside in scratch memory. All other datablocks will be excluded from scratch memory.

New Module: RESMODThe ACMS process entails computing residual vectors at each automatically generated component. Each step taken during residual vector calculations is carried out by a particular subDMAP call. In order to streamline the DMAP and reduce Executive System overhead, the RESMOD module has been developed for MD Nastran 2006. The RESMOD module is only invoked during MDACMS operations, when the size of the vectors is relatively small, which is a characteristic of MDACMS computations.

The module syntax is similar to the MATMOD module, since the first parameter (P1) defines the operation to be performed. However, unlike MATMOD, P1 is a character pneumonic instead of an integer code value. The complete DMAP description is below.

MEMLIST Specify Datablocks Eligible for SMEM

Describer Meaning

DBnamei Name of a MD Nastran datablock.


Perform linear algebra functions to support residual vector calculations.

Format:

Input Data Blocks:

Output Data Blocks:

Parameters:

Remark:

Each option corresponds to a different value of the first parameter, P1, as follows.

Details for each option are given in the following sections.

RESMOD RESVEC Calculations

RESMOD I1,I2,I3,I4,I5/O1,O2,O2,O3,O4,O5/P1/P2/P3/P4/P5/P6 $

Ii: Input data blocks. I1 is required. I2 through I5 may not be necessary depending on the value of P1.

Oi Output data blocks.

P1 Input-character-no default. Option selection described in the table below.

P2,P3,P4 Input-integer-default=0. Integer parametric data depending on P1.

P5,P6 Input-real-default=0.0. Real parametric data depending on P1.

P1 Value Brief Description

‘ATBC’ Performs [A]T[B][C] if [C] present; [A]T[B][A] otherwise

‘MPART’ Partitions stiffness, mass, and eigenvector matrices based on mass content

‘LININD’ Find linearly independent and dependent vectors of a matrix

‘LDSWEEP’ Sweeps “modal” loads for load vectors

‘USWEEP’ Sweeps a matrix for small vectors


86

Option P1 = ‘ATBC’

Performs the matrix multiplication [I1]T[I2][I3] if [I3] is present; [I1]T[I2][I1] otherwise.

Format:

Input Data Blocks:

Output Data Blocks:

Remark:

[I2] is assumed to be symmetric.

Example:

Compute the product [D] = [A] T [B] [C]

Option P1 = ‘MPART’Partitions stiffness, mass, and eigenvector matrices based on mass content.

Format:

Input Data Blocks:

RESMOD I1,I2,I3,,/O1,,,,/’ATBC’ $

I1,I2,I3 Any matrix data blocks.

O1 Matrix product.

RESMOD A,B,C,,/D,,,,/’ATBC’ $

RESMOD PHI,K,M,,/PHI0,K0,PHI1,M1,K1/’MPART’////ZROSTIFF/ZROMASS $

PHI A set of eigenvectors.

K Stiffness matrix associated with [PHI].

M Mass matrix associated with [PHI].


Output Data Blocks:

Parameters:

Remark:

Only real matrices are supported.

Option P1 = ‘LININD’Partitions a matrix into linearly independent and dependent sets.

Format:

Input Data Blocks:

Output Data Blocks:

Parameters:

PHI0 Massless eigenvectors.

K0 Stiffness associated with [PHI0].

PHI1 Eigenvectors which contain mass.

M1 Mass associated with [PHI1].

K1 Stiffness associated with [PHI1].

ZROSTIFF Input-real-default=1.0E-8. Null stiffness filter criteria.

ZROMASS Input-real-default=1.0E-16. Null mass filter criteria.

RESMOD U,M,,,/U0,U1,,,/’LININD’////ZROVEC $

U Any real matrix.

M Mass matrix associated with [U].

U0 Linearly dependent vector set from [U].

U1 Linearly independent vector set from [U].

ZROVEC Input-real-default=1.0E-6. Null filter criteria.


88

Remarks:1. M may be purged, in which case the identity matrix is assumed.

2. Output matrices [U0] and [U1] should satisfy the following conditions:

3. Only real matrices are supported.

Option P1 = ‘LDSWEEP’Sweeps “modal” loads for load vectors.

Format:

Input Data Blocks:

Output Data Blocks:

Parameters:

Remarks:1. The filtered load vectors are:


RESMOD LD,PHI,MXX,MQQ,/LDIND,,,,/’LDSWEEP’/NORMFLG $

LD A set of load vectors.

PHI Modal vectors.

MXX Mass matrix, physical degrees of freedom.

MQQ Mass matrix, modal degrees of freedom.

LDIND Filtered load vectors.

NORMFLG Input-integer-default=0. Normalization flag. Set to –1 to unit normalize load vectors.

U0[ ]TM[ ] U0[ ] computational zeros=

U1[ ]TM[ ] U0[ ] 0.0>

LDIND[ ] LD[ ]= M[ ] PHI[ ]– INV PHI[ ]TM[ ] PHI[ ]( ) PHI[ ]T

LD[ ]⋅ ⋅


Option P1 = ‘USWEEP’Sweeps a matrix for small vectors.

Format:

Input Data Blocks:

Output Data Blocks:

Parameters:

Remarks:1. The filtered vectors are:


RESMOD U,PHI,MXX,MQQ,/UIND,,,,/’USWEEP’/NORMFLG $

U A set of vectors.

PHI Modal vectors.

MXX Mass matrix, physical degrees of freedom.

MQQ Mass matrix, modal degrees of freedom.

UIND Filtered vectors.

NORMFLG Input-integer-default=0. Normalization flag. Set to –1 to unit normalize input vectors.

UIND[ ] U[ ]= INV PHI[ ] MQQ[ ] PHI[ ]T( )– MXX[ ] U[ ]⋅ ⋅


90

MPYAD Method 1 EnhancementThe Storage 3 option of matrix multiply and add (MPYAD) module Method 1 has been enhanced remove null rows of the [B] matrix, where [B] is the second matrix in the matrix product

This results in a reduction of the number of operations necessary to complete the matrix multiply. MPYAD Method 1 Storage 3 is frequently invoked during MDACMS reduction operations.

ExampleThis example demonstrates the potential impact of these enhancements.

Problem Definition:• Acoustic Analysis (modal frequency response, SOL 111)

• Over 600,000 grid points; 3.5 million degrees of freedom

• Over 4,000 structure modes up to 600 Hertz; 200 fluid modes

• 12 load cases; over 700 forcing frequencies

Machine Resources• Linux IA64 with 12Gb main memory

• HP DS2100 3-way striped scratch disk

The MSC.Nastran 2005 r2 run was made with one gigabyte of memory (“mem=1gb”). The MD Nastran 2006 run was made using “mem=8gb smem=7gb”. This resulted in the same Open Core size (1gb) but with 7gb memory devoted to SMEM. The standard MEMLIST specification found in SSSALTER:memlist.acms was used for MD Nastran 2006. Finally, both runs utilized serial processing.

Version Elap (sec) CPU (sec) Total I/O (gb) HiWater Disk (gb)

MSC.Nastran 2005 r2 12472 10734.3 37.303 1501.81

MD Nastran 2006 9369 8239.3 31.873 684.402

Speedup 24.88% 23.24% 14.56% 54.43%

D[ ] A[ ] B[ ] C[ ]±±=


Improved Robustness in the Lanczos MethodA new feature in the READ module is used to scale some intermediate quantities computed during the Lanczos procedure. The effect is a more stable factorization, with a lower MAT RATIO, particularly when Lagrange multipliers are used. In practical examples, this feature has reduced max ratios by six orders of magnitude.

This feature may be disabled by setting system cell 166 to 48.


92

MLDMP in Solution 111 (Pre-Release)The Multi-Level Distributed Memory Parallel (MLDMP) option is available for solution 111 in pre-release status. This option generates eigenvectors using the Lanczos method in a hierarchic parallel fashion. That is, the frequency range is divided into a user-specified number of segments, and each segment is assigned to a logical group or cluster of processors. The modes in each segment are computed in parallel, and in turn, each cluster uses a matrix-based domain decomposition to compute the modes for its segment in parallel. The new option provides improved scaling across a larger number of processors.

User InterfaceThe MLDMP option may be selected by specifying

DOMAINSOLVER MODES (PARTOPT=DOF)

in the Executive Control Section of the input file, and then using the DMP and NCLUST command line keywords to specify the number of processors and the number of logical clusters, respectively. Remember that the number of logical clusters is the same as the number of frequency segments. The value of DMP should be a multiple of NCLUST. The number of matrix domains will be the quotient DMP/NCLUST, so it is recommended that values of DMP and NCLUST be chosen so that DMP/NCLUST is a power of 2.

The upper frequency limit must be specified on the EIGRL bulk data entry, and it is recommended that a lower frequency limit be specified as well.

Case StudyA 1.3 Mdof body-in-white model was run, computing modes up to 300 Hz (1397 eigenvalues), using a cluster of 8 IBM P655 servers, each with 8 1.5-GHz POWER4+ processors and 16 GB of physical memory. Each node had two local, 73GB disks for scratch.

The parallel performance scaled well, achieving nearly a 6-fold improvement when using 16 processors.

0123456

Speedup

2 4 8 16

Number of Processors

DMP Performance (Elapsed Time)


The MLDMP option also reduces the per-processor resource requirements in terms of both memory required and I/O performed:

0

500

1000

1500

2000

I/O p

er

pro

cess

or

(GB

)

1 2 4 8 16


I/O Reduction

050

100150200250

Meg

awo

rds

1 2 4 8 16


Memory Hiwater


94


Ch. :

4 Elements

Three-Node Beam Element, 96

CWSEAM Connector Elements, 105

Line Interface Element, 117

Arbitrary Beam Cross-Section, 126


96

Three-Node Beam Element

IntroductionA general three-node beam element has been developed for linear static, modal, dynamic and buckling analyses. The element has been implemented as a curved one-dimensional Timoshenko beam element so that both the initial curvatures of beam reference axis and the cross-section shears are included in the formulation of linear strain-displacement relations. The geometry of beam axis is specified by the offset vectors from the grid points to the shear centers of the beam cross-sections. The quadratic interpolation is used for both beam axis and the shape functions. When a three-node beam element degenerates to a two-node straight beam element, the linear interpolation is adopted. Variable cross-sectional properties are interpolated quadratically for a three-node and linearly for a degenerate two-node beam element.

Unlike MD Nastran two-node straight beam element (CBEAM), the three-node beam element is developed based on the displacement method, in which the displacements at nodal points are taken as primary variables and the variational principle is applied to minimize the total element energy in formulating element stiffness, consistent mass and differential stiffness matrices.

At each beam element nodal point, there are three translative and three rotational degrees of freedom, respectively. When the beam cross-section torsional warping effect is considered, another degree of freedom, which represents the warping variable, is added to the six nodal degrees of freedom at each grid point. The warping degrees of freedom are represented by either scalar or grid points.

Element-related loads, such as distributed forces and moments, as well as thermal loads, can be applied on this element. The solution output includes element stresses, strains, forces and moments, element strain energy and grid point forces.

BenefitsPerhaps the most suitable situation of the application of three-node beam elements is that the element is used in conjunction with higher-order shell elements, such as TRIA6 and QUAD8 that are used to model stiffeners. It can also be applied as an alternative to the existing straight two-node beam element in modeling favorably a structural geometry with initial curvatures.

In addition to normal stresses and strains at beam cross-sections, both shear stresses and strains are also recovered at cross-sectional stress output points. When warping effect is considered, normal stresses caused by cross-sectional bi-moments are computed and output accordingly.

InputSeveral new Bulk Data entries have been created for three-node beam element connection, property, distributed thermal and mechanical loads. They are CBEAM3, PBEAM3, TEMPB3 and PLOADB3. For a detailed description of each entry, please refer to MD Nastran Quick Reference Guide included in this release.

97CHAPTER 4Elements

Guidelines and Limitations

Geometry and Coordinate Systems

The geometry of a three-node beam element is specified by element connection Bulk Data entry

CBEAM3. The offset vectors , , and , are measured from grid points GA, GB and GC to the corresponding shear centers, A, B and C, respectively, at the beam cross-sections, as shown in Figure 4-1. Shear centers, A, B and C, are coplanar points. They define a plane in space if they are non-collinear. A quadratic approximation of the locus of beam shear center is uniquely defined by the spatial locations of these three shear centers. In what follows, we will refer the locus of beam shear center as the beam reference axis, or simply, beam axis. Taking the locus of shear center as the beam primary reference axis is consistent with the CBEAM element. Theoretically, the beam reference axis can be chosen arbitrarily. We also assume that the beam reference axis is a smooth spatial curve. The beam cross-section is perpendicular to the beam axis.

Figure 4-1 Locus of Shear Center of Three-node Beam Element

The element coordinate system ( , , ) is established by the orientation vector in the same way as what is defined for CBEAM element, as shown in Figure 4-1.

For a spatial curve, such as the beam reference axis, the natural coordinate system is its Frenet-Serret

frame , as shown in Figure 4-1. Here , and are the unit tangential, normal and bi-normal

vectors, respectively. Tangent vector points to the direction from A to B along the beam axis. Vector

is in the plane defined by these three non-collinear shear centers and points inwardly with respect to

the bending of beam axis. Bi-normal vector is perpendicular to both and by following the right-

Wa Wb Wc

GA GC

GB

aw

cw

bw

A

C

B

Locus of Shear Center

te

ne

be

elemX

elemYelemZ

ν

Wc

GB

GCGA

Wa

Wb

B

et

eb

en

C

Locus of Shear Center

ν

YelemZelem

Xelem

A

Xelem Yelem Zelem ν

et en eb, ,( ) et en eb

et

en

et en


98

hand rule of . When the beam axis is a straight line, i.e., three sectional shear centers are collinear, the Frenet-Serret frame is undefined. Then it will be replaced by the element coordinate system.

To formulate finite element equations and define the beam element properties, a local convected

coordinate system is created. The x-axis is always along the beam axis and its convected x

coordinate is measured by the arc-length, s. Its base vector, , is taken as same as vector . The base

vectors of the local coordinate system, and , are defined in such a way that they rotate an angle

(pre-twist angle), from and , respectively, in the plane of beam cross-section, as shown in

Figure 4-2. The orthogonal curvilinear coordinate system is introduced here as the local convected coordinate system, instead of the Frenet-Serret frame, to model the pre-twist of the beam

cross-section. When , the Frenet-Serret frame (or the element coordinate system if the beam axis

is straight) becomes the local convected coordinate system. The angle, , may vary along the beam axis. The pre-twist angles at three beam cross-sections are given in Bulk Data entry, CBEAM3.

Figure 4-2 Local Coordinate System on a Beam Cross-Section

The properties of a three-node beam element listed in Bulk Data entry, PBEAM3, are referred to the local coordinate system. The output of element stresses, strains and forces is also presented in the local coordinate system.

Element Properties, Materials and Loads

There are some similarities between PBEAM and PBEAM3 entries in terms of both format and content. Attention, however, should be paid to their differences. The local coordinate system is primarily referred

eb et= en⋅

ex ey ez, ,( )

ex et

ey ez φen eb

ex ey ez, ,( )

φ 0=

φ

φ

ne

be

yeze

Shear Center

en

ey

eb

ez

ShearCenter

99CHAPTER 4Elements

in defining cross-sectional properties, such as area moments and product of inertia, and locations of neutral axis and nonstructural mass center of gravity. Four stress output points on a beam cross-section are also specified in the local coordinate system. Unlike PBEAM, in which you can specify the properties at as many as nine intermediate stations, PBEAM3 requires their definitions at only three grid locations. For a degenerate two-node beam element, those fields related to the mid-grid are ignored. Values of warping function and its gradients at stress output points are required if torsional warping stresses are to be recovered.

Shear effectiveness factors may not be zero. Since the element is formulated on the Timoshenko beam theory and quadratic shape functions are used for interpolation, zero shear effectiveness factors will not automatically lead to a three-node Euler-Bernoulli beam element.

Both MAT1 and MAT2 entries can be referred by PBEAM3.

The loads related to the three-node beam element are element thermal and distributed mechanical loads, given by TEMPB3 and PLOADB3, respectively. The distributed forces and moments can be specified in any one of local, element, basic and any user-specified coordinate systems. The load must be applied over entire length of the element along the beam axis.

Limitations

There are some limitations in the current implementation with the three-node beam element. First of all, it is limited to linear analysis solution sequences only. Heat transfer analysis with the three-node beam element is not supported. Other limitations are identified as follows.

• X-Y PLOT output

• Random analysis

• PBEAML and PBCOMP related features

• CBEAM related features, such as pin-flags and shear relief

Formulation

Strain-Displacement Relations

The formulation of a three-node beam element is based on Timoshenko beam theory. The kinematical assumption hereafter is that the displacement vector at an arbitrary point of the beam cross-section is uniquely defined by the displacement vector at the beam reference axis and the rotations of the cross-section, superposed by a longitudinal warping displacement. For small deformation theory, the rotation of the cross-section is a vector. The displacement vector at point (s, y, z) of a beam cross-section is

where:

u s y z, ,( ) Uxex= Uyey Uzez+ +


100

in which , and are three translative displacement components at the beam axis; ,

and are three rotational degrees of freedom of the beam cross-section; and is a given

warping function and the warping degree of freedom. The assumption of the warping displacement is based on the Saint-Venant torsion theory of straight bars.

The Green-Lagrangian normal and shear strains, , are

where:

in which , the derivative with regard to the arc-length of beam axis.

Constitutive Relation

The general stress-strain relations are given, including thermal loads, at an arbitrary point of a beam cross-section, as

Ux s y z, ,( ) u s( )= zθy s( ) yθz s( )– ω s( )ψ y z,( )+ +

Uy s y z, ,( ) ν s( )= zθx s( )–

Uz s y z, ,( ) w s( )= yθx s( )+

u s( ) v s( ) w s( ) θx s( )

θy s( ) θz s( ) ψ y z,( )

ω s( )

ε γy γz, ,

ε ε0= zχy yχz– ψωs+ +

γy γy0= zχx– ψyω+

γz γz0= yχx ψzω+ +

ε0 u s,= κyw κzv–+

γy0 ν s,= θz– κzu κxw–+

γz0 w s,= θy κyu– κxν+ +

χx θx s,= κzθy– κyθz+

χy θy s,= κzθx+

χz θz s,= κyθx–

ψy∂ψ∂y-------= κzψ+

ψz∂ψ∂z-------= κyψ–

( ) s, ∂ ( ) ∂s( )⁄=

σ

στy

τz C11 C12 C13

C22 C23

Sym C33

εγy

γz α∆T

0

0

–

= =

101CHAPTER 4Elements

where are material elastic constants, α the thermal expansion coefficient and the variation of

temperature.

Element Forces and Moments

The axial and shear forces as well as torsion and bending moments of the cross-section in the local coordinate system are

and the bi-shear force and bi-moment, which are associated with the warping degree of freedom and its derivative, are

OutputElement forces, moments, stresses and strains, are computed at three beam cross-sections, in the local coordinate system. These three cross-section locations are related to either three grid points or two Gauss integration points and the parametrized origin. Both normal and shear stresses and strains are output at four cross-sectional stress recovery points in the local coordinate system.

The output examples of element forces, stresses and strains are shown in Listing 4-1, Listing 4-2, and Listing 4-3.

Cij ∆T

Nx σdAA∫=

Vy τy AdA∫=

Vz τz AdA∫=

Mx yτz zτy–( ) AdA∫=

My σz AdA∫=

Mz yσ–( ) Ad∫=

Vb τyψy τzψz+( ) AdA∫=

Mb σψ AdA∫=


102

Listing 4-1 Output of Element Forces and Moments

Listing 4-2 Output of Element Stresses

Listing 4-3 Output of Element Strains

F O R C E S I N B E A M 3 E L E M E N T S ( C B E A M 3 ) - FORCES IN LOCAL COORDINATE SYSTEM - GRID/ - BENDING MOMENTS - - SHEAR FORCES - AXIAL TOTAL BI-SHEAR BI-MOMENT ELEMENT-ID GAUSS MY MZ QY QZ FORCE TORQUE FORCE0 2901 2901 0.0 -1.156075E+03 -2.348231E+01 0.0 1.087807E+02 0.0 0.0 0.0 2902 0.0 -1.125649E+02 -1.096482E+02 0.0 1.902465E+01 0.0 0.0 0.0 2903 0.0 -6.343201E+02 -6.656523E+01 0.0 6.390266E+01 0.0 0.0 0.00 3901 3901 0.0 -1.048109E+03 -3.558532E+00 0.0 1.042715E+02 0.0 0.0 0.0 3903 0.0 -7.528904E+02 -7.162810E+01 0.0 7.585925E+01 0.0 0.0 0.0 3904 0.0 -9.004999E+02 -3.759332E+01 0.0 9.006535E+01 0.0 0.0 0.00 3902 3903 0.0 -7.267761E+02 -7.611831E+01 0.0 7.135274E+01 0.0 0.0 0.0 3902 0.0 -1.843143E+01 -1.042837E+02 0.0 3.180659E+00 0.0 0.0 0.0 3905 0.0 -3.726037E+02 -9.020099E+01 0.0 3.726670E+01 0.0 0.0

S T R E S S E S I N B E A M 3 E L E M E N T S ( C B E A M 3 )

GRID/ STRESS - STRESSES IN LOCAL COORDINATE SYSTEM - ELEMENT-ID GAUSS COMPONENT SXC SXD SXE SXF S-MAX S-MIN M.S.-T M.S.-C0 2901 2901 SX 5.889157E+04 1.087807E+03 -5.671596E+04 1.087807E+03 5.889157E+04 -5.671596E+04 -9.8E-01 -9.6E-01 SY -2.348231E+02 -2.348231E+02 -2.348231E+02 -2.348231E+02 -2.348231E+02 -2.348231E+02 SZ 0.0 0.0 0.0 0.0 0.0 0.0 2902 SX 5.818494E+03 1.902465E+02 -5.438001E+03 1.902465E+02 5.818494E+03 -5.438001E+03 SY -1.096482E+03 -1.096482E+03 -1.096482E+03 -1.096482E+03 -1.096482E+03 -1.096482E+03 SZ 0.0 0.0 0.0 0.0 0.0 0.0 2903 SX 3.235503E+04 6.390266E+02 -3.107698E+04 6.390266E+02 3.235503E+04 -3.107698E+04 SY -6.656523E+02 -6.656523E+02 -6.656523E+02 -6.656523E+02 -6.656523E+02 -6.656523E+02 SZ 0.0 0.0 0.0 0.0 0.0 0.00 3901 3901 SX 5.344819E+04 1.042714E+03 -5.136276E+04 1.042714E+03 5.344819E+04 -5.136276E+04 -9.8E-01 -9.6E-01 SY -3.558532E+01 -3.558532E+01 -3.558532E+01 -3.558532E+01 -3.558532E+01 -3.558532E+01 SZ 0.0 0.0 0.0 0.0 0.0 0.0 3903 SX 3.840311E+04 7.585925E+02 -3.688593E+04 7.585925E+02 3.840311E+04 -3.688593E+04 SY -7.162810E+02 -7.162810E+02 -7.162810E+02 -7.162810E+02 -7.162810E+02 -7.162810E+02 SZ 0.0 0.0 0.0 0.0 0.0 0.0 3904 SX 4.592565E+04 9.006535E+02 -4.412434E+04 9.006535E+02 4.592565E+04 -4.412434E+04 SY -3.759331E+02 -3.759331E+02 -3.759331E+02 -3.759331E+02 -3.759331E+02 -3.759331E+02 SZ 0.0 0.0 0.0 0.0 0.0 0.0

S T R A I N S I N B E A M 3 E L E M E N T S ( C B E A M 3 )

GRID/ STRAIN - STRAINS IN LOCAL COORDINATE SYSTEM – ELEMENT-ID GAUSS COMPONENT SXC SXD SXE SXF S-MAX S-MIN M.S.-T M.S.-C0 2901 2901 SX 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 -1.0E+00 SY 8.765757E-17 8.765757E-17 8.765757E-17 8.765757E-17 8.765757E-17 8.765757E-17 SZ 0.0 0.0 0.0 0.0 0.0 0.0 2902 SX 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 SY 5.160202E-17 5.160202E-17 5.160202E-17 5.160202E-17 5.160202E-17 5.160202E-17 SZ 0.0 0.0 0.0 0.0 0.0 0.0 2903 SX 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 SY 6.962979E-17 6.962979E-17 6.962979E-17 6.962979E-17 6.962979E-17 6.962979E-17 SZ 0.0 0.0 0.0 0.0 0.0 0.00 3901 3901 SX 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 -1.0E+00 SY -7.548301E-16 -7.548301E-16 -7.548301E-16 -7.548301E-16 -7.548301E-16 -7.548301E-16 SZ 0.0 0.0 0.0 0.0 0.0 0.0 3903 SX 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 SY -4.543672E-16 -4.543672E-16 -4.543672E-16 -4.543672E-16 -4.543672E-16 -4.543672E-16 SZ 0.0 0.0 0.0 0.0 0.0 0.0 3904 SX 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 1.000000E-01 SY -6.045987E-16 -6.045987E-16 -6.045987E-16 -6.045987E-16 -6.045987E-16 -6.045987E-16 SZ 0.0 0.0 0.0 0.0 0.0 0.0


ExampleID MSC, b3arcbck $ ARCH BUCKLINGSOL 105TIME 10CEND$TITLE = BUCKLING OF AN ARCH WITH CBEAM3 ELEMENTSSUBTI = HALF CIRCLE, PRESSURE LOAD SPC = 10DISP = ALLFORCE = ALLSPCFORCE = ALL$SUBCASE 1LABEL= LOAD CASELOAD = 10SUBCASE 2LABEL= BUCKLING CASEMETHOD = 10$BEGIN BULK$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------EIGRL 10 5$PLOADB3 10 1 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0PLOADB3 10 2 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0PLOADB3 10 3 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0PLOADB3 10 4 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0PLOADB3 10 5 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0PLOADB3 10 6 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0PLOADB3 10 7 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0PLOADB3 10 8 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0PLOADB3 10 9 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0PLOADB3 10 10 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0PLOADB3 10 11 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0PLOADB3 10 12 LOCAL 0.0 1.0 0.0 FORCE 1.0 ++ 100. 100. 100.0$CBEAM3 1 1 1 2 21 100 CBEAM3 2 1 2 3 22 100 CBEAM3 3 1 3 4 23 100 CBEAM3 4 1 4 5 24 100 CBEAM3 5 1 5 6 25 100 CBEAM3 6 1 6 7 26 100 CBEAM3 7 1 1 8 31 100 CBEAM3 8 1 8 9 32 100 CBEAM3 9 1 9 10 33 100


104

CBEAM3 10 1 10 11 34 100 CBEAM3 11 1 11 12 35 100 CBEAM3 12 1 12 13 36 100 $PBEAM3 1 2 .1 .01 .01 0.0 .02 ++ 0.5 0.0 0.0 0.5 -0.5 0.0 0.0 -0.5$MAT1 2 1.0E+7 0.3 .05 .001 0.0 .01 +MAT1-2+MAT1-2 1000. 2000. 3000.$GRID 2 2.58819 9.659258 0.0GRID 3 5.0 8.660254 0.0GRID 4 7.07107 7.07107 0.GRID 5 8.66025 5.0 0.GRID 6 9.65926 2.58819 0.GRID 7 10. 0. 0.$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------GRID 8 -2.588199.659258 0.0GRID 9 -5.0 8.660254 0.0GRID 10 -7.071077.07107 0.GRID 11 -8.660255.0 0.GRID 12 -9.65926 2.58819 0.GRID 13 -10. 0.0 0.0$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------GRID* 21 1.30526 9.91445 ** 0.0GRID* 22 3.82683 9.2388 ** 0.0GRID* 23 6.08761 7.93353 ** 0.0GRID* 24 7.93353 6.08761 ** 0.0GRID* 25 9.2388 3.82683 ** 0.0GRID* 26 9.91445 1.30526 ** 0.0GRID* 31 -1.30526 9.91445 ** 0.0GRID* 32 -3.82683 9.2388 ** 0.0GRID* 33 -6.08761 7.93353 ** 0.0GRID* 34 -7.93353 6.08761 ** 0.0GRID* 35 -9.2388 3.82683 ** 0.0GRID* 36 -9.91445 1.30526 ** 0.0$GRID 100 0.0 0.0 0.0$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------SPC1 10 12345 7 13SPC1 10 123456 100$ENDDATA


CWSEAM Connector Elements

IntroductionThe functionality of connector elements is enhanced by supporting a seam element to connect two surface patches. To define the seam weld, you must select two surface patches by their property IDs and specify the width and the thickness of the seam. You also have to specify start point “GS” and end point “GE” of the seam segment. These two points do not have to lie on or in between the shell planes. The program will project these two points onto the selected surface patches to find the connecting shell grids.

Inputs The seam connection is modeled by the new CWSEAM and PWSEAM Bulk Data entries and the modified SWLDPRM Bulk Data entry.

Defines a seam element connecting two surface patches.

Format:

Alternate Format:

Example:

CWSEAM A Shell Patch Seam Connection

1 2 3 4 5 6 7 8 9 10CWSEAM EID PID “GRIDID” PIDA PIDB

GS GE

1 2 3 4 5 6 7 8 9 10CWSEAM EID PID “XYZ” PIDA PIDB

XS YS ZS XE YE ZE

CWSEAM 3 17 GRIDID 2305 7116

30024 65467


106

Remarks:1. Element ID numbers must be unique with respect to all other element ID numbers.

2. GS and GE define the start and end points of the seam element. At these points and using the value W specified on the PWSEAM entry, surface patches A and B are determined. Points projected onto the surface patches A and B from GS and GE are used to determine the auxiliary points that form faces of a CHEXA element. These auxiliary points are then connected to the physical grids of the patches. The total number of unique physical grids ranges from a possibility of 6 to 32 grids. The auxiliary points must have a projection on patches A and B, but they do not have to lie on patch A or B.

3. A maximum of three shell elements of patch A and three shell elements of patch B can be connected with one CWSEAM element, see Figure 4-3.

Figure 4-3 Connected Shell Elements for a CWSEAM Element

Field Contents

EID Element identification number. (0 < Integer < 100,000,000)

PID Property identification number of a PWSEAM entry. (Integer > 0)

LTYPE Connectivity search type. (Character)If LTYPE=”GRIDID”, location is defined by GS and GE.If LTYPE=”XYZ”, location is defined by two XYZ locations.

PIDA,PIDB Property identification numbers of PSHELL entries defining surface A and B respectively. (Integer > 0)

GS, GE Grid ID’s of piercing points on patches A and B of the Start and End of the seam. (Integer > 0)

XS,YS,ZS Location of the start of the seam in basic coordinate system. (Real or blank)

XE,YE,ZE Location of the end of the seam in basic coordinate system. (Real or blank)

E

S


Defines the property of seam connector (CWSEAM) elements.

Format:

Example:

Remarks:1. The length of the seam is the distance between GS and GE. The width of the seam is measured

perpendicular to the length and lies in the plane of the patches A and B (see Figure 4-4). The width is also used to find the projection of the seam on the two patches A and B.

Figure 4-4 Dimensions of a CWSEAM Element

2. If left blank, the thickness will be computed as where is the thickness of patch A and is the thickness of patch B.

PWSEAM Seam Connector Element Property

1 2 3 4 5 6 7 8 9 10

PWSEAM PID MID W T

PWSEAM 7 1 16.

Field Contents

PID Property identification number. (Integer > 0)

MID Material identification number. (Integer > 0)

W Width of the seam. See Remark 1. (Real > 0.)

T Thickness of the seam. See Remark 2. (Real > 0. or blank)

GEGS

T

W

T TA TB+( ) 2⁄= TA

TB


108

Overrides default values of parameters for CFAST, CWELD, and CWSEAM connectivity search.

Format:

Example:

SWLDPRM Parameters for CFAST, CWELD, and CWSEAM Connectors

1 2 3 4 5 6 7 8 9 10

SWLDPRM PARAM1 VAL1 PARAM2 VAL2 PARAM3 VAL3 PARAM4 VAL4

PARAM5 VAL5 -etc.-

SWLDPRM GSPROJ 15.0 GSMOVE 2 PRTSW 1

Field Contents

PARAMi Name of the spot weld parameter. Allowable names are listed in Table 4-1. (Character)

VALi Value of the parameter. (Real or Integer; see Table 4-1.)


Table 4-1 PARAMi Names and Descriptions

Name Type Default Description

CHKRUN Integer 0, 1, 2 0 Stop the program after the connectivity of connector CWELD elements are generated. 0=abort on first error or run to completion; 1=stop after weld connectivity has been checked; 2=continue run if no errors are found or stop run after all weld connectivity errors have been found.

GMCHK Integer 0, 1, 2 0 For CWELD with PARTPAT format and CWSEAM only. 0=no geometry error checks; 1=check errors of CWELD elements with patch A and patch B tilting toward each other or check errors of the CWSEAM across a cutout or over a corner with patch elements in plane or out of plane; 2=check errors and output all candidate shell elements if an error is encountered. If GMCHK=1 or 2 and an error is detected, the program will loop back to search for next candidate element until a good pair of connection is found or all adjacent elements have been checked. In the latter case, a user fatal message 7595, 7638, or 7667 will be issued. A UFM 7595 is issued if the angle between the normal vectors of the patches at end GS or between the normal vectors of the patches at end GE exceeds the value of GSPROJ; a UFM 7638 is issued if either the length of the seam spans more than three elements or the seam spans a cutout; a UFM 7667 is issued if the angle between the normal vectors of the top patches at GS and GE or between the normal vectors of the bottom patches at GS and GE exceeds GSPROJ or if the angle between the free edges of the shell elements onto which GS and GE are projected is less than 160o (if GSPROJ < 20.0) or (180o-GSPROJ) (if GSPROJ > 20.0).

GSMOVE Integer > 0 0 Maximum number of times GS for the CFAST or CWELD (PARTPAT or ELPAT options only) or GS/GE for the CWSEAM is moved in case a complete projection of all auxiliary points has not been found.

GSPROJ Real 20.0 Maximum angle allowed between the normal vectors of shell A and shell B. The spot weld element will not be generated if the angle between these two normal vectors is greater than the value of GSPROJ. If GSPROJ is set to -1.0, the program will skip the checking of GSPROJ.


110

Remarks:1. This entry changes the default settings of control variables for the CFAST, CWELD, and

CWSEAM connector elements. None of the parameters of this entry are required. Only one SWLDPRM entry is allowed in the Bulk Data Section.

2. Connectivity information is generated for the CFAST and CWSEAM elements. For the CWELD, connectivity information is only generated for the PARTPAT, ELPAT, ELEMID, and GRIDID options.

Error Conditions for the CWELD and CWSEAM ElementsThe GMCHK parameter specified in the SWLDPRM Bulk Data entry checks the errors of CWSEAM elements across cutouts or over corners. There are three allowable values of GMCHK. This parameter is also used by CWELD elements with PARTPAT format to check the angle between patches A and B and to find the next candidate element if the angle check fails.

• GMCHK = 0 (Default) Do not check errors

GSTOL Real > 0.0 0.0 For CFAST or CWELD (PARTPAT and ELPAT only), if GSTOL > 0.0 and the distance between GS and the projected point GA or GB is greater the GSTOL, a UFM 7549 is issued and the CFAST or CWELD is rejected. For CWSEAM, if GSTOL > 0.0 and the distance between GS and the projected point GSA or GSB or the distance between GE and the projected point GEA or GEB is greater than the GSTOL, a UFM 7549 is issued and the CWSEAM is rejected.

NREDIA 0 < Integer < 4 0 CFAST or CWELD (PARTPAT and ELPAT) only. Maximum number of times the diameter D is reduced in half in case a complete projection of all points has not been found.

PROJTOL 0.0 < Real < 0.2

0.02 For CFAST or CWELD, tolerance to accept the projected point GA or GB if the computed coordinates of the projection point lie outside the shell element but is located within PROJTOL*(dimension of the shell element forming the patch). For the PARTPAT option for the CWELD or the PROP option for the CFAST it is recommended that PROJTOL=0.0. For the CWSEAM, a projection from GS/GE will always be attempted as if PROJTOL=0.0 and if one cannot be found then the non-zero value of PROJTOL will be used.

PRTSW Integer 0, 1, 2 0 Print diagnostic output. 0=no diagnostic output;1=print diagnostic output to f06 file;2=punch diagnostic output.

Table 4-1 PARAMi Names and Descriptions

Name Type Default Description


• GMCHK = 1 Check errors

• GMCHK = 2 Check errors and output all candidate shell elements if there is an error encountered

If GMCHK is turned on, MD Nastran will perform the following checking while searching for the projected shell elements. Note that SHSA is the shell element that gets projection from GS on shell A; SHEA is the shell element that gets projection from GE on shell A. Same algorithms are applied to SHSB and SHEB for shell B.

Check the Angle and Find Next Candidate Element for CWELD and PARTPAT FormatIf GSPROJ is greater than zero, MD Nastran will check the angle between SHSA and SHSB while searching for the projected shell elements. If the angle is greater than GSPROJ, the program will loop back to find next possible projection pair and check the angle between them again, until the angle of the new pair is less than GSPROJ or all candidate elements have been checked.

Check the CWSEAM Across a Cutout or Over a Corner with Elements in Plane

1. If SHSA is equal to SHEA, the seam lies within one element. No checks are required.

2. If SHSA and SHEA share two corner grids, these elements are adjacent. No checks are required.

3. If SHSA and SHEA share only one corner grid, the seam is over a corner. There are two exceptions:

• There exists a shell element (SHMA) that shares two corner grids with SHSA and SHEA. Also, either the angle between vector and vector is greater than theta degrees (where theta=160o if GSPROJ < 20.0; theta=180 o -GSPROJ if GSPROJ > 20.0) or the middle point (M) of line segment projects to SHSA, SHMA, or SHEA.

This model is acceptable.

S1S2 E1E4

S2E4

S2

S3

S4

S1 E1⁄

E2

E3

E4M

SHEA

SHSA

SHMA


112

This model fails.

• This shared grid is a shell grid of another two different shell elements.

4. If SHSA and SHEA do not share any corner grid, MD Nastran will check if there is an element (SHMA) lying between SHSA and SHEA. SHMA must share two corner grids with SHSA and another different one corner grid with SHEA, or vice versa. The following five examples demonstrate the acceptable and failed cases.

• SHMA shares one edge with SHSA and shares one corner grid with SHEA. This case is acceptable.

• SHMA shares one edge with SHEA and shares one corner grid with SHSA. This case is acceptable.

S2

S3

S4

E4

E3

E2

M

SHMA

SHEASHSA

S1 E1⁄

S1 E1⁄

S3

S4

S2

E2 E3

E4

S1

S2

S4

S3

E3

E4E1

E2


• SHMA shares one corner grid with SHSA and shares another corner grid with SHEA. An error is detected because the seam spans a cutout.

• SHMA shares one edge with SHSA and shares another edge with SHEA. This case is acceptable.

• There does not exist a single element that shares an edge or corner grid with SHSA or SHEA. An error is detected because the length of the seam spans more than three elements.

S1

S2

S4

S3

E3

E4E1

E2

S1

S2

S4

S3E3

E4E1

E2

S1 S4

S2 S3 E2 E3

E4E1


114

Check the CWSEAM Over a Corner with Elements Out of PlaneThe GSPROJ parameter is used to check the error of a seam over a corner with SHSA and SHEA not lying on a same plane. If the angle between the shell normal vectors of SHSA and SHEA is greater than

GSPROJ, an error is detected. The default value of GSPROJ is 20o. No angles will be checked if GSPROJ=-1.

Example – A Symmetric Hat Profile (cwseam_hut.dat)This example demonstrates the application of CWSEAM elements to analyze a symmetric hat profile model, see Figure 4-5. Each edge of the hat is connected by 27 CWSEAM elements. The grids with identification numbers 6000 to 6028 and 8000 to 8028 are used as the piercing points to define the seams, see Figure 4-6. A rigid body element (RBE2) is specified to constrain one end of the hat.

Figure 4-5 Hat Profile

S1 S4

S2 S3 E2 E3

E4E1


Figure 4-6 Piercing Points and Seams

The input for the seam welds is listed as follows.

CWSEAM 7000 500 GRIDID 100 200 6000 6001 CWSEAM 7001 500 GRIDID 100 200 6001 6002:CWSEAM 7026 500 GRIDID 100 200 6026 6027CWSEAM 7027 500 GRIDID 100 200 6027 6028$CWSEAM 9000 500 GRIDID 100 200 8000 8001 CWSEAM 9001 500 GRIDID 100 200 8001 8002:CWSEAM 9026 500 GRIDID 100 200 8026 8027CWSEAM 9027 500 GRIDID 100 200 8027 8028$PWSEAM 500 1 1.0


116

The normal mode analysis results are shown below.

R E A L E I G E N V A L U E SMODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS 1 1 -3.607717E-05 6.006427E-03 9.559526E-04 1.000000E+00 -3.607717E-05 2 2 2.210966E-05 4.702091E-03 7.483609E-04 1.000000E+00 2.210966E-05 3 3 4.523934E-05 6.726020E-03 1.070479E-03 1.000000E+00 4.523934E-05 4 4 4.937511E-05 7.026743E-03 1.118341E-03 1.000000E+00 4.937511E-05 5 5 1.087932E-04 1.043040E-02 1.660049E-03 1.000000E+00 1.087932E-04 6 6 1.537703E-04 1.240041E-02 1.973587E-03 1.000000E+00 1.537703E-04 7 7 1.154947E+07 3.398451E+03 5.408803E+02 1.000000E+00 1.154947E+07 8 8 1.585229E+07 3.981493E+03 6.336742E+02 1.000000E+00 1.585229E+07 9 9 2.653947E+07 5.151647E+03 8.199102E+02 1.000000E+00 2.653947E+0 10 10 2.959784E+07 5.440389E+03 8.658648E+02 1.000000E+00 2.959784E+07 11 11 3.002028E+07 5.479077E+03 8.720222E+02 1.000000E+00 3.002028E+07 12 12 3.041736E+07 5.515193E+03 8.777703E+02 1.000000E+00 3.041736E+07 13 13 3.328896E+07 5.769658E+03 9.182696E+02 1.000000E+00 3.328896E+07 14 14 3.757468E+07 6.129819E+03 9.755909E+02 1.000000E+00 3.757468E+07 15 15 4.259932E+07 6.526814E+03 1.038775E+03 1.000000E+00 4.259932E+07 16 16 4.738684E+07 6.883810E+03 1.095592E+03 1.000000E+00 4.738684E+07


Line Interface Element

IntroductionLine interface element is used to connect dissimilar meshes along the edges of finite element mesh subdomains. These subdomains have boundaries usually associated with either two-dimensional shell elements or one dimensional beam elements. A set of MPC (Multipoint Constraint) equations are internally generated with the interface boundary grids to enforce the compatibility of displacements and rotations across the interface.

There are perhaps three situations in which finite element analysts want to use the interface element technique to connect two or more independently meshed regions. They are:

• Different groups of engineers work almost independently in building finite element models.

• Global-local modeling is used in the analysis, where a fine mesh is required in a particular area due to high stress gradients while the rest of area only needs a coarse mesh, in consideration of the balance of computing resources and the solution accuracy.

• Some regions of a structural model need constant changes or modifications, while the rest of structure needs little or no change.

The purpose of interface element technology is to provide engineers a simple and useful tool in building a more flexible finite element model. The interface element technology is not intended to raise the overall solution accuracy with the existing mesh resolutions of individual subdomains. It is rather how to preserve the solution accuracy in the regions where the finite element results are more interesting to an analyst than in others. The method that we have developed for the line interface element is to achieve primarily the continuity of displacements and rotations across the interface in a way that a measure of their discontinuity is minimized. Since the smoothness (continuity of derivatives) of displacement components across the interface is not enforced by this method, some fluctuation of stresses in the vicinity of the interface could be expected. This stress unevenness or interface effect, however, diminishes quickly in the area away from the interface. This is a phenomenon that can be explained by Saint-Venant’s Principle.

When applying an interface element, you are asked to specify a boundary on which all the degrees of freedom at the grids are taken as the independent. The degrees of freedom associated with the grids on other boundary or boundaries referenced by the interface element are taken as the dependent and put into the m-set. In the terminology of contact mechanics, the interface boundaries are categorized as the master and slave ones. The nodal points on the master boundary are the independent grids and the nodes on the slave boundary are the dependent grids. An interface element is equivalent to a glued or tied contact that connects the dissimilar meshes.

The conventional way to specify the dependency or master-slave relationship of the interface boundaries is that the boundary with a fine mesh is tied to the one with a coarse mesh. In other words, the boundary with a fine mesh is chosen as a dependent or slave boundary and the one with a coarse mesh as an independent or master boundary. This practice, however, sometimes introduces a seemingly stiff connection along the interface. In this case, it may yield better solutions by switching the dependency relation between the interface boundaries.


118

The line interface element is intended for linear and non-superelement analyses. It should not be used for heat transfer analyses at this moment.

User InterfaceThere are two Bulk Data entries used to define a line interface element. CINTC is the element connection entry which specifies the connectivity of line interface boundaries, represented by Bulk Data entry, GMBNDC.

Bulk Data Entry: CINTC

Defines a line interface element with specified boundaries.

Format:

Example:

Remarks:1. Line interface element identification numbers must be unique with respect to all other line

interface elements.

CINTC Line Interface Element Connection

1 2 3 4 5 6 7 8 9 10

CINTC EID TYPE

LIST=(BID1(INTP1), BID2(INTP2),…, BIDn(INTPn) )

CINTC 1001 GRDLIST

LIST=(101,102(Q),-103(Q),104(L))

Field Contents

EID Element identification number. (0<Integer<100,000,000)

TYPE Connectivity. (Character; Default = "GRDLIST”)

If TYPE=”GRDLIST” or blank (default), the user will specify the boundaries via Bulk Data entry GMBNDC. See Remark 2.

BIDi Boundary curve identification number, referenced to Bulk Data entry GMBNDC. See Remark 2. (Integer 0)

INTPi Interpolation scheme. (Character; Default=”L”)

INTP=”L”: Linear interpolation;

INTP=”Q”: Quadratic interpolation.


2. There must be at least two BIDi specified. If all BIDi are positive, by default, the degrees of freedom associated with the grids on the boundary represented by the first BID will be taken as the independent (n-set), and the degrees of freedom with the grids on the rest of boundaries are taken as the dependent (m-set). If there is a single negative BID, the degrees of freedom associated with the grids on the boundary represented by this BID will be taken as the independent (n-set), and the rest of the degrees of freedom with other boundaries are used as the dependent (m-set). If there are two or more negative BIDs, the degrees of freedom with the first negative one will be taken as the independent.

3. Forces of multipoint constraints may be recovered with the MPCFORCE Case Control command.

4. The m-set degrees of freedom specified on the boundary grids by this entry may not be specified by other entries that define mutually exclusive sets.

Bulk Data Entry: GMBNDC

This is an existing Bulk Data entry originally designed for p-element edges along a curve interface. If it is referenced by Bulk Data entry CINTC, the value of Field ENTITY must be GRID.

Applications of Line Interface Element

Line Interface Element

A line interface element is a computational entity which consists of two or more interface boundaries along a virtual common interface curve. An interface boundary coincides with an edge of a finite element mesh subdomain. Primarily, an interface boundary is defined by a set of sequentially listed grid points, as specified by Bulk Data entry GMBNDC. On each boundary, there are at least two grids for a linear interpolation scheme and three for a quadratic one.

There is a dependency (or master-slave) relationship among the interface boundaries. This dependency relation is used to internally generate MPC equations between the independent and dependent degrees of freedom. At each grid point on a boundary, there are six degrees of freedom, three translational and three rotational. An interface boundary is called the dependent if all the degrees of freedom related to its grids are put in the m-set. An independent boundary is the one that all the degrees of freedom related to its grids are assigned to the n-set. There is only one independent boundary in an interface element.

In terms of element characteristics, an interface element is similar to a rigid or constraint element, such as RBE1 and RSPLINE. Unlike rigid elements, however, its processing is not selectable by Case Control command RIGID. In other words, only the linear elimination method is applied to this element. The degrees of freedom associated to the grids on a dependent interface boundary may not be simultaneously assigned dependent by other rigid, constraint or connection elements, a multipoint constraint or another interface element. On the other hand, the degrees of freedom with the grids on an independent interface boundary can be made dependent by another element or a multipoint constraint. This recursive dependent-independent relationship should be carefully examined to avoid potential conflicts when an interface element interacts with a multipoint constraint, a rigid, constraint or connection element, or another interface element. In addition, the dependent set (m-set) specified by the dependent interface boundary may not be specified on other entries that define mutually exclusive set (See “Degree-of-Freedom Set Definitions (p. 940) in the MD Nastran Quick Reference Guide. AUTOMSET can be used


120

with the interface element. It is designed to handle potentially ill-conditioned matrix by reassigning

dependent set (m-set) from the existing MPC equations, based on its rank deficiency. It needs further verifications to see how well the interface element works with AUTOMSET.

Line Interface Boundary

An interface element has two or more boundaries. Each boundary is defined primarily by a set of grid points listed sequentially from the initial grid through the final one, as specified by Bulk Data entry GMBNDC with Field ENTITY=”GRID”. All the boundaries in a line interface element must have their initial grids at the starting end and final grids at the terminal end of the interface.

One of the interface boundaries is specified as the independent by Bulk Data entry CINTC. If there are three or more boundaries in an interface element, the boundaries are internally grouped in pairs by the dependent-independent relationship. There are N-1 pairs of boundaries where N is the total number of boundaries with the interface element. MD Nastran generates the MPC equations between the dependent and independent grids on the pair of boundaries.

A boundary can be either open, i.e., the initial and final grids are different grids, or closed, i.e., the initial and final grids are the same grid, as shown in Figure 4-7. For a closed boundary, we have GRIDI=GRIDF in GMBNDC. There is a requirement for the minimum number of grids on a boundary. There must be at least two grids for the linear and three for the quadratic interpolation scheme.

Figure 4-7 Open and Closed Boundaries

Both dependent and independent open boundaries may share either initial or final grids or both of them. By assigning the same end grid to a pair of boundaries, the you have more flexibility in applying the interface element when one interface element connects or intersects with another interface element. This rule, however, may not apply to the closed boundaries.

A pair of interface boundaries can either be matching or non-matching, as shown in Figure 4-8. The non-matching boundaries have at least one dangling end grid. The interface line integration is taken along the common arc-length shared by both boundaries. Redundant dangling grids, as shown in Figure 4-9, are excluded from the processing of interface element.

Rmg[ ]

GRIDI GRIDF

Open Boundary

GRIDI=GRID

Closed Boundary

GRIDI GRIDF

Open Boundary

GRIDI=GRID

Closed Boundary


Figure 4-8 Matching and Non-matching Boundaries

Figure 4-9 Redundant Dangling Grids on Boundary

For an interface element with closed boundaries, special caution must be taken when selecting the initial grids. Since the initial grid can be any one on a closed boundary, it is required that the two initial grids on the dependent-independent closed boundaries be as closed as possible, as shown in Figure 4-10. In other words, a selection of an initial grid being a redundant grid in terms of the other initial grid is not supported. When one of the boundaries is open, this rule does not apply.

Matching Boundaries

Non-matching Boundaries and Integration Path

Matching Boundaries

Non-matching Boundaries and Integration Path

Redundant Dangling Grids


122

Figure 4-10 Selection of Initial Grids on Closed Boundaries

When the interface consists of curved boundaries, as shown in Figure 4-11, the interface boundary grids should be aligned along the actual line of structural geometry. In this release we have not implemented a capability that enables MD Nastran to check the integrity of interface boundary geometries. The existence of awry grids in the boundary grid list will lead to some interface malfunction without notice.

GRIDIA

GRIDIB GRIDIB

GRIDIA

Acceptable Selection of Initial Grids GRIDIA and GRIDIB

Unsupported Selection of Initial Grids GRIDIA and GRIDIB


Figure 4-11 Curved Boundaries

Example and ResultsAs shown in Figure 4-12, two independently meshed plates are connected by a line interface element. The plate structure is constrained at one edge and subject to a pressure load. The interface element is defined by Bulk Data entries, CINTC and GMBNDC, as shown in Listing 4-4. The solution results of displacement and von Mises stress distributions are presented in Figure 4-13 and Figure 4-14, respectively.

Listing 4-4 Interface Element Definition

CINTC 1001LIST=( 101, 102 )GMBNDC 101 67 107GRID 72 77 82 87 92 97 102GMBNDC 102 6 66GRID 12 18 24 30 36 42 4854 60

Actual structure geometry

Finite element model on boundary A

Finite element model on boundary B


124

Figure 4-12 Two Plates Connected by Line Interface Element

Figure 4-13 Displacement


Figure 4-14 von Mises Stress


126

Arbitrary Beam Cross-Section

IntroductionIn MD Nastran, enhancements have been made to ABCS in the area of cross-section outline display, stress data recovery and design optimization. In addition, ABCS algorithm has become the default formulation for pre-defined shapes of PBARL/PBEAML.

BenefitsUsually, MD Nastran recovers axial stresses at four ‘extreme’ points of the BAR/BEAM element cross-section. Although this may be acceptable on typical usage scenario for 1D element, the contribution of torsion and shear forces are simply assumed to be very minor and ignored. In MD Nastran 2006, for the first time a venue is provided to perform complete stress recovery for the whole cross-section with torsion and shear effect included. The stresses recovered can be post-processed as familiar GPSTRESS via SURFACE for each distinct cross-section. In addition, MD Nastran SOL 200 users can also perform optimization with the ‘screened’ stresses of BAR/BEAM elements.

Furthermore, an alternative formulation using ABCS logic for PBARL/PBEAML is also offered in MD Nastran 2006. Previously the equations used for PBARL/PBEAML were constructed under the assumption that the cross-sections are thin-walled. The properties, especially J, K1, K2, Cwa and Cwb, computed by such equations may have significant error. With the alternative formulation as default for PBARL/PBEAML, the correct properties are computed regardless if the section is thin-walled or not.

ABCS enhancements includes the following items

1. Output a PostScript, ‘.ps’, file for displaying the outline of cross-section. Also included in the ‘.ps’ file is the markers of center of gravity and shear center and sectional properties.

2. Generation of nodal and connection bulk data entries of FEM discretization for arbitrary beam cross-section

3. Stress data recovery for whole cross-section with contribution from torsion and shear included. In addition, ‘screened’ version of full stress recovery is also available which has the maximum/minimum direct stresses and max von Mises stress.

4. New RTYPE=ABSTRESS for ‘screened’ stresses can be utilized as constraints in optimization.

5. Alternative formulation for PBARL/PBEAML – selectable via SYSTEM(606), or TWBRBML on MDLPRM

InputsMinimal user input is required to control the new features. For each item of the ABCS enhancements, its input is discussed in following sections.

http://www.cs.wisc.edu/~ghost/


Post-Script File Generation

PARAM,ARBMPS,YES (default)

The default value for parameter ARBMPS is ‘YES’ which flags the generation of PS file. The PS file has the name of ‘mydeck.ps’ for an input file of ‘mydeck.dat’. The PS file includes following important information.

• outline of the cross-section

• marker for the location of center of gravity. For ABCS via PBMSECT, marker for the location of shear center is also shown.

• Properties of the cross-section

‘PARAM,ARBMPS,NO’ turns off the generation of PS file.

Generation of Finite Element Model, FEM, for the Cross-Section

PARAM,ARBMFEM,YES (default)

The default value for parameter ARBMFEM is ‘YES’ which flags the generation of file(s) of FEM of each distinct cross-section. ‘PARAM,ARBMFEM,NO’ switches off the generation of ‘.bdf’ file for FEM of cross-section.

Stress recovery for whole cross-section The required input for ABCS logic to perform stress recovery for whole cross-section is the element force. Hence, to activate stress recovery for whole cross-section, the following input must be present in the input file.

1. ELFORCE (or simply FORCE) output request in the case control and

2. ‘PARAM,ARBMSS,YES’ (Default=NO) as bulk data entry

Due to the potential of a huge amount of output, these stresses are only available in OUTPUT2 format. In addition, the stresses recovered are prepared in a pattern consistent with GPSTRESS via SURFACE. The recovered stresses for each grid of FEM of cross-section are σx, τxy, τzx, principal stresses and von Mises stress. Note that recovered ABCS direct stresses are placed in stress tensor consistent with direct stress of SURFACE. The following table shows where recovered direct stresses in stress tensor.

Stress Tensor Recovered ABCS DIrect Stress

σx σx

σy τxy

σz

τxy τzx


128

As a data reduction process, max/min of , , τzx and max von Mises stress of each station of every

selected element are collected from stress recovery for the whole cross-section and is available in print file (f06). These collected stresses are called ‘screened’ stresses which can be utilized as design response for SOL 200 job.

New response type RTYPE=ABSTRESS is available on DRESP1 for using ‘screened’ stresses of BAR/BEAM elements as design response. An example for the new response type is as follows

DRESP1,23,ABSVM,ABSTRESS,PBMSECT, , 9, , 32

where max von Mises stress (item code 9) of all elements refers to PBMSECT,32 is selected as design response.

Alternative formulation for PBARL/PBEAML The default formulation is now set to use Finite Element Method to compute sectional properties. The alternate formulation will be active under the following conditions

1. GROUP field of PBARL/PBEAML must be either left BLANK or has “MSCBML0” as input

2. job run on a short-word (32 bits) machine

To switch back to the beam library equations, use either ‘NASTRAN twbrbml=1’ in executive control file or ‘mdlprm,twbrbml,1’ in bulk data.

OutputPost-Script file for the outline of ABCS A ‘.ps’ file for all PBRSECT/PBMSECT of a job will be available at the conclusion of a job. GhostScript/GSview, available for download at http://www.cs.wisc.edu/~ghost/, can be utilized for viewing of PostScript file.

Generation of FEM for cross-sections The file generated has the following naming convention

AAA_xxyyy_zz.bdf

where AAA – By default, it assume the input file name. To alter AAA to a name other than input file name, use

ASSIGN opcase=’any character string’ $

τyz

τzx

Stress Tensor Recovered ABCS DIrect Stress

σ τxy


As naming implies, there should be as many files holding FEM of cross-sections as PBRSECT/PBMSECT Bulk Data entries at conclusion of a job. Note that PBMSECT supports constant section beam only.

Stress output for the whole cross-section The file holding stresses for whole cross-section in OP2 format has same naming convention as the FEM for cross-section. For stresses, the file has the extension of ‘.op2’ instead.

For ‘screened’ stresses, an output example is shown as follows

New response type, ABSTRESS, for optimization An example of output for ABSTRESS sensitivity is shown as follows

Alternate Formulation for PBARL/PBEAML

A message as follows will be available in f06 to indicate which method is used to compute sectional properties for PBARL/PBEAML.

If alternative formulation is utilized

If original beam equations are utilized

xx character string of ‘BR’ for PBRSECT and ‘BM’ for PBMSECT

yyy ID of PBRSECT or PBMSECT

zz station ID. ‘01’ for end A of PBMSECT. No zz section for PBRSECT.

1 BEAM LIBRARY TEST CASE BLO MAY 29, 2005 MSC.NASTRAN 5/27/05 PAGE 10 TRANSVERSE TIP LOAD 0 SUBCASE 1 S T R E S S E S I N B E A M E L E M E N T S ( S C R E E N E D ) AXIAL SHEAR-XY SHEAR-XZ VON MISES ELEMENT-ID STATION MAX MIN MAX MIN MAX MIN MAX 2 0.000 2.206054E+00 -2.254727E+00 2.075935E-01 -2.175731E-02 1.687584E-01 -1.681947E-01 2.258905E+00 2 1.000 6.117611E-17 -6.315223E-17 2.075935E-01 -2.175731E-02 1.687584E-01 -1.681947E-01 3.694130E-01

-------------------------------------------------------------------------------------------------------------------------------- DRESP1 ID= 323 RESPONSE TYPE= ABSTRESS ELEM ID= 2 COMP NO= 9 SEID= 0 SUBCASE RESP VALUE DESIGN VARIABLE COEFFICIENT DESIGN VARIABLE COEFFICIENT -------------------------------------------------------------------------------------------------------------------------------- 1 2.2589E+00 31 DBOXGS 0.0000E+00 232 DBOXCP -2.2693E+00 2 2.0246E+00 31 DBOXGS 0.0000E+00 232 DBOXCP -1.7749E+00

*** USER INFORMATION MESSAGE 4379 (IFP9A) THE USER SUPPLIED PBEAML/PBMSECT BULK DATA ENTRIES ARE REPLACED BY THE FOLLOWING PBEAM ENTRIES. CONVERSION METHOD FOR PBARL/PBEAML - FINITE ELEMENT METHOD.

*** USER INFORMATION MESSAGE 4379 (IFP9A) THE USER SUPPLIED PBARL/PBRSECT BULK DATA ENTRIES ARE REPLACED BY THE FOLLOWING PBAR ENTRIES. CONVERSION METHOD FOR PBARL/PBEAML - BEAM LIBRARY EQUATIONS.


130

If both formulations are utilized

Guidelines1. Finite element formulation for computing cross-sectional properties is considered more accurate,

especially for thin-walled cross-sections, across wider spectrum of beam cross-sections. Hence, it is the default formulation for PBARL/PBEAML. However, there is a minor performance penalty that came with the accuracy.

2. Use only matching ‘.bdf’ and ‘.op2’ files from the same job to visualize the stress pattern,

3. For SOL 200 optimization jobs, finite element formulation for PBARL/PBEAML is highly recommended due to the potential that new design can cross the thin-/thick-walled line.

Limitations1. Finite element formulation for arbitrary beam cross-section is available only on short-word

machines. Hence, the alternative formulation for PBARL/PBEAML using finite element method is supported only on short-word machine. Typically, Cray is a long-word machine and finite element formulation for arbitrary beam cross-section is not supported.

2. Arbitrary beam cross-section supports constant section for beam elements via PBMSECT. Cross-sectional variation from end A to end B is not supported via PBMSECT. However, tapered cross-section is supported via PBEAML even if finite element formulation is utilized.

3. Stress recovery for the full cross-section is available only for Static (SOL 101), Modes (SOL 103) and Optimization (SOL 200).

4. Stress recovery for the full cross-section is available for the first cycle of a SOL 200 job.

5. For SOL 200 jobs, the stresses recovered can be successfully post-processed with the companion ‘.bdf’ file only if the properties have no discrepancy between analysis and design model.

ExampleA simple file, zbm5a1, with two PBMSECT entries is utilized here to demonstrate the features implemented. Double box cross-section is modeled with PBMSECT,31 using FORM=GS and PBMSECT,32 using FORM=CP. The overall width of PBMSECT,31 and the thickness of outer wall of PBMSECT,32 are selected as design variables. Some key bulk data entries are shown as follows

*** USER INFORMATION MESSAGE 4379 (IFP9A) THE USER SUPPLIED PBARL/PBRSECT BULK DATA ENTRIES ARE REPLACED BY THE FOLLOWING PBAR ENTRIES. CONVERSION METHOD FOR PBARL/PBEAML – MIXED FORMULATION


Zbm5a1 uses default value for PARAM,ARBMPS and PARAM,ARBMFEM. Hence, output files are:

1. zbm5a1.ps – the content is shown in Figure 4-15 and Figure 4-16.

2. zbm5a1_bm31_01.bdf - FEM for PBMSECT,31 shown as Table 4-2

3. zbm5a1_bm32_01.bdf – FEM for PBMSECT,32 shown as Table 4-3.

$$ DBOX section using pbmsect with GS optionPOINT 111 0.0 0.0 POINT 112 20.0 0.0 POINT 113 20.0 19.4 POINT 114 0.0 19.4 POINT 125 1.0 1.0 POINT 126 10.0 1.0 POINT 127 10.0 18.4 POINT 128 1.0 18.4 POINT 132 11.0 1.0 POINT 133 19.0 1.0 POINT 134 19.0 18.4 POINT 135 11.0 18.4 $SET1 111 111 THRU 114 SET1 122 128 127 126 125 128SET1 133 132 133 134 135 $pbmsect 31 10 GS OUTP=111,inp=122,inp=133DESVAR 31 DBOXGS15.00.0160.0DVPREL1112pbmsect31 W 31 1.0$$ DBOX section using pbmsect with CP option$DESVAR 232 DBOXCP 1.00 0.01 3.0DVPREL1 312 pbmsect 32 T 232 1.0$POINT 201 0.5 0.5POINT 202 10.5 0.5POINT 203 19.5 0.5POINT 204 19.5 18.9POINT 205 10.5 18.9POINT 206 0.5 18.9POINT 224 10.5 10.0SET1 201 201 THRU 206SET1 202 202 224 205pbmsect 32 10 CP OUTP=201,T=1.0,BRP=202, T(11)=[1.2,PT=(202,224)],T(12)=[1.2,PT=(224,205)]


132

Figure 4-15 Outline and properties of PBMSECT,31


Figure 4-16 Outline and properties for PBMSECT,32


134

Table 4-2 FEM for PBMSECT,31 (abridged)

GRID and CTRIA6 entries for PBMSECT 31 BEGIN

NUMBER OF GRID = 683 NUMBER OF CTRIA6= 262

CTRIA6 10001 10000 10013 10038 10211 10033 10273 10212CTRIA6 10002 10000 10065 10082 10399 10013 10288 10213CTRIA6 10003 10000 10067 10161 10557 10014 10294 10215..CTRIA6 10260 10000 10002 10054 10335 10181 10336 10680CTRIA6 10261 10000 10003 10055 10338 10115 10339 10668CTRIA6 10262 10000 10001 10056 10341 10196 10342 10683GRID* 10001 0.00000000D+00* 0.00000000D+00 GRID* 10002 2.00000000D+01* 0.00000000D+00 GRID* 10003 2.00000000D+01* 1.93999996D+01 ..GRID* 10682 1.00898438D+01* 1.90601559D+01 GRID* 10683 6.25000000D-01* 0.00000000D+00

GRID and CTRIA6 entries for PBMSECT 31 END


Table 4-3 FEM for PBMSECT,32(abridged)

The output of stress recovery of whole cross-section is available in OUTPUT2 format. For zbm5a1, the files are

1. zbm5a1_bm31_01.op2 – stress recovery for all elements referencing PBMSECT,31

2. zbm5a1_bm32_01.op2 – stress recovery for all elements referencing PBMSECT,32

Contour plots with data from zbm5a1_bm31_01.op2 are shown in the following figures. Axial stress, shear stress in xy, shear stress in zx and von Mises stress are shown in Figure 4-17, Figure 4-18, Figure 4-19 and Figure 4-20, respectively. In these figures, the number after ‘Grid Point Stresses’ has XXYY format where

GRID and CTRIA6 entries for PBMSECT 32 BEGIN NUMBER OF GRID = 629 NUMBER OF CTRIA6= 238

CTRIA6 20001 20000 20017 20064 20196 20009 20612 20197CTRIA6 20002 20000 20048 20113 20332 20017 20290 20198CTRIA6 20003 20000 20018 20007 20199 20027 20227 20200..CTRIA6 20236 20000 20155 20059 20322 20154 20607 20513CTRIA6 20237 20000 20003 20045 20282 20049 20597 20292CTRIA6 20238 20000 20001 20054 20306 20181 20307 20628GRID* 20001 0.00000000D+00* 1.93999996D+01 GRID* 20002 0.00000000D+00* 0.00000000D+00 GRID* 20003 1.05000000D+01* 0.00000000D+00 ..GRID* 20628 0.00000000D+00* 1.87937489D+01 GRID* 20629 1.41625004D+01* 5.00000000D-01

GRID and CTRIA6 entries for PBMSECT 32 END

Note: The GRID and CTRIA6 numbering are based on the processing sequence of the arbitrary beam cross-section. The first GRID (or CTRIA6) of the first cross-section processed will have ID of 10001. The first GRID of 2nd cross-section processed has ID of 20001.


136

Figure 4-17 Axial Stress of End A of CBEAM,1 referencing PBMSECT,31

XX EID of a BAR/BEAM element.

YY station ID. ‘00’ for end A. ‘01’ for end B if no intermediate station.


Figure 4-18 Shear Stress in XY of End A of CBEAM,1 referencing PBMSECT,31


138

Figure 4-19 Shear Stress in ZX of End A of CBEAM,1 referencing PBMSECT,31


Figure 4-20 von Mises Stress of End A of CBEAM,1 referencing PBMSECT,31

The ‘screened’ stresses which can be utilized in optimization is shown as follows.


140

1 BEAM LIBRARY TEST CASE BLO JUNE 16, 2005 MSC.NASTRAN 6/15/05 PAGE 17 TRANSVERSE TIP LOAD 0 SUBCASE 1 S T R E S S E S I N B E A M E L E M E N T S ( S C R E E N E D ) AXIAL SHEAR-XY SHEAR-XZ VON MISES ELEMENT-ID STATION MAX MIN MAX MIN MAX MIN MAX 2 0.000 2.206054E+00 -2.254727E+00 2.075935E-01 -2.175731E-02 1.687584E-01 -1.681947E-01 2.258905E+00 2 1.000 6.117611E-17 -6.315223E-17 2.075935E-01 -2.175731E-02 1.687584E-01 -1.681947E-01 3.694130E-011 BEAM LIBRARY TEST CASE BLO JUNE 16, 2005 MSC.NASTRAN 6/15/05 PAGE 18 LATERAL TIP LOAD 0 SUBCASE 2 S T R E S S E S I N B E A M E L E M E N T S ( S C R E E N E D ) AXIAL SHEAR-XY SHEAR-XZ VON MISES ELEMENT-ID STATION MAX MIN MAX MIN MAX MIN MAX 2 0.000 2.023472E+00 -2.023472E+00 8.784060E-02 -8.598299E-02 1.045674E-01 -8.338179E-03 2.024639E+00 2 1.000 2.304938E-16 -2.304893E-16 8.784060E-02 -8.598299E-02 1.045674E-01 -8.338179E-03 1.998240E-01


Ch. :

5 Dynamics and Superelements

Efficiency Enhancements to MTRXIN Module for Handling DMIG Data, 142

Enhancements to BSETi/BNDFIXi and CSETi/BNDFREEi Bulk Data Entry Processing, 143

Enhancements to MATMOD Module Option 16, 144

Enhancements to External Superelement Usage Via EXTSEOUT Case Control Command, 149

Changes to Rotordynamic for MD Nastran 2006, 153

Exterior Acoustics, 172


142

Efficiency Enhancements to MTRXIN Module for Handling DMIG DataThe MTRXIN module generates matrix data blocks from DMIG data resident on a MATPOOL-type data block. If the matrix generation is handled in memory, then the processing is very efficient. However, if it involves out-of-memory operations, then the processing efficiency decreases, especially for large matrices and particularly so for large symmetric matrices.

Enhancements have been made to the MTRXIN module in MD Nastran 2006 to improve out-of-memory processing. With these enhancements, decreases in CPU times of 50% to 65% for large rectangular matrices and 20% to 35% for large symmetric matrices have been observed. In general, the larger the matrix size, the greater will be the decrease in the CPU time.

143CHAPTER 5Dynamics and Superelements

Enhancements to BSETi/BNDFIXi and CSETi/BNDFREEi Bulk Data Entry ProcessingBNDFIX/BNDFIX1 and BNDFREE/BNDFREE1 Bulk Data entries are alternatives to the existing BSET/BSET1 and CSET/CSET1 Bulk Data entries, respectively. However, the program did not allow the new Bulk Data entries to be used in conjunction with their alternate forms in the same Bulk Data file. This restriction has been removed in MD Nastran 2006, thereby allowing mixed usage of the BNDFIXi and BNDFREEi entries with their alternatives of BSETi and CSETi entries in the same Bulk Data file. This is also reflected in the enhanced description of these Bulk Data entries in the MD Nastran Quick Reference Guide.


144

Enhancements to MATMOD Module Option 16

IntroductionOption 16 of the MATMOD module was designed to put a matrix into DMIG format in a MATPOOL-type data block as well as to optionally generate DMIG punched output. This option is very useful, particularly in analyses involving part and external superelements. However, its implementation suffers from several deficiencies and inconveniences as explained below.

1. Only G-size matrices are handled. In particular, if the input matrix is square or symmetric, both the rows and columns must be of G-size. If it is a rectangular matrix, the rows must be of G-size, while the columns are regarded as just sequential entities.

2. The rows and columns of the input matrix must be in external sort. This is a particularly inconvenient requirement since it requires re-arrangement of its rows and columns that are normally in internal sort. This requirement forces the use of Option 9 of the MATGEN module to generate a transformation matrix to convert from internal sort to external sort and then employing this transformation matrix to perform the required transformation of the desired matrix before it can be used as input to the MATMOD module.

3. The name of the matrix in the DMIG output is the same as the name of the data block containing the input matrix. There is no way to give an arbitrary name to the matrix in the DMIG output.

4. Even if only the DMIG punched output is desired, the MATPOOL-type output data block still has to be generated even though it may never be used thereafter.

Major enhancements have been made to Option 16 of the MATMOD module in order to overcome the above deficiencies and inconveniences. These enhancements utilize an additional input data block and several additional parameters to accomplish their purpose. These enhancements are explained below.

1. The size of the input matrix is no longer restricted to G-size. Instead, any size corresponding to any valid displacement set of the User Set (USET) table is allowed. Also, for the first time, Option 16 can handle rectangular matrices wherein the columns correspond to a displacement set and are not necessarily regarded as sequential entities. This allows Option 16 to handle the more general case of rectangular matrices wherein the rows and columns correspond to different displacement sets.

2. The rows and columns of the input matrix need not be in external sort. They can be in internal sort which is their normal arrangement.

3. The name of the matrix in the DMIG output need not be the same as the name of the data block containing the input matrix. An arbitrary name can be specified for the matrix in the DMIG output.

4. The MATPOOL-type output data block need not be generated if only the DMIG punched output is desired.


UsageAs indicated earlier, the above enhancements are accomplished by using one additional input data block and several additional parameters. The new usage of Option 16 is as follows:

Input data block USET and the parameters P3, P13, P14 and P15 represent additions as part of the enhancements. The default values for these additional parameters have been chosen such that legacy files employing the old usage of Option 16 will continue to give the same results as before. A full description of the enhanced Option 16 usage is given in the Appendix.

ExampleThe power of the enhancements is well illustrated by the example given under the description of Option 16 in the Appendix. This example clearly shows that the enhanced features of Option 16 result in much simpler and more efficient DMAP programs than was the case in earlier versions.

Enhancements to MATMOD Module

Option=16

Put matrix into DMIG format in a MATPOOL-type data block and/or generate DMIG punched output.

Format:

Input Data Blocks:

Output Data Block:

MATMOD MATRIX,EQEXIN,USET,,,/MATPOOLX,/16/P2/P3/P4////////P12/P13/P14/P15 $

MATMOD MATIN,EQEXIN,USET,,,/MATPOOLX,/16/PUNCHFLG/SORTFLG/TYPOUT////////CONTCHR/DMIGNAME/ROWSETNM/COLSETNM $

MATIN Matrix to be converted to DMIG format. (Real or complex). See Remark 1.

EQEXIN EXEQXIN table from module GP1. See Remark 7.

USET USET table from module GP4 or GPSP. See Remark 8.

MATPOOLX MATPOOL-type table data block containing MATIN in DMIG format. See Remark 9.


146

Parameters:

Remarks:1. The program checks to ensure that the form of MATIN is either 1 (square), 6 (symmetric) or 2

(rectangular). If this is not so, the program issues a warning message and proceeds without generating any output from this call to the MATMOD module.

2. If the default value of 0 for SORTFLG is used, the rows of MATIN must be of G-size. If MATIN is square or symmetric, its columns must also be of G-size. Further, the default value of 0 for SORTFLG also assumes that the rows and columns of MATIN are in external sort. In order to accomplish this, it is necessary to first generate a transformation matrix via MATGEN module Option 9 and then employ this matrix to transform the rows and columns of MATIN from internal sort to external sort. (This is illustrated in the Example shown below.)

PUNCHFLG Input-integer-default=0. If PUNCHFLG is non-zero, then DMIG punched output will be generated. See Remark 9.

SORTFLG Input-integer-default=0. The default assumes that the rows (and columns, if applicable) of MATIN are in external sort. If SORTFLG is non-zero, then it is assumed that they are in internal sort. See Remark 2.

TYPOUT Input-integer-default=0. The default sets the DMIG precision to machine precision. The default maybe overridden by specifying the following:

1 Real single precision format2 Real double precision format3 Complex single precision format4 Complex double precision format

CONTCHR Input-character-default=blank. Continuation characters to be used for DMIG punched output. Only the first two characters of the non-blank mnemonic are used for the continuation string. See Remark 3.

DMIGNAME Input-character-default=blank. The default will cause the name of the MATIN input data block to the used for the matrix name in the DMIG output. A non-blank name will cause that specified name to be used for the matrix name in the DMIG output.

ROWSETNM Input-character-default=blank. The default assumes that the rows of MATIN are of G-size. Any non-blank mnemonic specifies the displacement set for the rows. See Remarks 4, 5 and 6.

COLSETNM Input-character-default=blank. If the form of MATIN is 1 (square) or 6 (symmetric), then the default assumes that the displacement set for the columns is the same as that of the rows. If the form of MATIN is 2 (rectangular), then the default (or a mnemonic of ‘H’) assumes that the columns do not represent any displacement set, but just sequential entities. Any non-blank mnemonic other than ‘H’ specifies the displacement set for the columns. See Remarks 4, 5 and 6.


3. If non-blank continuation characters are specified for CONTCHR, then a maximum of 99,999 DMIG entries can be generated for any single matrix. If this maximum number is exceeded, the program terminates the job with a fatal error.

4. The program checks to ensure that the number of rows and columns of MATIN correspond to the displacement sets specified (or implied) by ROWSETNM and COLSETNM. If this condition is not satisfied, the program issues a warning message and proceeds without generating any output from this call to the MATMOD module.

5. If the form of MATIN is either 1 (square) or 6 (symmetric), then the IFO field on the generated DMIG entry is set to 1 or 6. If the form is 2 (rectangular), then IFO is set to 2 if a displacement set is specified (or implied) for COLSETNM. Otherwise, IFO is set to 9. (If the form is 6, only the terms in one triangle are output. The MTRXIN module, which converts DMIG data in MATPOOL-type data blocks into matrices, fills in the other triangle for symmetric matrices.)

6. The rows of the DMIG entry are always labeled with the appropriate grid/scalar IDs and component numbers. If a displacement set is specified (or implied) for COLSETNM, then the columns of the DMIG entry are also labeled with the appropriate grid/scalar IDs and component numbers. Otherwise, the columns of the DMIG entry are labeled sequentially, starting with unity.

7. The EQEXIN input data block may not be purged.

8. The USET input data block may be purged if (a) the default value of 0 is used for SORTFLG or (b) the displacement set specified (or implied) by ROWSETNM is ‘G’ and the displacement set specified (or implied) by COLSETNM is either ‘G’ or the columns are just sequential entities.

9. The MATPOOLX output data block may be purged if PUNCHFLG is specified as non-zero and only the DMIG punched output is desired.

Example:

Generate DMIG punched output for the boundary stiffness matrix KAA, the boundary load matrix PA and the matrix GMN (representing the MPC/rigid element equations) for an external superelement. The KAA DMIG entry is to be named KAAEXTSE, the PA DMIG entry is to be named PAEXTSE and the GMN DMIG entry is to be named GMNEXTSE.

The DMAP shown illustrates the usage of Option 16 using input matrices in internal sort (capability available in MD Nastran 2006) as well as using input matrices in external sort (usage only possible prior to MD Nastran). It can be seen that the DMAP for the former case is much simpler and more efficient than for the latter case.

It should be pointed out here that, if the internal and external sorts are different, the DMIG output resulting from the two scenarios shown below will “appear” to be different. This is because the matrix elements will be output in different order, but their values will be the same. The DMIG output from the two scenarios will yield identical matrices if they are used in turn by the MTRXIN module to re-generate the matrices.

DMAP using input matrices in internal sort (MD Nastran 2006 and subsequent releases)TYPE PARM,,I,N,PUNCHFLG=1 $ GENERATE DMIG PUNCHED OUTPUT


148

TYPE PARM,,I,N,SORTFLG=1 $ INPUT MATRICES ARE IN INTERNAL SORT

DMAP using input matrices in external sort (In prior releases)TYPE PARM,,I,N,PUNCHFLG=1 $ GENERATE DMIG PUNCHED OUTPUT$ EXPAND BOUNDARY MATRICES TO G-SIZEUMERGE1USET,KAA,,,/KAAGG/’G’/’A’ $ EXPAND ROWS AND COLUMNSUMERGE1USET,PA,,,/PAG/’G’/’A’//1 $ EXPAND ROWSUMERGE1USET,GMN,,,/GMNGN/’G’/’M’//1 $ EXPAND ROWSUMERGE1USET,GMNGN,,,/GMNGG/’G’/’N’//2 $ EXPAND COLUMNS$ GET G-SIZEPARAMLUSET//’TRAILER’/2/S,N,GSIZE $$ GENERATE MATRIX TO TRANSFORM FROM INTERNAL SORT$ TO EXTERNAL SORTMATGENEQEXIN/INTEXT/9/0/GSIZE $$ TRANSFORM MATRICES FROM INTERNAL SORT TO$ EXTERNAL SORT WITH APPROPRIATE DESIRED NAMESMPYADINTEXT,KAAGG,/KAAGGX/1 $MPYADKAAGGX,INTEXT,/KAAEXTSE $MODTRLKAAEXTSE////6 $MPYADINTEXT,PAG,/PAEXTSE/1 $MPYADINTEXT,GMNGG,/GMNGGX/1 $MPYADGMNGGX,INTEXT,/GMNEXTSE $$GENERATE DMIG FORMATMATMODKAAEXTSE,EQEXIN,,,,/MATPOOLK,/16/PUNCHFLGMATMODPAEXTSE,EQEXIN,,,,/MATPOOLP,/16/PUNCHFLGMATMODGMNEXTSE,EQEXIN,,,,/MATPOOLG,/16/PUNCHFLG$ MATPPOLK, MATPPOLP AND MATPOOLG OUTPUT DATA BLOCKS$ HAVE TO BE GENERATED ABOVE EVEN THOUGH ONLY DMIG$ PUNCHED OUTPUT IS DESIRED

MATMOD KAA,EQEXIN,USET,,,/,/16/PUNCHFLG/SORTFLG//////////

’KAAEXTSE’/’A’ $

MATMOD PA,EQEXIN,USET,,,/,/16/PUNCHFLG/SORTFLG//////////

’PAEXTSE’/’A’ $

MATMOD GMN,EQEXIN,USET,,,/,/16/PUNCHFLG/SORTFLG//////////

’GMNEXTSE’/’M’/’N’ $


Enhancements to External Superelement Usage Via EXTSEOUT Case Control Command

IntroductionThe EXTSEOUT Case Control command allows for the creation of an external superelement (SE) for subsequent use in an assembly process. In response to many user needs and requirements, several enhancements have been introduced to this feature in MD Nastran 2006. These enhancements are described below. Complete details are given in the expanded description of the EXTSEOUT command in the MD Nastran 2006 Quick Reference Guide.

Addition of Options to ASMBULK KeywordPreviously the ASMBULK keyword for the EXTSEOUT command has no options. Its use results in the generation of the following Bulk Data entries in the assembly punch (.asm) file:

SEBULK seid … (with MANUAL as the method for searching boundary points)SECONCT seid … (defines connections for boundary grid and scalar points)GRID entries for boundary grid pointsSPOINT entries for boundary scalar pointsCORD2x entries associated with the boundary GRID entries

The above entries are generated in order to avoid fatal errors that will be generated if there are coincident points associated with the boundary grid points in the assembly run. However, there are situations wherein there are no such coincident grid points in the assembly run. In such cases, there is no need to define or reference the boundary grid points in the .asm file and the SEBULK entry can have the default AUTO option. A new option, ASMBULK = AUTO, has therefore been introduced for this purpose. Under this usage, the current usage will be assumed to be equivalent to the default scenario of ASMBULK = MAN (for MANual).

Notice also that the SECONCT entry mentioned above references only boundary grid and scalar points. Scalar Q-set points (representing generalized coordinates) are not referenced. There are, however, situations wherein you may want to have explicit control on the Q-set DOFs of an external SE in the assembly run. In order to facilitate such a scenario, yet another option, ASMBULK = MANQ, has been introduced. This results in Q-set points being specified in SECONCT entries as well as on explicit SPOINT entries, thereby allowing them to be manipulated in the assembly run.


150

Thus, with the above usage, we have the following possible values for the ASMBULK keyword:

Addition of New FSCOUP KeywordA new keyword called FSCOUP has been added to control the storing of the boundary fluid-structure coupling matrix.

Addition of New DMIGSFIX KeywordIf the DMIGPCH option is employed, the DMIG Bulk Data entries for the boundary matrices that are generated in the standard punch (.pch) file are given the following names:

The above usage often causes confusion when the user is dealing with more than one external SE in an assembly run. In order to provide more flexibility and convenience to the user, a new keyword called DMIGSFIX (for DMIG suffix) has been added to the EXTSEOUT Case Control command. The format of this keyword is

DMIGSFIX = cccccc

where “cccccc” is a suffix (up to six characters) that will be appended to the appropriate letters to give unique names to the DMIG Bulk Data entries of the boundary matrices. Thus, with this usage, the DMIG Bulk Data entries for the boundary matrices will have the following names:

ASMBULK = MAN (default)

Simulates usage in pre-MSC.Nastran 2005 r3 versions

ASMBULK = MANQ

Similar to the usage in pre-MSC.Nastran 2005 r3 versions except that the SECONCT entry includes scalar Q-set points and SPOINT entries are generated for these scalar Q-set points

ASMBULK = AUTO

Generates a SEBULK entry (with AUTO as the assumed method for searching boundary points) along with an SECONCT entry with only boundary scalar points appearing on it and SPOINT entries for these boundary scalar points (if any)

KAAX (boundary stiffness matrix)

MAAX (boundary mass matrix)

BAAX (boundary viscous damping matrix)

K4AAX (boundary structural damping matrix)

PAX (boundary load matrix)

AAX (boundary fluid-structure coupling matrix)


If the name specified for DMIGSFIX is EXTID, it is regarded as a special case. In this case, the ID of the external SE specified via the EXTID keyword is used as part of the DMIG names. Thus, for example, if the user has specified EXTID = 15 and DMIGSFIX = EXTID, then the DMIG Bulk Data entries for the boundary matrices will have the following names:

The above design makes it very convenient for the user to associate the names of the boundary DMIG matrices with specific external SEs.

Automatic Numbering Scheme for Q-set DOFs Via AUTOQSET UsageWith the incorporation of the new AUTOQSET feature in MD Nastran 2006, it is no longer necessary for you to specify manual QSET / QSET1 and SPOINT entries to handle the Q-set DOFs (generalized coordinates) of an external SE. The program automatically generates SPOINT entries for these entities by using an internal numbering scheme that gives them IDs of the form 9sssnnnn where sss is the superelement ID specified by the EXTID keyword and nnnn is a mode number. Both sss and nnnn will have leading zeros inserted in them to ensure that sss is a three-digit number and nnnn is a four-digit

number. Thus, for example, the Q-set DOF corresponding to the 8th mode of external SE 5 would be represented by an SPOINT with an automatically generated ID of 90050008 while the Q-set DOF

corresponding to the 50th mode of external SE 25 would be represented by an SPOINT with an automatically generated ID of 90250050. The above numbering scheme offers great flexibility and convenience, particularly when dealing with several external SEs in an assembly run.

Kcccccc (boundary stiffness matrix)

Mcccccc (boundary mass matrix)

Bcccccc (boundary viscous damping matrix)

K4cccccc (boundary structural damping matrix)

Pcccccc (boundary load matrix)

Acccccc (boundary fluid-structure coupling matrix)

K15 (boundary stiffness matrix)

M15 (boundary mass matrix)

B15 (boundary viscous damping matrix)

K415 (boundary structural damping matrix)

P15 (boundary load matrix)

A15 (boundary fluid-structure coupling matrix)


152

Automatic Availability of Output for Boundary Points and PLOTEL Points of External Superelements in Assembly RunThe output for an external superelement is generated in the assembly process. This output consists of displacements, velocities, accelerations, SPC forces and element stresses and forces. However, in order for this output to be generated in the assembly run, the output requests must be specified in the external superelement creation run. Previously the only output requests for an external superelement that were honored in the assembly run were those that were specified in its creation run.

If there are many, many PLOTELs in an external SE creation run and you are interested in utilizing them for animation in a subsequent assembly run, the above scheme forces you to have explicit output requests for the grid points associated with the PLOTEL entries. This is an extremely cumbersome requirement. Similar comments also apply to boundary points of an external SE whose output you are interested in obtaining in the assembly run.

In order to avoid the above cumbersome and inconvenient requirement, the program has been enhanced to ensure that the output for the boundary grid and scalar points as well as for all grid points associated with PLOTEL entries for an external SE can be obtained in the assembly run even if there are no output requests specified for these points in the external SE creation run. This will be of tremendous convenience to users.

New MATDB Option As Equivalent to Current MATRIXDB OptionTo simplify user specifications, a new option named MATDB has been introduced to be equivalent to the MATRIXDB option. Both MATDB and MATRIXDB options are available and will be regarded as equivalent to each other, with MATDB being regarded as the new default option. This design will also ensure that legacy files will continue to run as before.


Changes to Rotordynamic for MD Nastran 2006

Additional Damping Options for RotorsIn MD Nastran 2006, additional rotor damping options were implemented. To support these enhancements, the RSPINR and RSPINT entries were modified. These modified entries are NOT compatible with previous versions of MD Nastran. Additionally, a new entry, HYBDAMP, was added to support ‘hybrid’ damping of rotors. For reference, the modified rotordynamic equations are given in Modified Basic Equations Used in Rotordynamics, 166.

RSPINR – Specifies the relative spin rates between rotors for complex eigenvalue, frequency response, and static analyses.

Format:

1 2 3 4 5 6 7 8 9 10

RSPINR ROTORID GRIDA GRIDB SPDUNIT SPTID

GR ALPHAR1 ALPHAR2 HYBRID

Field Contents

ROTORID Identification number of rotor. (Integer > 0; Required)

GRIDA/GRIDB Positive rotor spin direction is defined from GRIDA to GRIDB (Integer > 0; Required. See Remark 2.)

SPDUNIT Specifies whether the listing of relative spin rates is given in terms of RPM (revolutions/minute) or frequency (revolutions (cycles)/unit time). (Character; ’RPM’ or ’FREQ’; Required)

SPTID Relative spin rate. See Remark 3. (Real or Integer; if integer, must be > 0, Required)

GR Rotor structural damping factor. See Remark 3. (Real, Default = 0.0)

ALPHAR1 Scale factor applied to the rotor mass matrix for Rayleigh damping (Real, Default = 0.0. See Remark 5.)

ALPHAR2 Scale factor applied to the rotor stiffness matrix for Rayleigh damping (Real; Default = 0.0. See Remark 5.)

HYBRID Identification number of HYBDMP entry for hybrid damping (Integer > 0; Default = 0. See Remark 6.)


154

Remarks:1. An RSPINR entry must be present for each rotor defined by a ROTORG entry.

2. The rotor spin axis is determined from the ROTORG entries. The positive rotation vector is from GRIDA to GRIDB. GRIDA and GRIDB must be specified on the ROTORG entry.

3. If the entry is a real number, the value is considered constant. If the entry is an integer number, the value references a DDVAL entry that specifies the relative rotor spin rates. The number of spin rates for each rotor must be the same. Relative spin rates are determined by correlation of table entries. The ith entry for each rotor specifies the relative spin rates between rotors at RPMi/FREQi. Spin rates for the reference rotor must be in ascending or descending order.

4. Rotor structural damping specified by the GR entry will be added as equivalent viscous damping. The equivalent damping will be calculated using:

where is a user parameter

5. Rayleigh damping for the rotor will be calculated as

6. For hybrid damping of the rotors, only the rotor mass and stiffness will be used for the modes calculation.

Brotor[ ]s tructural

GRWR3------------ Krotor[ ]=

WR3

Brotor[ ]Rayleigh

αR1 Mrotor( ) αR2 Krotor[ ]+=


RSPINT– Specifies rotor spin rates for nonlinear and direct linear transient analysis.

Format:

Remarks:1. A RSPINT entry must be present for each rotor defined by a ROTORG entry.

2. The rotor spin axis is determined from the ROTORG entries. The positive rotation vector is from GRIDA to GRIDB. GRIDA and GRIDB must be specified on the ROTORG entry.

3. If the entry is a real number, the value is considered constant. If the entry is an integer number, the value references a TABLED1 entry that specifies the rotor spin rate history.

4. Rotor structural damping specified by the GR entry will be added as equivalent viscous damping. The equivalent damping will be calculated using:

1 2 3 4 5 6 7 8 9 10

RSPINT ROTORID GRIDA GRIDB SPDUNIT SPTID SPDOUT

GR ALPHAR1 ALPHAR2 HYBRID

Field Contents

ROTORID Identification number of rotor. (Integer > 0; Required)

GRIDA/GRIDB Positive rotor spin direction is defined from GRIDA to GRIDB.See Remark 2. (Integer > 0; Required.)

SPDUNIT Specifies whether the spin rates are given in terms of RPM (revolutions/minute) or frequency (revolutions(cycles)/unit time). (Character; ’RPM’ or ’FREQ’; Required)

SPTID Rrotor spin rate. See Remark 3. (Real or Integer; if integer, must be > 0, Required)

SPDOUT EPOINT to output the rotor speed vs. time. Output will be in SPDUNITs (Integer > 0 or blank)

GR Rotor structural damping factor. See Remark 3. (Real, Default = 0.0)

ALPHAR1 Scale factor applied to the rotor mass matrix for Rayleigh damping (Real,Default = 0.0. See Remark 5.)

ALPHAR2 Scale factor applied to the rotor stiffness matrix for Rayleigh damping. See Remark 5. (Real; Default = 0.0.)

HYBRI Identification number of HYBDMP entry for hybrid damping. See Remark 6. (Integer > 0, Default = 0)

Brotor[ ]s tructural

GRWR3------------ Krotor[ ]=


156

where WR3 is a user parameter.

5. Rayleigh damping for the rotor will be calculated as

6. For hybrid damping of the rotors, only the rotor mass and stiffness will be used for the modes calculation.

Brotor[ ]Rayleigh

αR1 Mrotor( ) αR2 Krotor[ ]+=


HYBDAMP– Hybrid modal damping for direct dynamic solutions.

Format:

Remarks:1. For KDAMP = “YES”, the viscous modal damping is entered into the complex stiffness matrix

as structural damping.

2. Hybrid damping is generated using modal damping specified by the user on TABDMP entries.

For KDAMP = “YES”

1 2 3 4 5 6 7 8 9 10

HYBDAMP ID METHOD SDAMP KDAMP

Field Contents

ID Identification number of HYBDMP entry (Integer > 0; Required)

METHOD Identification number of METHOD entry for modes calculation. (Integer > 0, Required)

SDAMP Identification number of SDAMP entry for modal damping specification. (Integer > 0; Required)

KDAMP Selects modal “structural” damping (Character: “Yes” or “NO”, see Remark 1; Default = “NO”)

BH φ1 φ2 … φn

b ω1( )

b ω2( )

b ωn( )

φ1T

φ2T

φnT

=

KH φ1 φ2 … φn

g ω1( )

g ω2( )

g ωn( )

φ1T

φ2T

φnT

=


158

where

Squeeze Film Damper as Nonlinear ForceThe squeeze film damper (SFD) was implemented as a nonlinear force similarly to the NLRGAP. The SFD forces are activated from the Case Control Section using the NONLINEAR command. The new NLRSFD Bulk Data entry has the following form:

Format:

= modes of the structure

= modal damping values,

= twice the critical damping ratio determined from user specified TABDMP entry

= natural frequency of mode

= generalized mass of mode

φi

b ωi( ) b ωi( ) g ωi( )ωimi=

g ωi( )

ωi φi

mi φi

1 2 3 4 5 6 7 8 9 10

NLRSFD SID GA GB PLANE BDIA BLEN BCLR SOLN

VISCO PVAPCO NPORT PRES1 THETA1 PRES2 THETA2 NPNT

OFFSET1 OFFSET2

Field Contents

SID Nonlinear load set identification number. (Integer > 0, Required)

GA Inner (e.g., damper journal) grid for squeeze film damper. (Integer > 0, Required)

GB Outer (e.g., housing) grid for squeeze film damper. (Integer > 0, Required)

PLANE Radial gap orientation plane: XY, XZ, or ZX. See Remark 1. (Character, Default = XY)

BDIA Inner journal diameter. (Real > 0.0, Required)

BLEN Damper length. (Real > 0.0, Required)

BCLR Damper radial clearance. (Real > 0.0, Required)

SOLN Solution option: LONG or SHORT bearing. (Character, Default = LONG)

VISCO Lubricant viscosity. (Real > 0.0, Required)

PVAPCO Lubricant vapor pressure. (Real, Required)

NPORT Number of lubrication ports: 1 or 2 (Integer, no Default)


Remarks:1. The XY, YZ, and ZX planes are relative to the displacement coordinates of GA and GB. The

plane coordinates correspond to the NLRSFD directions 1 and 2. GA and GB should be coincident grids with parallel displacement coordinate systems. Wrong answers will be produced if this rule is not followed.

2. The angular measurement is counterclockwise from the displacement x-axis for the XY plane, the y-axis for the YZ plane, and the z-axis for the ZX plane.

Squeeze Film Damper as Nonlinear ElementFor better accuracy and to facilitate use in other solution sequences the NLRSFD was also be implemented as an element. The Squeeze Film Damper was added as an option of a more general 2-D bearing element (CBUSH2D).

CBUSH2D

Format:

PRES1 Boundary pressure for port 1. (Real > 0.0, Required if NPORT = 1 or 2)

THETA1 Angular position for port 1. (0.0 < Real > 360.0, Required if NPORT = 1 or 2). See Remark 2.

PRES2 Boundary pressure for port 2. (Real > 0.0, Required if NPORT = 2).

THETA2 Angular position for port 2. See Remark 2. (0.0 < Real < 360.0, Required if NPORT = 2)

NPNT Number of finite difference points for damper arc. (Odd integer < 201, Default = 101)

OFFSET1 Offset in the SFD direction 1. (Real, Default = 0.0)

OFFSET2 Offset in the SFD direction 2. (Real, Default = 0.0)

Field Contents

1 2 3 4 5 6 7 8 9 10

CBUSH2D EID PID GA GB CID PLANE SPTID


160

PBUSH2D

Format:

Field Contents Default Values

EID Element identification number. (Integer > 0) Required

PID Property identification number of a PBUSH2D entry. (Integer > 0).

Required

GA Inner grid. (Integer > 0) Required

GB Outer grid. (Integer > 0) Required

CID Coordinate system used to define 2-D plane. (Integer > 0) 0

PLANE Orientation plane in CID, XY, YZ, ZX (Character) “XY”

SPTID Optional rotor speed input for use with table lookup or DEQTN generation of element properties (Integer > 0 or blank)

1 2 3 4 5 6 7 8 9 10

PBUSH2D PID K11 K22 B11 B22 M11 M22

“SQUEEZE” BDIA BLEN BCLR SOLN VISCO PVAPCO

NPORT PRES1 THETA1 PRES2 THETA2 OFFSET1 OFFSET2

Field Contents Default

PID Property identification number. (Integer > 0). Required

K11 Nominal stiffness in T1 rectangular direction. (Real) Required

K22 Nominal stiffness in T2 rectangular direction. (Real) Required

B11 Nominal damping in T1 rectangular direction. (Real) Default = 0.0

B22 Nominal damping in T2 rectangular direction. (Real) Default = 0.0

M11 Nominal acceleration-dependent force in T1 direction. (Real) Default = 0.0

M22 Nominal acceleration-dependent force in T2 direction. (Real) Default = 0.0

“SQUEEZE” Indicates that squeeze-film damper will be specified. (Character) Required

BDIA Inner journal diameter (Real > 0.0) Required


Gyroscopic Terms Added to Aero Solution SequencesThe rotordynamics option is available in the Aerodynamic Flutter (SOL 145) and Aeroelastic Gust Response (SOL 146) solutions. SOL 145 uses the same gyroscopic equations as Complex Eigenvalues; SOL 146 uses the frequency response formulation (see Modified Basic Equations Used in Rotordynamics, 166).

Campbell DiagramsCampbell diagram generation is activated in complex modes analysis (SOLs 107 and 110) by the CAMPBELL Case Control command. The command will have the following format:

CAMPBELL= n

The CAMPBELL command references the following Bulk Data entry.

Format:

BLEN Damper length (Real > 0.0) Required

BCLR Damper radial clearance. (Real > 0.0) Required

SOLN Solution option: LONG or SHORT bearing (Character) Default = LONG

VISCO Lubricant viscosity. (Real > 0.0) Required

PVAPCO Lubricant vapor pressure. (Real) Required

NPORT Number of lubrication ports: 1 or 2 (Integer) No Default

PRES1 Boundary pressure for port 1 (Real > 0.0) Required if NPORT = 1 or 2

THETA1 Angular position for port 1. See Remark 2. (0.0 < Real <360.0) Required if NPORT = 1 or 2

PRES2 Boundary pressure for port 2 (Real > 0.0) Required if NPORT = 2

THETA2 Angular position for port 2. See Remark 2. (0.0 < Real < 360.0) Required if NPORT = 2

OFFSET1 Offset in the SFD direction 1 (Real) Default = 0.0

OFFSET2 Offset in the SFD direction 2 (Real) Default = 0.0

Field Contents Default

1 2 3 4 5 6 7 8 9 10

CAMPBLL CID VPARM DDVALID TYPE ID NAME/FID


162

Rotor Forward and Backward Mode IdentificationForward and backward rotor modes are identified using proportional kinetic and strain energies of the reference rotor compared to the total structure. The motion of the reference rotor is split into forward and backward components using a least-mean-square fit of shape vectors that represent ‘pure’ forward and backward rotor whirl motion. The ‘pure’ forward and backward components are then used to calculate the kinetic and strain energies of the reference rotor.

‘Pure’ forward and backward whirl modes represent unit circular motion. For example, with rotation along the positive z-axis, ‘pure’ whirl for translation or rotation are given by:

(5-1)

Field Contents

CID Identification number of entry (integer > 0, required).

VPARM Variable parameter, allowable entries are: ‘SPEED’, ‘PROP’, ‘MAT’.

‘SPEED’, reference rotor speed will be varied (rotordynamic option only).

‘PROP’, element property values will be varied (currently not implemented)

‘MAT’, element material properties will be varied (currently not implemented).

DDVALID Identification number of DDVAL entry that specifies the values for the variable parameter (integer > 0, required).

TYPE For VPARM set to ‘SPEED’ allowable entries are: ‘FREQ’ and ‘RPM’.

For VPARM set to ‘PROP’, allowable entries are the names of property entries, such as ‘PBAR’, ‘PELAS’, etc.

For VPARM set to ‘MAT’, allowable entries are the names of material entries, such as ‘MAT1’ or ‘MAT2’, etc.

ID Property or material entry identification number (integer > 0, not required for VPARM set to ‘SPEED’, required for VPARM set to ‘PROP’ or ‘MAT’).

NAME/FID For VPARM set to ‘SPEED’, no entry required.For VPARM set to ‘PROP’, property name, such as ‘T’, ‘A’, or field position of the property entry, or word position in the element property table of the analysis model. For VPARM set to ‘MAT’, material property name, such as ‘E’ or ‘RHO’, or field position of the material entry.

φ forward

1

i–

0

= φ backward

1

i

0

=


The forward and backward components are found by minimizing the error between the calculated modes and the ‘pure’ forward and backward whirl vectors of the reference rotor.

(5-2)

where: is the calculated mode are the forward and backward ‘pure’ whirl modes for all rotor grid translations

and rotations. are the whirl mode scale factors

(5-3)

(5-4)

(5-5)

(5-6)

The error is minimized using a least-mean-square procedure. The square of the error is:

(5-7)

The derivative of the above equation with respect to is

err φ = A[ ] α –

φ A[ ]

α

A[ ] A[ ]forward A[ ]backward[ ]=

A[ ]forward

φ forward

0

0

.

.

.

0

φ forward

0

.

.

.

0

0

.

.

.

φ forward

=

A[ ]backward

φ backward

0

0

.

.

.

0

φ backward

0

.

.

.

0

0

.

.

.

φ backward

=

α αforward

αbackward

=

err 2err

* T

err φ* A*[ ] α* –( )

Tφ A[ ] α –( )T

= =

φ* T

φ φ* T

A[ ] α – α* T

A*[ ]

Tφ – α*

TA

*[ ]T

A[ ] α +=

α


164

(5-8)

Setting the above equation to zero and taking the complex transpose results in

(5-9)

Solving for produces

(5-10)

Using Eq. (5-1) and Eq. (5-3), the following simplification can be made,

(5-11)

The terms are used to calculate the forward and backward components of the modes,

(5-12)

The proportional rotor kinetic and strain energies are determined using the following procedure:

(5-13)

(5-14)

where:

(5-15)

(5-16)

and the norm of the vector is defined as the sum of the absolute values of all the terms.

Note that scale factors in the above equations have been removed because the proportional calculation will cancel these terms.

Modes with kinetic or strain energies greater than a user specified value will be considered forward or backward whirl modes.

∂err2

∂α-------------- φ* A[ ]– α*

TA

*[ ]T

A[ ]+=

A*[ ]

Tφ – A

*[ ]T

A[ ] α + 0 =

α

α A*[ ]

TA[ ]( )

1–A

*[ ]T

φ =

α 12--- A

*[ ]T

φ =

α

φrotor forward

12--- A[ ]forward A

*[ ]forwardT

φ ( )=

φrotor backward

12--- A[ ]backward A

*[ ]backwardT

φ ( )=

Proportional Kinetic Energynorm KE φrotor( )

norm KE φ( )-----------------------------------------------=

Proportional Strain Energynorm SE φrotor( )

norm SE φ( )----------------------------------------------=

KE u( ) M[ ] u ( ) u ⋅=

SE u( ) K[ ] u ( ) u ⋅=


Rotor Mode TrackingFor Campbell diagram plotting, the rotor modes will need to be tracked in case the eigenvalues of the modes change ordering. Forward and backward modes should be separated using the previous procedure and tracked separately. Tracking can be done using a method similar to the previous procedure to determine forward and backward modes. Defining an error function as

(5-17)

where: is a weighting matrix (usually , , or )

are the normalized forward and backward whirl modes (rotor dofs only)

are the scaling factors to fit the modes

the subcase increment number

The modes are normalized by the following method.

(5-18)

Using the same method in the above procedure produces the following results for the scaling matrix

. (5-19)

The matrix is used to whether the modes have shifted position in the LAMA table.

The matrix columns are examined for the largest term. This term is set to 1.0 and the other terms

in the column are set to 0.0. The matrix can now be used to shuffle the eigenvalues.

(5-20)

The new order is appended to the LAMA matrix for Campbell Diagram plotting.

(5-21)

CommentsFor speed-dependent Campbell diagrams, at low speeds, the split into forward and backward modes may not be very pronounced. It may be best to start at the higher speeds and move down instead of moving up. Also, do not try to find forward and backward modes at zero RPM.

When forward and backward modes cross, they may be difficult to separate. If this happens, it is probably best to ‘jump’ (ignore) these modes and continue to the next rotor speed. They should be picked-up at the next speed step. We will need to ‘fill-in’ later so PATRAN can plot the results.

err[ ] X[ ] φ[ ]i 1–= X[ ] φ[ ]i β[ ]–

X[ ] M[ ] K[ ] I[ ]

φ[ ]

β[ ]

i

φ φ

φ* T

X*[ ]

TX[ ] φ

--------------------------------------------------=

β[ ] φ*[ ]iT

X*[ ]

TX[ ] φ[ ]i( )

Tφ*[ ]i

TX

*[ ]T

X[ ] φ[ ]i 1–( )=

β[ ]

β[ ]β[ ]

LAMA new LAMA old β[ ]=

LAMA[ ] LAMA 1 LAMA 2 LAMA 3…[ ]=


166

Modified Basic Equations Used in RotordynamicsThe NASTRAN time-domain equation solved by the new dynamic solution sequences is:

(5-22)

= total mass matrix

= support viscous damping matrix

= support mass contribution for Rayleigh damping

= support stiffness contribution for Rayleigh damping

= support viscous damping equivalent to structural damping

= support viscous damping equivalent to material structural damping

= rotor viscous damping matrix

= rotor hybrid damping matrix

= rotor mass contribution for Rayleigh damping

= rotor stiffness contribution for Rayleigh damping

= rotor viscous damping equivalent to structural damping

= rotor viscous damping equivalent to material structural damping

= rotor viscous damping equivalent to hybrid structural damping

= gyroscopic force matrix

= support stiffness matrix

= rotor stiffness matrix

= support material damping matrix

= rotor material damping matrix

Mu·· t( )Bs α1Ms α2Ks+ +( ) g

W3-------- Ks

1W4-------- K4s+ +

BR BHR α1RMR α2RKR+ + +( )gR

WR3------------ KR

1WR4------------ K4R

1WRH-------------- KHR ΩB

G+ + + + +

u· t( )+

Ks Kr+

Ω KCB

KCBH α1RK

CM α2RKCK gr

WR3------------ K

CK 1WR4------------ K

CK4 1WRH-------------- K

CKH+ + + + + + +

u t( )+ F t( )=

M

Bs

α1Ms

α2Ks

gW3-------- Ks

1W4-------- K4s

Br

BH

α1RMR

α2RKRgr

WR3------------ KR

1WR4------------ K4R

1WRH-------------- KHR

BG

Ks

KR

K4s

K4R


The NASTRAN frequency-domain equation is:

(5-23)

In the special situation where , the above equation is converted to:

(5-24)

Eq. (5-23), asynchronous excitation, and Eq. (5-24), synchronous excitation, are used in frequency response and complex modes analyses.

To order to support multiple rotors spinning at different rates, Eqs. (5-23) and (5-24) are modified to the following forms:

Frequency ResponseFor frequency response with asynchronous excitation, for each rotor is constant and can be determined from the rotation speed of the reference rotor, , and relative rotation rates specified by

the user. The equation of motion to be solved is:

= rotor rotation rate

= “circulation” matrix due to

“circulation” matrix due to




, , and are users parameters

Ω

KCB

BR

KCBH

BHR

gRKRCK gRKR

KRCK4

K4R

KCKH

KHR

WR3 WR4 WRH

ω2M–( iω Bs α1Ms α2Ks B+ +

rBHR α1RMR α2RKR Ω+ + + B

G+ +( )+

1 ig+( )KS iK4S 1 igR+( )KR iK4R iKHR+ + + +

Ω KCB

KCBH α1RK

CM α2RKCK gR

ω------ K

CK 1ω---- K

CK4 1ω---- K

CKH+ + + + + +

+

+ u ω( ) F ω( )=

ω Ω=

Ω2M iB

G–( )– iΩ

BS α1MS α2KS BR BHR α1RMR α2RKR+ + + + + +

i KCB

KCBH α1RK

CM α2RKCK

+ + +( )–

+

1 ig+( )KS iK4S+

1 igR+( )KR iK4R iKHR gRKCK

KCK4

KCKH

+ + + + + +

u Ω( ) F Ω( )=+

ΩΩref


168

(5-25)

where the subscript j references the individual rotors.

will be determined for each excitation frequency, similar to frequency-dependent elements.

For the option to bypass the frequency-dependent looping, the equation of motion to be solved is:

(5-26)


For frequency response with synchronous excitation, the excitation frequency is equal to the spin rate of the reference rotor, . The spin rates of the additional rotors can be determined from the

relative spin rates specified by the user. The equation of motion to be solved is:

(5-27)


will be determined for each excitation frequency, similar to frequency-dependent elements.

ω2M– iω

BS α1MS α2KS+ +

BRj

j 1=

n

∑ BHRj α1RjMRj α2RjKRj Ωj Ωre f( )BjG

+ + + + +

+

1 ig+( )KS iK4S+

1 igRj+( )KRj iK4Rj iKHRj+ +

Ωj Ωref( ) KjCB

KjCBH α1RjKj

CM α2RjKjCK gRj

ω------- Kj

CK 1ω---- Kj

CK4 1ω---- Kj

CKH+ + + + + + +

j 1=

n

∑+

u ω( ) F ω( )=+

1 ω⁄( )

ω2M– iω

BS α1MS α2KS + + +

BRj BHRj α1RjMRj α2RjKRj Ωj Ωref( )BjG gRj

WR3------------ KRj

1WR4------------ K4Rj

1WRH-------------- KHRj+ + + + + + +

j 1=

n

∑

+

1 ig+( )KS iK4S+

KRj Ωj Ωref( )( )+

j 1=

n

∑+

+

KjCB

KjCBH α1RjK

CM α2RjKCK gRj------------

KjCK 1------------

KjCK4 1--------------

KRjCKH+ + + + + +

u ω( ) F ω( )=

ω Ωref=

Ωref2

M iΩref

BS α1MS α2KS+ +

BRj

j 1=

n

∑ BHRj α1RjMRj α2RjKRj Ωj Ωre f( )BjG

+ + + + +

+–

1 ig+( )KS iK4S+

1 igj+( )KRj iK4Rj iKHRj+ +

ΩjΩre f+

j 1=

n

∑+

KjCB

KjCBH α1RjKj

CM α2RjKjCK gRj

Ωre f------------

KjCK 1

Ωref---------- Kj

CK4 1Ωref---------- Kj

CKH+ + + + + +

u Ωref( ) F Ωref( )=

+

Ωj Ωref( )


For the option to bypass the frequency-dependent lookup of rotor speeds, for each rotor is written as a linear function dependent on the reference rotor spin rate . The scaling factors,

and , are determined from the relative spin rates specified by the user. The in the terms

are replaced by the values of user parameters WR3, WR4, and WRH. The equation of motion to be solved is:

(5-28)


Complex ModesFor complex modes with asynchronous excitation, the spin rate for each rotor is constant and can be determined from user input and the reference rotor spin rate, . The equation of motion to be

solved is:

ΩΩj Ωref( ) αj βjΩre f+=( )

αj βj Ωref 1 Ωre f⁄

Ωref2

M i βjBjG

j 1=

n

∑–

–

iΩre f BS α1MS α2KS

j 1=

n

∑+ + +

+

BRj BHRj α1RjMRj α2RjKRj αjBjG gRj

WR3------------ KRj

1WR4------------ K4Rj

1WRH-------------- KHRj+ + + + + + +

iβj KjCB

KjCBH α1RjKj

CM α2RjKjCK gRj

WR3------------ Kj

CK 1WR4------------ Kj

CK4 1WRH-------------- Kj

CKH+ + + + + +

–

1 ig+( )KS iK4S + +

KRj αj+

j 1=

n

∑

+

KjCB

KjCBH α1RjKj

CM α2RjKjCK gRj

WR3------------ Kj

CK 1WR4------------ Kj

CK4 1WRH-------------- Kj

CKH+ + + + + +

u Ωref( ) F Ωref( )=

ΩΩref


170

(5-29)


For complex modes analysis with synchronous excitation, the excitation frequency is equal to the spin rate of the reference rotor, . for each rotor is written as a linear function dependent on the

reference rotor spin rate . The scaling factors, and , are determined from the

relative spin rates specified by the user. The equation of motion to be solved is:

(5-30)


ω2M– iω

BS α1MS α2KS + + +

j 1=

n

∑

+

BRj BHRj α1RjMRj α2RjKRj Ωj Ωre f( )BjG gRj

WR3------------ KRj

1WR4------------ K4Rj

1WRH-------------- KHRj+ + + + + + +

1 ig+ KS iK4S + +

j 1=

n

∑+

+

KRj Ωj Ωref( ) KjCB

KjCBH α1RjK

CM α2RjKCK gRj

WR3------------ Kj

CK 1WR4------------ Kj

CK4 1WRH-------------- Kj

CKH+ + + + + + +

u ω( ) 0=

ω Ωref= ΩΩi Ωref( ) αj βjΩre f+=( ) αj βj

Ωref2

M i βjBjG

j 1=

n

∑––

iΩref BS α1MS α2KS

j 1=

n

∑+ + +

+

BRj BHRj α1RjMRj α2RjKRj αjBjG gRj

WR3------------ KRj

1WR4------------ K4Rj

1WRH-------------- KHRj+ + + + + + +

iβjKjCB

KjCBH α1RjKj

CM α2RjKjCK gRj

WR3------------ Kj

CK 1WR4------------ Kj

CK4 1WRH-------------- Kj

CKH+ + + + + +–

1 ig+( )KS iK4S + +

KRj αj+

j 1=

n

∑

+

KjCB

KjCBH α+ 1RjKj

CM α2RjKjCK gRj

WR3------------ Kj

CK 1WR4------------ Kj

CK4 1WRH-------------- Kj

CKH+ + + + +

u Ωref( ) 0=


Nonlinear Transient ResponseFor nonlinear transient response, is time dependent, the equation of motion to be solved is:

(5-31)

Ω

Mu·· t( )

Bs BRj α+ 1Ms α2Ks+ +g

W3-------- Ks

1W4-------- K4s+ +

BRj BHRj α1RjMRj α2RjKRj+ + +

j 1=

n

∑gR

WR3------------ KR

1WR4------------ K4Rj

1WRH-------------- KHRj Ωj t( )Bj

G+ + + + +

u· t( )+

KS

j 1=

n

∑+ KRj Ω

·j t( )Kj

T+

Ωj t( ) KjCB

KjCBH α1RjKj

CM α2RjKjCK gr

WR3------------ Kj

CK 1WR4------------ Kj

CK4 1WRH-------------- Kj

CKH+ + + + + +

+

+

u t( ) F t( )=


172

Exterior Acoustics

IntroductionNastran has been used to analyse interior acoustic problems for a long time. With interior acoustic problems, the acoustic domain considered is bounded. A typical example is the determination of the sound pressure inside a car.

With exterior acoustic problems, the acoustic domain is unbounded. The analysis studies the sound pressure in the vicinity of the vibrating body or far away from the body. A further important result is the acoustic power radiated from the vibrating structure. A typical example is the determination of the radiated acoustic power of an engine.

In MD Nastran 2006 the infinite elements from MSC.Actran have been integrated to allow the analysis of exterior acoustic problems. The infinite elements are attached to the boundary of the acoustic finite element mesh to provide the correct non-reflecting boundary condition. This is a prerelease and should be used for production work with care.

Apart from standard acoustic results within the finite region it is possible to compute acoustic results at points within the infinite elements. These points, the so-called field points, may be connected by elements to form a field point mesh. If a field point mesh is defined, also the acoustic power through this field point mesh is computed.

BenefitsThe integration of the proven and tested infinite elements from MSC.Actran into MD Nastran largely facilitates the analysis of exterior acoustic problems. It is no longer necessary to transfer data between different programs but the analysis can be done completely within MD Nastran.

InputNew Bulk Data entries, CACINF3 and CACINF4, are used to define the connectivity of the infinite elements. The properties of the infinite elements are defined on PACINF Bulk Data entries.

Field points and field point meshes are defined in separate sections of the bulk data file. These sections must follow the main bulk data section.

Output of radiated power from the wetted surface and intensities on the wetted surface is controlled by Case Control commands ACPOWER and INTENSITY. Output of field point mesh results is controlled by Case Control command ACFPMRESULT.

Definition of Infinite ElementsThe geometry of an infinite element is defined by the geometry of its base and the location of the pole, see Figure 5-1. The base of the infinite element is that part that is in contact with the finite domain. The


geometry of the base is defined by its connectivity and the location of the corner grids. In order to avoid overlapping of the infinite elements, the surface they are attached to must be convex. However, it is not necessary that this surface is smooth.

Figure 5-1 Geometry of Infinite Element

Within an infinite element, the acoustic pressure is expanded into a power series of (1/r) where r is the distance from the pole.The radial interpolation order is the number of terms kept in this series.

The connectivity of the base is defined on the CACINF3 and CACINF4 Bulk Data entries. The orientation should be such that the normal vector on the base points into radial direction. However, MD Nastran will automatically change the orientation if the normal vector does not point away from the pole. The location of the pole as well as the radial interpolation order are defined on PACINF Bulk Data entries.


174

Defines an acoustic conjugate infinite element with triangular base

Format:

Defines an acoustic conjugate infinite element with quadrilateral base

Format:

Defines the properties of acoustic conjugate infinite elements.

CACINF3 Acoustic Conjugate Infinite Element Base Connection

1 2 3 4 5 6 7 8 9 10

CACINF3 EID PID G1 G2 G3

Field Contents

EID Element Identification Number (Integer > 0)

PID Property Identification Number of a PACINF entry (Integer > 0)

Gi Grid Point Identification Numbers of Element Base Connection Points (Integer > 0)

CACINF4 Acoustic Conjugate Infinite Element Base Connection

1 2 3 4 5 6 7 8 9 10

CACINF4 EID PID G1 G2 G3 G4

Field Contents

EID Element Identification Number (Integer > 0)

PID Property Identification Number of a PACINF entry (Integer > 0)

Gi Grid Point Identification Numbers of Element Base Connection Points (Integer > 0)

PACINF Acoustic Conjugate Infinite Element Property


Format:

Definition of Field Point MeshesAcoustic field point meshes are defined in separate sections of the bulk data file. These sections follow the main bulk data section. Each of the sections begins with

BEGIN BULK AFPM = afpmid

or

BEGIN AFPM = afpmid

where afpmid is the acoustic field point mesh identifier (integer > 0). Acoustic field points are defined using the standard GRID Bulk Data entry. Because all grid points defined in this section of the bulk data file are acoustic field points, it is not necessary to place a -1 into field 7.

The grid points can be connected by any type of elements. However, only CTRIA3 and CQUAD4 elements define a field point mesh that is used to compute normal components of the acoustic intensity and the power through the field point mesh. Legal property identifiers have to be specified on the CTRIA3 and CQUAD4 Bulk Data entries. However, the referenced PSHELL entries need not be defined.

If output to an .op2 file is requested, parameter POST has to be defined within the section of the acoustic field point mesh. Output of different field point meshes can be sent to different .op2 files using parameter OUNIT2 within the sections of the acoustic field point meshes.

ExampleBEGIN AFPM=100$PARAM, POST, -1$$ Isolated Field Points along a Line$GRID 1001 2 5. 0. 0.GRID 1002 2 6. 0. 0.GRID 1003 2 7. 0. 0.GRID 1004 2 8. 0. 0.

1 2 3 4 5 6 7 8 9 10

PACINF PID MID RIO X1 X2 X3

Field Contents

PID Property Identification Number of PACINF entry (Integer > 0)

MID Material Identification Number of a MAT10 entry (Integer > 0)

XP, YP, ZP Coordinates of the Pole of the Infinite Elements (in the Basic Coordinate System)


176

GRID 1005 2 9. 0. 0.GRID 1006 2 10. 0. 0.CORD2R, 2,, 0., 0., 0., -.5, -.5, .707107 , .5, .5, .707107$BEGIN AFPM = 200$PARAM, POST, -1$GRID, 1,, -1., -1., 2.GRID, 2,, 0., -1., 2.GRID, 3,, 1., -1., 2.GRID, 4,, -1., 0., 2.GRID, 5,, 0., 0., 2.GRID, 6,, 1., 0., 2.GRID, 7,, -1., 1., 2.GRID, 8,, 0., 1., 2.GRID, 9,, 1., 1., 2.$GRID, 11,, -1., -1., 2.GRID, 12,, 0., -1., 3.GRID, 13,, 1., -1., 2.GRID, 14,, -1., 0., 3.GRID, 16,, 1., 0., 3.GRID, 17,, -1., 1., 2.GRID, 18,, 0., 1., 3.GRID, 19,, 1., 1., 2.$CQUAD4, 1, 1, 1, 2, 5, 4CQUAD4, 2, 1, 2, 3, 6, 5CQUAD4, 3, 1, 4, 5, 8, 7CQUAD4, 4, 1, 5, 6, 9, 8$CQUAD4, 5, 1, 12, 16, 18, 14CTRIA3, 6, 1, 11, 12, 14CTRIA3, 7, 1, 12, 13, 16CTRIA3, 8, 1, 16, 19, 18CTRIA3, 9, 1, 14, 18, 17$ENDDATA

Case Control CommandsThe following new case control commands control postprocessing which is related to exterior acoustics.

Requests output of the power radiated from the wetted surface.

ACPOWER Acoustic Power Output Request


Format:

Requests output of acoustic intensity on wetted surface.

Format:

Describer Meaning

SORT1 Output will be presented as tabular listing of panels for each excitation frequency

SORT2 Output will be presented as tabular listing of excitation frequencies for each panel (Default)

PRINT The printer will be the output medium (Default).

PUNCH The punch file will be the output medium.

PLOT Results are generated but not output.

CSV Results will be written to a .csv file.

unit Unit of the .csv file as used on the ASSIGN statement

ALL Radiated power will be processed for the wetted surface and all panels.

n Set identification of a previously defined set of panels. Radiated power will be processed for the wetted surface and all panels in the referenced set.

NONE Radiated power will not be processed.

INTENSITY Acoustic Intensity Output Request

ACPOWER SORT1

SORT2

PRINT,PUNCH

PLOTCSV unit=[ ], ,

ALL

n

NONE

=

INTENSITY SORT1

SORT2

PRINT,PUNCH

PLOT,

ALL

n

NONE

=


178

Requests output of field point mesh results.

Format:

Describer Meaning

SORT1 Output will be presented as tabular listing of grid points for each excitation frequency (Default)

SORT2 Output will be presented as tabular listing of excitation frequencies for each grid point




ALL Intensities will be computed for all grid points of the wetted surface.

n Set identification of a previously defined set of grid points. Intensities will be computed for the grid points in this set only.

NONE Acoustic intensities will not be processed.

ACFPMRESULT Acoustic Field Point Mesh Results Output Request

Describer Meaning

SORT1 Output will be presented as tabular listing of grid points for each excitation frequency (Default)

SORT2 Output will be presented as tabular listing of excitation frequencies for each grid point


ACFPMRESULT SORT1

SORT2

PRINT,PUNCH

PLOTVELOCITY YES

NO

=, ,

REAL or IMAG

PHASEPOWER YES

NO

=

,ALL

n

NONE

=


OutputIn addition to the standard acoustic results, the following results may be requested:

• Acoustic energy radiated from the wetted surface or from panels

• Normal component of the acoustic intensity at grid points of the wetted surface

• Acoustic pressure and intensity at the field points

• Acoustic velocity at the field points

• Acoustic energy flowing through the field point mesh

Field point mesh results can be written to the .f06 file or the .op2 file. The .xdb file is not yet supported.

Guidelines1. The surface the infinite elements are attached to must be convex but it need not be smooth.

Infinite elements have to be connected to acoustic grid points. Thus it is necessary to model the vicinity of the vibrating structure with acoustic finite elements until a convex surface is reached.

2. The radial interpolation order required depends on the directivity of the pressure field. Usually, a higher order is needed for higher frequencies.

3. It is recommended to study the sensitivity of the results with respect to the radial interpolation order by repeating the analysis with a different radial interpolation order.

4. Infinite elements are supported in direct and modal frequency response analysis (SOL 108 and SOL 111). Experience shows that a large number of fluid modes is needed to get converged results. Thus, modal reduction of the fluid is not recommended. However, modal reduction can be applied to the structure.



VELOCITY Requests output of particle velocities (Default: NO)

REAL or IMAG Requests rectangular format (real and imaginary) of complex output. Use of either REAL of IMAG yields the same output.

PHASE Requests polar format (magnitude and phase) of complex output. Phase output is in degrees.

POWER Requests output of power through field point mesh (Default: YES)

ALL Results of all field point meshes will be processed

n Set identification of a previously defined set of field point mesh identifiers. Results will be processed for the field point meshes in this set only.

NONE Field point mesh results will not be processed.

Describer Meaning


180

5. Efficiency can be increased if the iterative solver is used. It is recommended to use the Jacobi preconditionner with an epsilon of 10-4.

Limitations1. Infinite elements are supported in a frequency response analysis only (SOL 108 and SOL 111).

2. In this prerelease, case control commands ACPOWER and INTENSITY are not yet supported.

ExampleIn this example, the sound transmission through an elastic plate embedded in an infinite rigid wall is analysed. Figure 5-2 shows the geometry of the plate and of the fluid region meshed with finite elements. The finite element mesh of the structure and of one quarter of the fluid can be seen in Figure 5-3.

Figure 5-2 Geometry

Infinite Elements are attached to the top and the four lateral faces but not to the bottom. The pole of all infinite elements is at the center of the plate. The finite element mesh of the structure together with one quarter of the infinite element mesh is shown in Figure 5-4.

The field point mesh is a cube which completely encloses the fluid mesh. Thus, the power through this field point mesh equals the total power radiated from the plate. Figure 5-5 shows the fluid mesh and one quarter of the field point mesh.


Figure 5-3 Structure and Quarter of Fluid Mesh

Figure 5-4 Structure and Quarter of Infinite Element Mesh


182

Figure 5-5 Fluid Mesh and Quarter of Field Point Mesh

The excitation is a uniform pressure applied to the plate. The acoustic pressure in the finite element mesh and acoustic results at some discrete field points located along the z-axis and at the field points of the field point mesh are computed. Acoustic results at the field points include the acoustic pressure and the acoustic intensities.

Input FileSOL 108CENDTITLE = Vibrating Plate ExampleSUBTITLE = Direct Frequency Response$ECHO = SORT(EXCEPT, GRID, CHEXA, CQUAD4, CACINF4)$DLOAD = 10FREQ = 20SMETHOD = 30SPC = 1$DISP(PLOT) = ALLACFPMRESULT(PHAS) = ALL$BEGIN BULK$PARAM, POST, -1$ACMODL, IDENT


$RLOAD1, 10, 200,,, 300PLOAD2, 200, 1., 1, THRU, 150TABLED1, 300 , 0., 1., 1000., 1., ENDT$FREQ, 20, 10.$ITER, 30 PRECOND = J, ITSEPS = 1.0E-4$$ Fluid$GRDSET,,,,,, -1INCLUDE 'fluid1.bdf'$$ Structure$INCLUDE 'structure.bdf'$BEGIN AFPM=100$$ Isolated Field PointsGRID, 10001,, 0., 0., 3.5GRID, 10002,, 0., 0., 5.GRID, 10003,, 0., 0., 10.$BEGIN AFPM=200$$ Field Point MeshINCLUDE 'fpm.bdf'$ENDDATA

Excerpt of fluid1.bdf

$ Exterior Acoustics - Vibrating Plate Example$ Fluid Model of Domain 1: Finite and Infinite Elements$$ -------------------------------------------------------------------$$ PID MID RIO XP YP ZPPACINF 10 20 10 0. 0. 0.PSOLID 2 20 PFLUIDMAT10 20 1.21 340.$CHEXA 1001 2 1001 1002 1018 1017 1177 1178 1194 1193CHEXA 1002 2 1002 1003 1019 1018 1178 1179 1195 1194


184

…$ Infinite Elements$CACINF4 13901 10 3641 3642 3658 3657CACINF4 13902 10 3642 3643 3659 3658CACINF4 13903 10 3643 3644 3660 3659CACINF4 13904 10 3644 3645 3661 3660CACINF4 13905 10 3645 3646 3662 3661CACINF4 13906 10 3646 3647 3663 3662 …

ResultsFigure 5-6 shows the acoustic pressure in the Finite Element mesh and Figure 5-7 shows some results printed to the .f06.

Figure 5-6 Acoustic Pressure in the Finite Element Mesh


00

H

Figure 5-7 Results in .f06

FREQUENCY = 1.000000E+01 ACOUSTIC FIELD POINT MESH = 1 A C O U S T I C F I E L D P O I N T M E S H R E S U L T S ACOUSTIC PRESSURE INTENSITY COMP. INTENSITY INTENSITY INTENSITY POINT ID. MAGNITUDE PHASE NORMAL TO FPM X Y Z 10001 5.867592E-03 3.224626E+02 0.0 3.901852E-16 1.102822E-09 4.101243E-08 10002 4.148942E-03 3.068220E+02 0.0 1.168128E-16 3.946748E-10 2.071128E-08 10003 2.089879E-03 2.542063E+02 0.0 1.290767E-17 5.147245E-11 5.294778E-091 VIBRATING PLATE EXAMPLE DECEMBER 6, 2005 MSC.NASTRAN 12/ 5/05 PAGE 16 DIRECT FREQUENCY RESPONSE 0 *** USER INFORMATION MESSAGE 3119 (AFPINI) DATA RECOVERY OF ACOUSTIC FIELD POINT MESH 200 INITIATED1 VIBRATING PLATE EXAMPLE DECEMBER 6, 2005 MSC.NASTRAN 12/ 5/05 PAGE 17 DIRECT FREQUENCY RESPONSE 0 FREQUENCY = 1.000000E+01 ACOUSTIC FIELD POINT MES= 200 A C O U S T I C F I E L D P O I N T M E S H R E S U L T S ACOUSTIC PRESSURE INTENSITY COMP. INTENSITY INTENSITY INTENSITY POINT ID. MAGNITUDE PHASE NORMAL TO FPM X Y Z 46567 2.959861E-03 2.856447E+02 7.442431E-09 -7.647572E-09 7.442431E-09 1.545178E-10 46568 2.930327E-03 2.848879E+02 7.258169E-09 -7.408595E-09 7.258169E-09 1.340973E-09 46569 2.846820E-03 2.826632E+02 6.691689E-09 -6.762688E-09 6.691689E-09 2.608988E-09 46570 2.722373E-03 2.790949E+02 5.876647E-09 -5.877888E-09 5.876647E-09 3.492858E-09 46571 2.572942E-03 2.743544E+02 4.970530E-09 -4.929979E-09 4.970530E-09 3.970974E-09 46572 2.412938E-03 2.686276E+02 4.189022E-09 -4.042182E-09 4.189022E-09 4.023463E-09 46573 3.274509E-03 2.928127E+02 1.022698E-08 -8.121219E-09 1.022698E-08 2.107736E-10 46574 3.234508E-03 2.919741E+02 9.893179E-09 -7.820792E-09 9.893179E-09 1.809509E-09


186


Ch. :

6 Aeroelasticity

Monitor Points, 188

Spline6/7, 195

Combination of Controllers/User Input Loads Enhancements, 197

Separate Rigid and Flexible Aero Meshes, 199

Miscellaneous Aeroelastic Enhancements, 201


188

Monitor Points

Introduction“Monitor Points” is a term used collectively to refer to four data items that have been implemented in MD Nastran:

1. MONPNT1 – The MONPNT1 provides integrated loads at a user defined point in a user defined coordinate system. The user also identifies the nodes (on either the structural or aerodynamic model) whose loads are to be integrated. MD Nastran 2006 adds the ability to specify an output coordinate system in addition to the coordinate system used in defining the location of the integration point. It availability has been extended from SOL 144 to SOL’s 101 and 146.

2. MONPNT2 – The MONPNT2 provides element results (Stress, Strain, Force) in a tabulated fashion. For the results to be accurate, the term selected must be a linear function of the displacements.

3. MONPNT3 – The MONPNT3 provides a summation of grid point forces at a user specified integration points. This can be used to provide the net load acting at a fuselage or wing station by making a “cut” in the structure and then identifying all the grids and elements on one side of the cut

4. MONDSP1 – The MONDSP1 allows for the sampling of a displacement vector to create a blended displacement response at a user specified point and coordinate system. The displacement monitor point is essentially an RBE3 element (limited to a single dependent point) and the dependent grid is now an arbitrary point.

While Monitor Points have been developed with primarily aeroelastic considerations in mind, their applicability in any type of analysis is recognized. The following table shows which solution sequences currently support monitor point processing.

Special Considerations for the MONPNT3

The original implementation of the MONPNT3 relied on the GPFDR (grid point force data recovery) module to compute the grid point forces and two new modules to post-process this information to obtain the point information. This proved to have significant performance problems so that an alternative was developed. The enhanced process identifies the elements that participate in the calculation of the monitor point result and then does a mini EMA (element matrix assembly) to form a stiffness matrix that just includes those elements. Multiplying this matrix by an integration matrix that transfers forces to the

Solution Sequence MONPNT1 MONPNT2 MONPNT3 MONDSP1

SOL 101 X x x x

SOL 144 X x x x

SOL 146 X x

189CHAPTER 6Aeroelasticity

monitor point results in a matrix S that can be multiplied by the set of solution vectors U to provide the monitor point results:

(6-1)

The S matrix (denoted MP3INT in the dmap sequences) is computed as a preprocessing operation. The monitor point results are then calculated using Equation (6-1) or 2 once the displacements have been computed.

In this enhanced process, the exclusion flag (XFLAG) has special significance. This flag can be used to exclude specified force types from the calculation. If the XFLAG field is set by the user to exclude all of the candidate force types (i.e., XFLAG=SMAD), then the enhanced algorithm can be employed and a filtering process is applied to see which set of the elements and grids listed in the GRIDSET and ELEMSET will result in a non-zero resultant force. I.e., if all the elements attached to a particular grid are included in the ELEMSET, the grid can be filtered out and if all the grids a particular element attaches to are included in the GRIDSET, then the element can be filtered out. The remaining grids and elements are then included in the mini-EMA step.

If the XFLAG is blank, then a complementary filtering process occurs. Excluding of grids and elements occurs as above but now the remaining set of elements is discarded and the mini-EMA includes those elements that are attached to the retained grids that are NOT included in the ELEMSET.

If some, but not all, of the candidate force type are excluded (e.g., XFLAG=A), then the enhanced method cannot be applied and the MONPNT3 processing reverts to the original grid point force methodology.

BenefitsThe MONPNT1 was first introduced in MSC.Nastran 2001 and provides the user with a way to extract the applied loading for a specified set of structural nodes or aerodynamic elements. This enables the batch calculation of VMT (shear, moment and torque) data as well at aerodynamic coefficient data for user specified regions and locations.

The MONPNT2 provides a way of pinpointing a particular response for output, as opposed to finding a particular item in a large OFP listing.

The MONPNT3 provides a summation of the internal loads and therefore useful in calculating resultant forces at a cut in the structure.

The MONDSP1’s ability to provide an averaged displacement is seen as providing a qualitative assessment of the elastic deflection of a vehicle. An example is to monitor the nominal pitch and plunge at a station along the wing.

InputThe MONITOR Case Control command provides control over the print of the monitor points results Toggles can be used to control the print of the individual monitor types. This command must be placed

MP3 ST

U=


190

above the subcase level or in the first subcase and applies to all subcases. The print associated with SOL 146 results can be particularly voluminous since data can be given for every frequency or time point.

The MONPNT1, MONPNT2, MONPNT3 and MONDSP1 entries are shown in the Quick Reference Guide. As mentioned, the MONPNT1 has been enhanced to provide an output coordinate system for displaying the results. Note that the loads can be on the structural or the aerodynamic model as specified by the COMP field that, in turn, identifies a AECOMP entry that can invoke CAEROi or AELIST entries for aerodynamic elements or a SET1 entry for structural grids.

The MONPNT2 entry requests that the user identify the element type and NDDL item. The type is obtained from the table given in Remark 5 of this entry and it is seen that there are separate types for composite and element corner results.

The MONPNT3 entry identifies a piece of structure by identifying the elements and nodes associated with it. The grid point force data associated with these entities is then integrated to the location specified on the entry. The XFLAG can be used to exclude certain grid point force types from consideration.

The MONDSP1 entry is similar to the MONPNT1 entry but now it is displacements that are being averaged. The AECOMP entry can invoke either structural grids or aerodynamic elements.

Output A comprehensive depiction of the prints of the monitor points across all the solution sequences would be too detailed for the purposes of this document. Several key tables are presented here and it is suggested that the examples of the following subsection be exercised to get an idea of the printout to expect. For SOL 144, the MONPNT1 and MONDSP1 entries can be on either the aerodynamic or the structural mesh. An example of MONPNT1 output on both meshes that is extracted from the m31chk example file is shown here:


It is seen that the trim state is first printed and this is followed by labeling information and finally the data. The monitor points extend over the same portion of the vehicle and it is seen that the results compare well. In this case, there is no externally applied load so that the structural results show zeroes and there are no applied loads on the aero mesh. If applied structural loads were present, the rigid and elastic total loads would be printed in the two columns while only the elastic increment would be printed for the aerodynamic model.

A print of MONDSP1 data extracted from the msimpms example is shown next.

S T R U C T U R A L M O N I T O R P O I N T I N T E G R A T E D L O A D S CONFIGURATION = AEROSG2D XY-SYMMETRY = ASYMMETRIC XZ-SYMMETRY = ASYMMETRIC MACH = 5.000000E-01 Q = 7.000000E+02

CONTROLLER STATE: ANGLEA = 9.6005E-03 URDD3 = -1.0000E+00 ELEV = 1.7303E-01

MONITOR POINT NAME = CANARD COMPONENT = CANARDS CLASS = GENERAL LABEL = THE CANARD STRUCTURAL POINTS CP = 900 X = 5.00000E+00 Y = 2.00000E+00 Z = 0.00000E+00 CD = 900

AXIS RIGID AIR ELASTIC REST. INERTIAL RIGID APPLIED REST. APPLIED ---- ------------- ------------- ------------- ------------- ------------- CX 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 CY 0.000000E+00 0.000000E+00 5.530298E-14 0.000000E+00 0.000000E+00 CZ 4.735976E+03 4.835128E+03 5.000000E+01 0.000000E+00 0.000000E+00 CMX 7.039471E+03 7.187045E+03 6.000000E+01 0.000000E+00 0.000000E+00 CMY 1.717664E+04 1.727710E+04 0.000000E+00 0.000000E+00 0.000000E+00 CMZ 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

A E R O D Y N A M I C M O N I T O R P O I N T I N T E G R A T E D L O A D S CONFIGURATION = AEROSG2D XY-SYMMETRY = ASYMMETRIC XZ-SYMMETRY = ASYMMETRIC MACH = 5.000000E-01 Q = 7.000000E+02

CONTROLLER STATE: ANGLEA = 9.6005E-03 URDD3 = -1.0000E+00 ELEV = 1.7303E-01

MONITOR POINT NAME = CANARD COMPONENT = CANARDA CLASS = GENERAL LABEL = THE CANARD AERO PANEL CP = 900 X = 5.00000E+00 Y = 2.00000E+00 Z = 0.00000E+00 CD = 900

AXIS RIGID AIR ELASTIC REST. ---- ------------- ------------- CX 0.000000E+00 0.000000E+00 CY 0.000000E+00 0.000000E+00 CZ 4.735976E+03 4.835128E+03 CMX 7.039471E+03 7.187045E+03 CMY 1.717664E+04 1.727710E+04 CMZ 0.000000E+00 0.000000E+00


192

In this case, different displacement requests have been made so that the structural and the aerodynamic results do not compare.

The final output shown here is for MONPNT2 and MONPNT3 results from a SOL 101 run made with example q2010601.

S T R U C T U R A L M O N I T O R P O I N T D I S P L A C E M E N T S CONFIGURATION = AEROSG2D XY-SYMMETRY = ASYMMETRIC XZ-SYMMETRY = SYMMETRIC MACH = 4.500000E-01 Q = 2.000000E+00

CONTROLLER STATE: URDD3 = 1.4909E-04 URDD5 = -2.5493E-05

MONITOR POINT NAME = SWTIP COMPONENT = SWTIP CLASS = DISPLACEMENT LABEL = TRANSVERSE DISP AND TWIST AT WING TIP CP = 0 X = 2.51500E+00 Y = 5.52500E+00 Z = 0.00000E+00 CD = 0

AXIS ELASTIC REST. ---- ------------- TZ 2.835612E+00 RY -2.929023E-02

A E R O D Y N A M I C M O N I T O R P O I N T D I S P L A C E M E N T S CONFIGURATION = AEROSG2D XY-SYMMETRY = ASYMMETRIC XZ-SYMMETRY = SYMMETRIC MACH = 4.500000E-01 Q = 2.000000E+00

CONTROLLER STATE: URDD3 = 1.4909E-04 URDD5 = -2.5493E-05

MONITOR POINT NAME = AWTIP COMPONENT = ACAERO CLASS = DISPLACEMENT LABEL = PITCH AND PLUNGE AT THE WING TIP CP = 0 X = 2.30000E+00 Y = 4.70000E+00 Z = 0.00000E+00 CD = 0

AXIS ELASTIC REST. ---- ------------- TX 0.000000E+00 TY 0.000000E+00 TZ 2.207074E+00 RX 5.431858E-01 RY -3.140820E-02 RZ 0.000000E+00


It is seen that each MONPNT2 produces its own line of data for each subcase while the MONPNT3 results contain as many rows as the have been specified in the AXES field on the MONPNT3 entry.

ExamplesThe monitor point capability extends across solutions sequences and monitor point types. The following table contains the names of tpl files that demonstrate a particular combination.

Guidelines and LimitationsThe MONITOR Case Control command is required to obtain monitor point output in SOL’s 101 and 146. For SOL 144, the case control is not required for the MONPNT1 and MONDSP1 prints, but is needed for MONPNT2 and MONPNT3.

S T R U C T U R A L I N T E R N A L M O N I T O R P O I N T L O A D S (MONPNT2)

MONITOR POINT NAME = MONPNT2

VALUE EID ETYPE CLASS RESPONSE LABEL SUBCASE NO. ------------- ---------- -------- -------- -------- ---------------------------------------------------------------------- 1.504374E+00 1100081 QUAD4 STRESS SY1 MPT21 THIS IS A STRESS-MONPT2 MONITOR POINT 1

MONITOR POINT NAME = MONPNT2

VALUE EID ETYPE CLASS RESPONSE LABEL SUBCASE NO. ------------- ---------- -------- -------- -------- ---------------------------------------------------------------------- 3.008748E+00 1100081 QUAD4 STRESS SY1 MPT21 THIS IS A STRESS-MONPT2 MONITOR POINT 2

S T R U C T U R A L F R E E B O D Y M O N I T O R P O I N T I N T E G R A T E D L O A D S

MONITOR POINT NAME = MPT31 COMPONENT = 5 CLASS = GENERAL SUBCASE NO. 1 LABEL = THIS IS A FREE BODY MONITOR POINT ICID = 52 X = 1.00000E+00 Y = 2.00000E+00 Z = 3.00000E+00

AXIS REST. APPLIED ---- ------------- CX 2.433662E-01 CY 1.720859E-01 CZ 0.000000E+00 CMX -2.460616E+00 CMY 3.479837E+00 CMZ -1.559533E+00

SOLution 101 144 144 146(time) 146(time) 146(freq) 146(freq)

Type Structure Structure Aero Struct Aero Structure Aero

Monitor

MONDSP1 Q2010601 msimpms msimpms fmondsp fmondsp Gustfff Gustfff

MONPNT1 Q2010601 freedlm freedlm fmondsp fmondsp Gustfff gustfff

MONPNT2 Q2010601 M31chk n/a n/a n/a n/a n/a

MONPNT3 Q2010601 M31chk n/a n/a n/a n/a n/a


194

The prints in SOL 146 can be voluminous since each component that is printed requires its own table for the list of frequency or time points.

For the aeroelastic solutions, the MONPNT1 and MONDSP1 data can be calculated based on structural grids or aerodynamic elements. MONPNT2 and MONPNT3 results are only available on the structural model.

The MONPNT2 results are computed by multiplying a predefined matrix times the solution vector. This assumes that the desired quantity is a linear function of the solutions. Clearly, this is not the case for synthesized responses; e.g. (von Mises stress).


Spline6/7

Introduction Two new spline method are available in MD Nastran 2006: 3D finite surface spline (SPLINE6) and 3D finite beam spline (SPLINE7). These splines support 6 degrees of freedom for both the aerodynamic and structural meshes and may be used to couple the aerodynamic and structural models.

Both methods use the same basic approach to solving the interpolation problem: they form a small, virtual finite element enforced motion statics problem to measure the motion of the dependent dofs. The computed displacements under unit enforced motion of the independent grids are then the spline interpolant. In the case of the beam spline (as shown in Figure 6-1 below), the virtual mesh is comprised of a set of bar elements laid along a user-defined axis. The independent and dependent points are connected to the virtual beam by RBE3 and RBE2 elements. In the case of the plate spline, the user defines the mesh and RBE3 elements are used to connect the DOF’s to the virtual surface mesh. The user can specify the elements that are to be used in the virtual mesh. Typically, the aerodynamic elements are used as the virtual mesh.

Figure 6-1


196

Benefits These new methods work across almost all aero mesh types and are suitable for “external” aero methods in addition to structure-to-structure splines. These new methods are the only ones that are full 6DOF to 6DOF spline methods; hence, they are the only ones that can be used in structure-to-structure loads mapping applications. With a little work using standard Nastran or by using the MD Nastran toolkit, these two new spline methods may be used to perform structure-to-structure splining.

Standard MD Nastran does not support the user interface to drive the methods for structure-to-structure mapping so it would be necessary to develop custom mapping tools, perhaps using MD Nastran Toolkit to drive the mapping of loads from the aeroelastic finite element model to the internal loads FE using these methods.

InputThe SPLINE6 and SPLINE7 entries are described in some detail in the MD Nastran Quick Reference Guide. These entries do not result in additional output.


Combination of Controllers/User Input Loads Enhancements

IntroductionChanges were made in the user interface for aeroelasticity to facilitate synthesizing controllers from multiple inputs. The first change was a simple change in AELINK Bulk Data entry that is of significant benefit when many subcases are being run. The AELINK entry now supports the character string “ALWAYS” or ID=0 in place of the trim set ID specified at the subcase level in case control. The effect of this is that a single AELINK entry can now apply to all of the subcases in the run.

The AEFORCE Bulk Data entry was enhanced in several ways: the resulting description of AEFORCE Bulk Data entry in Appendix D shows two additional features, both when MECH=STRUCT is being used:

1. The PERQ option of field 9 was activated.

2. Field 7 (LSET) can point to any type of loading whereas previously it could only select FORCE of MOMENT load types.

Two other enhancements applicable to AEDW and AEPRESS entries as well as AEFORCE:

The first is in the nature of the correction in a design flaw. In previous releases of MD Nastran, if a UXVEC entry only contained Label INTERCPT with a value of 1.0, the forces were added to all v-space terms that included the intercept. This has been corrected so that the forces are only present for the INTERCPT state.

The second is if AExxxx (i.e., AEFORCE/AEDW/AEPRESS) entries that point to the same UXVEC are summed. Previously only a single AExxxx/UXVEC combination was permitted.

BenefitsWith these enhancements, the user can now sum forces from a series of AExxxx entries to achieve a single controller. For example, there may be wind tunnel results on a number of components (e.g., missiles and fuselage segments) at a unit angle of attack that are not included in the aerodynamic model. Multiple AEFORCE entries that point to a single UXVEC vector that has INTERCPT and ANGLEA terms can now be used to add these effects in the simulation. Note that the LSET call out can also refer to a LOAD Bulk Data entry so that load superposition can occur and the import load feature of Section x.1 can be utilized.

The benefit of the ID=”ALWAYS” on the AELINK entry is significant when hundreds of subcases are run in a single job submittal.


198

Input/OutputThe introduction has already described the changes available on the AELINK, AEDW, AEFORCE and AEPRESS entries. There is no change in the output due to these enhancements.

Guidelines and LimitationsAExxxx entries that point to the same combination of control point values are summed. For example, AEFORCE entries that are for the same Mach and symmetry and either point to the same UXID or point to different UXID’s that have identical control point values all act together. AEFORCE entries that have MESH=AERO are combined with entries with MESH=STRUCT in this fashion.

Note that the forces that are created based on the AExxxx entries are absolute so that the UXVEC states need to include the label INTERCPT with a value of 1.0 when associated with (?)

Examples (aelinka.dat, aelinkb.dat,i3fusa.dat,aepload4.dat,fusae.dat)Aelinka.dat shows how ALWAYS can be used to make the linking condition apply to all subcases while aelinkb.dat has one controller using the ALWAYS feature while another has subcase dependent linking so that a scheduled deployment can be simulated.

i3fusa.dat is a variation of tpl file osprey.dat. It removes the engine controllers but adds user input aerodynamics for the fuselage at the intercept. The following fragment of this file shows how this concept is implemented:

$ aerodynamics on the fuselage at zero angle of attack $ using an aeforce/uxvec combination with no perq$ since the uxvec vector only reference the intercept, these $ forces are added to the intercept value and nowhere else. $aeforce0.9asymmasymm5011struct5011uxvec5011intercpt1.0 force 50119712000.0.00.01.0force 50119860000.0.00.01.0force 50119930000. 0.00.01.0

The results of running this file show that the forces produced by these data are applied only to the intercept state and not to the remaining states, such as ANGLEA.

Aepload4.dat uses pressure loads in conjunction with an AEFORCE entry while fusae.dat demonstrates that the AEFORCE entry with a UXVEC that specifies ANGLEA and INTERCPT with a value of 1.0 with add the additional forces to the angle of attack. Previously, it was necessary to include and AEPARM and a separate controller to add this type of force into the analysis.


Separate Rigid and Flexible Aero Meshes

IntroductionMD Nastran has been enhanced to support the ability to generate the rigid aerodynamic loads on one mesh while the aeroelastic increments are generated from a second mesh.

BenefitsThis enhancement adds to the infrastructure of the static aeroelastic analysis of SOL 144, but is not accompanied by any immediate useful application. A possible application would be to use CFD generated or wind tunnel derived aerodynamics to provide the rigid loads while the aeroelastic increments could be generated using the current aerodynamic methods in MD Nastran. Having the concept of separate rigid and flexible meshes available does simplify the task of incorporation these alternative aerodynamics using a customized solution.

InputThe AERCONFIG Case Control command is provided to identify the aerodynamic configuration that represents the rigid aerodynamics. The use of this command can be demonstrated by making two separate runs: the first contains the rigid mesh and is run with SCR=NO to save the needed data blocks. The AECONFIG command is used to identify this mesh. The second run inputs the flexible mesh using standard bulk data input and the AECONFIG command while the flexible mesh is input using a combination of DBLOCATE statements and the AERCONFIG command to identify the rigid mesh. See the example below for the DBLOCATE requests.

OutputThe following data related to aeroelastic results are written to the DBC and are therefore available in the .xdb output:

Datablock Description Mesh

UKS Trimmed displacements Flexible

PERKS Trimmed forces Flexible

FFERJS Trimmed pressures Flexible

RUKS Trimmed displacements Rigid

PRKS Trimmed forces Rigid

FFRJS Trimmed pressures Rigid

UERVKS Unit solution restrained displacements Flexible


200

UEUVKS Unit solution unrestrained displacements Flexible

RUERVKS Unit solution restrained displacements Rigid

RUEUVKS Unit solution unrestrained displacements Rigid

PERVKS Unit solution restrained forces Flexible

PEUVKS Unit solution unrestrained forces Flexible

FERVJS Unit solution restrained pressures Flexible

FEUVJS Unit solution unrestrained pressures Flexible

PRVKS Unit solution rigid forces Rigid

FRVJS Unit solution rigid pressures Rigid

Datablock Description Mesh


Miscellaneous Aeroelastic Enhancements

Revision in the Aerodynamic Splining to the StructureStarting with MD Nastran 2006, the splining that transfers the loads from the aerodynamic to the structural models in static aeroelastic analysis (SOL 144 and SOL 200) occurs in the f-set. Previously, this had been done in the g-set. This should not results in any change in results unless some of the structural degrees of freedom that are being splined to part of the single point constraint set. Previously, this load was reported in the rigid splined airloads, but now it will be discarded. Therefore, if the rigid splined and unsplined derivatives agreed in the past but now differ, you need to examine the model to see if you are splining to constrained dof’s and, if so, that is your intent.

Flutter Analysis with Singular Mass MatricesA long time requirement of the PK and KE flutter methods is that the diagonal terms of the mass matrix must be non-zero. This was a requirement of the underlying eigenanalyses being used and presented a problem with the modeling of control systems using the TF Bulk Data entry. As indicated by the servoelastic test case of Estimation of Dynamic Stability Derivatives (Example HA145I) (Ch. 8) in the MSC.Nastran Aeroelastic Analysis User’s Guide, this created a requirement that the transfer functions be differentiated a sufficient number of times to create a non-zero B0 term. This introduces additional zeroes in the eigensolution that can be ignored, but that complicate the interpretation of the results. An alternative QZ algorithm, as developed in Reference 1 (C. Moler and G.W. Stewart, “An Algorithm for Generalized Matrix Eigenvalue Problems,” SIAM J. Numerical Analysis, 10:241-256, 1973) has been implemented into the flutter solutions in MD Nastran that removes the requirement that the mass matrix be non-singular. The result is that test cases that used to require differentiation to make the mass matrix non-singular can now input the transfer functions in their original form. The results should be identical in either case so that this enhancement should not result in different answers for existing files. If you wish to investigate whether the new eigenanalysis methods are giving different answers, the old method are still available by setting Nastran System Cell 108 to 1.


202


Ch. :

7 Optimization

Topology Optimization with Manufacturability Constraints, 204

Revised Optimizer Options, 220

Supporting Trust Region in SOL 200 for Adaptive Move Limits, 223

Support of Analysis Model Value Overriding Design Model Value, 230


204

Topology Optimization with Manufacturability Constraints

Introduction Topology optimization is a powerful tool to generate design concepts in the early design stage. MD Nastran 2006 contains substantial enhancements to this capability that provides a number of manufacturability constraints to aid in producing designs that are more practical in terms of actually manufacturing the proposed design. The constraints include minimum member size, symmetry constraints, casting constraints (also called draw direction constraints), and extrusion constraints.

Benefits

Minimum Member Size (Constraints)

The minimum member size constraint is mainly used to control the size of members in topology optimal designs. By avoiding thin members enhances the simplicity of the design and hence its manufacturability. Minimum member size is more like quality control than quantity control.

Casting Constraints (Draw Direction Constraints)

Topology optimized designs can contain cavities that are not achievable by casting or some machining processes. The casting constraints allow users to impose die draw direction constraints and prevent hollow profiles so that the die can slide in a given direction.

Extrusion Constraints

It is often desirable to produce a design with a constant cross-section along a given direction. This constraint is particularly essential for a design manufactured through an extrusion process. By using the extrusion manufacturing constraints in topology optimization, constant cross-section designs can be obtained for solid models regardless of the boundary conditions, loads, and finite element mesh.

Symmetry Constraints

It is often desirable to design a symmetric component or system. However, regular topology optimization cannot guarantee a perfect symmetric design, even if the design space, boundary conditions, and loads are symmteric. By using symmetry constraints in topology optimization, a symmtric design can be obtained regardless of the boundary conditions or loads. These symmetric constraints can also be used for irregular finite element meshes.

CASI Iterative Solver

As detailed in the New Iterative Solver Option (Ch. 3) of this Guide, the CASI iterative method can provide a major speedup in the solution of large (>3 million dof) static analyses. This benefit has been extended to topology optimization with compliance responses.

205CHAPTER 7Optimization

Input The TOPVAR Bulk Data entry has been enhanced to provide manufacturing constraints. To select a topologically designable region, the user needs to specify a group of elements by using a Bulk Data entry, TOPVAR. All elements that reference property ID given on a TOPVAR entry are topologically designable. Topology design variables are automatically generated with one design variable per designable element. The manufacturability constraints are then applied on all elements referencing the given property ID.

The basic format for TOPVAR is:

1 2 3 4 5 6 7 8 9 10

TOPVAR ID LABEL PTYPE XINIT XLB DELXV POWER PID

“SYM” CID MSi MSi MSi

“CAST” CID DDi DIE

“EXT: CID EDi

“TDMIN” TV

Field Contents

ID Unique topology design region identification number. (Integer > 0)

LABEL User-supplied name for printing purpose. (Character)

PTYPE Property entry name. Used with PID to identify the elements to be designed. (Character: “PBAR”, “PSHELL”, ‘PSOLID”, etc.)

XINIT Initial value. (Real, XLB < XINIT). Typically, XINIT is defined to match the mass target constraint, so the initial design does not have violated constraints. For example, if the mass target is 30% on DRESP1=FRMASS, then it is recommended XINIT=0.3.

XLB Lower bound to prevent the singularity of the stiffness matrix. (Real; Default = 0.001)

DELXV Fractional change allowed for the design variable during approximate optimization. (Real > 0.0; Default = 0.2. See Remark 3).

POWER A penalty factor used in the relation between topology design variables and element Young’s modulus. (Real > 1.0; Default = 3.0). 2.0 < POWER < 5.0 is recommended.

PID Property entry identifier (Integer > 0)

“SYM” Indicates that this line defines symmetry constraints.

CID Rectangular coordinate system ID used for specifying manufacturing constraints. See Remark 4 (Blank or Integer > 0; Default = 0 = the basic coordinate system)

MSi Mirror symmetry plane. See Remark 5 & 7 (Character, ‘XY’, ‘YZ’, or ‘ZX’)


206

Remarks:1. The topologically designable element properties include PROD, PBAR, PBARL, PBEND,

PBEAM, PBEAML, PSHELL, PSHEAR, PSOLID, and PWELD. Multiple TOPVAR’s are allowed in a single file.

2. All designed element properties must refer to a MAT1 entry; therefore, a PCOMP cannot be used as designed property in topology optimization. PCOMP’s can be used as non-designed properties in a topology optimization job.

3. If DELXV is blank, the default is taken from the specification of DELX parameter on the DOPTPRM entry.

4. Only CORD1R and CORD2R can be used as a referenced coordinate system to specify topology manufacturing constraints. Only one reference coordinate system CID is allowed for each TOPVAR entry.

5. One, two or three different mirror symmetry planes can present (such as MS1=XY, MS2=YZ, and MS3=ZX).

6. Casting (“CAST”) and Extrusion (“EXT”) manufacturability constraints can be applied to PTYPE=”PSOLID” only. Casting constraints cannot be combined with extrusion constraints for the same TOPVAR entry.

7. Some symmetry constraint types can be combined with casting or extrusion constraints. The referenced coordinate system CID must be the same for the combined constraints. Some possible combinations are:

“CAST” Indicates that this line defines casting constraints (i.e., die draw direction constraints). See Remarks 6 and 7.

DDi Draw Direction. DDi=X, Y, Z or X-, Y-, Z- for a single die option (DIE=1) where X-, Y-, Z- indicates the opposite direction of X, Y, and Z respectively. DDi=X, Y, and Z for two die option (DIE =2) (Character)

DIE Die Options. (Blank or integer 1 or 2; Default = 1)

= 1 (or blank). A single die will be used and the die slides in the given draw direction (i.e., material grows from the bottom in the draw direction)

= 2. Two dies will be used and the dies split apart along the draw direction (i.e., material grows from the splitting plane in opposite direction along the axis specified by the draw direction DDi. The splitting plane is determined by optimization)

“EXT” Indicates that this line defines extrusion constraints (i.e., enforce constant cross-section) See Remark 6 and 7.

EDi Extrusion direction. (Character, X, Y, or Z)

“TDMIN” Indicates that this line defines a minimum member size, See Remarks 9 and 10.

TV Minimum member size. See Remark 9. (Real > 0.0)

Field Contents


For “EXT” constraints, possible combinations are (EDi=X, MSi=XY and/or ZX), (EDi=Y, MSi=YZ and/or XY), (EDi=Z, MSi=ZX and/or YZ).

For “CAST” constraints, possible combinations are (DDi=X or -X, MSi=XY and/or ZX), (DDi=Y or -Y, MSi=YZ and/or XY), (DDi=Z or -Z, MSi=ZX and/or YZ).

8. For two dies option (DIE=2), the splitting plane is optimized. For a single die DIE=1, the parting plane is the bottom surface of the designed part in the draw direction.

9. TDMIN is a dimensional quantity with a guideline that it be set to at least three times a representative element dimension.

10. Without a TDMIN continuation line, the minimum member size constraint is taken from the specification of TDMIN parameter on the DOPTPRM entry. This option is applied on 2 and 3 D elements only. Minimum member size constraints can be used with “SYM”, “CAST”, and “EXT” constraints.

Minimum Member Size Parameter TDMIN

TDMIN on Bulk Data entry TOPVAR is allowed users to define an individual minimum member size for each designed property. A parameter TDMIN on the DOPTPRM entry is introduced to allow users to define a minimum member size applied for all TOPVAR entries that do not have the TDMIN continuation line.

Invoking the CASI Iterative Solver

The CASI Iterative Solver is invoked in topology optimization in one of two ways:

1. Specifying SMETHOD=ELEMENT in Case Control for an ANALYSIS=STATICS subcase.

2. Specifying SMETHOD=IID in Case Control for an ANALYSIS=STATICS subcase where IID identifies and ITER Bulk Data entry that can be used to override default options when using the iterative solver.

Guidelines and Limitations• The casting constraints may have difficulty dealing with a design model that has one or more

non-smoothed boundary surfaces to be designed. It is recommended to use smooth top surface in the draw direction for one die casting constraints, and smooth top and bottom surfaces in the draw direction for two die casting constraints.

• MSC.Patran 2005 r2 can smooth, remesh, and generate IGES files for 2D topology designs and smooth 3D topology designs.

Table 7-1 DOPTPRM Design Optimization Parameter: TDMIN

Name Description, Type and Default Value

TDMIN Minimum diameter of members in topology optimization (real >0.0). This option is applied on 2 and 3 D elements only.


208

• MSC.Patran 2005 r3 can support topology optimization with manufacturability constraints.

• The use of the CASI iterative solver for topology optimization is subject to all the limitations listed in Chapter 3 for this capability. In addition, only the compliance response can be invoked at the subcase level. That is, the design task is to minimize the compliance for a specified fractional mass.


Example 1 – MBB Beam Baseline (topex3.dat)An MBB beam example (a half model shown in Figure 7-1) is used to demonstrate basic MD Nastran topology optimization capabilities without manufacturing constraints. The structural compliance is minimized with a mass target 0.5 (i.e., remove 50% of the material). The loading and boundary conditions are shown in Figure 7-1. The structure is modeled with 4800 CQUAD4 elements.

Figure 7-1 MBB Beam

Input

The input data for this example related to topology optimization model is given in Listing 7-1.

Listing 7-1 Input File for Example 1

DESOBJ = 1DESGLB = 1SUBCASE 1$ Subcase name : Default SUBTITLE=Default SPC = 2 LOAD = 2 ANALYSIS = STATICSBEGIN BULKDCONSTR 1 2 .5TOPVAR, 1 , Tshel, Pshell, .5, , , , 1DRESP1 1 COMPL COMP DRESP1 2 FRMASS FRMASS


210

Output

Figure 7-2 shows the topology optimized result that is smoothed and remeshed by using MSC.Patran 2005 r2. It is noticed that there are some small members.

Figure 7-2 MBB Beam Topology Design


Example 2 - MBB Beam with Minimum Member Size (topex3a.dat)The MBB beam (shown in Figure 7-1) is used here to demonstrate the minimum member size capability.

Input

The input data for this example related to topology optimization with “minimum member size” is given in Listing 7-2. The minimum member size value is defined by the parameter TDMIN = 0.5 on the DOPTPRM entry and corresponds to the length of 10 elements.


DESOBJ = 1DESGLB = 1SUBCASE 1$ Subcase name : Default SUBTITLE=Default SPC = 2 LOAD = 2 ANALYSIS = STATICSBEGIN BULKDOPTPRM, TDMIN, 0.5DCONSTR 1 2 .5TOPVAR, 1 , Tshel, Pshell, .5, , , , 1DRESP1 1 COMPL COMP DRESP1 2 FRMASS FRMASS

Output

Figure 7-3 shows the topology optimized result with “minimum member size” TDMIN=0.5. Compared the design shown in Figure 7-2, this design with “minimum member size” is obviously much simpler and there are no tiny members at all.

Figure 7-3 MBB Beam Topology Design with “Minimum Member Size”


212

Example 3 - MBB Beam with Symmetric Constraints (topex3b.dat)Since the loads applied on the MBB beam are not symmtric, the topology optimized designs Figure 7-2 and Figure 7-3 are not symmetric. The MBB beam is employed again to demonstrate the symmetric constraint capability that enforces the design to be symmetric about a given plane.

Input

To apply symmetric constraints on designed properties, users need to create a reference coordinate system using a rectangular coordinate system CORD1R or CORD2R. In this example, grid 10001 (location x=3, y=1, and z=0) is defined as the origin. Grid 10002 (x=3, y=1, and z=1) lies on the z-axis, and grid 1003 (x=4, y=1, and z=0) lies in the x-z plane. CORD1R CID=1 defines a reference coordinate system. A continuation line “SYM” enforces the property PSHELL=1 to be symmetric about the planes YZ and ZX in the reference coordinate system CID=1. In addition, a minimum member size TDMIN=0.15 is applied. The input data for this example is given in Listing 7-3.


DESOBJ = 1DESGLB = 1SUBCASE 1$ Subcase name : Default SUBTITLE=Default SPC = 2 LOAD = 2 ANALYSIS = STATICSBEGIN BULKCORD1R 1 10001 10002 10003GRID 10001 3. 1. 0.0GRID 10002 3. 1. 1.0GRID 10003 4. 1. 0.0TOPVAR, 1 , Tshel, Pshell, , , , , 1 , SYM , 1 , YZ , ZX

, TDMIN, 0.15DRESP1 1 COMPL COMP DRESP1 2 FRMASS FRMASS DCONSTR 1 2 .5

Output

Figure 7-4 shows the topology optimal result with symmetric constraints and minimum member size.


Figure 7-4 MBB Beam with Symmetric Constraints and Minimum Member Size


214

Example 4 - A Torsion Beam with Extrusion Constraints (topex5.dat)A torsion beam is used here to demonstrate the extrusion constraints. The Figure 7-5 shows the FEM model of the torsion beam. A pair of twisting forces is applied on one end while the other end is fixed. 2048 CHEXA elements are used for this model. The objective is to minimize the structural compliance with mass target of 0.3 (i.e., remove 70% material).

Figure 7-5 Torsion Beam

Input

The extrusion constraints enforce a constant cross-section design along the given extrusion direction. The input data related to imposing an extrusion constraint along the z-axis in the basic coordinate system (as the default option) is given in Listing 7-4.


DESOBJ = 1DESGLB = 1SUBCASE 1$ Subcase name : Default SUBTITLE=Default ANALYSIS = STATICS SPC = 2 LOAD = 2


$ Direct Text Input for this SubcaseBEGIN BULKDRESP1 2 Frmass FRMASSDRESP1 1 COMPL COMPDCONSTR 1 2 .3TOPVAR, 1 , TSOLID, PSOLID, .3, , , , 1 , EXT , , ZPSOLID 1 1 0

Output

Figure 7-6 shows the topology optimized result with extrusion constraints. It is obvious that the design has a constant cross-section along the z-axis.

Figure 7-6 Torsion Beam with Extrusion Constraints in Z-Axis


216

Example 5 - A Torsion Beam with One Die Casting Constraints (topex5a.dat)A torsion beam (shown in Figure 7-5) is used here to demonstrate the combination of one die casting manufacturability constraints and symmetric constraints. It also demonstrates the use of the iterative solver.

Input

The casting constraints with one die option enforce the material can only be added to the region by “filling up” in the given draw direction from the bottom (or, stated another way, that voids extend from the top surface and do not reappear in the die direction). To apply casting constraints and symmetric constraints on designed properties, a reference coordinate system CID=1 is defined by using a rectangular coordinate system CORD1R. A “CAST” continuation line defines casting constraints in the Y direction and one die is a default option. Another “SYM” continuation line defines symmetric constraints about the YZ plane. The input data related to the topology optimization model is given in Listing 7-5.


DESOBJ = 1DESGLB = 1SUBCASE 1$ Subcase name : Default SMETHOD=ELEMENT

SUBTITLE=Default ANALYSIS = STATICS SPC = 2 LOAD = 2$ Direct Text Input for this SubcaseBEGIN BULKDRESP1 2 Frmass FRMASSDRESP1 1 COMPL COMPDCONSTR 1 2 .3CORD1R 1 5 167 7PSOLID 1 1 0TOPVAR, 1 , TSOLID, PSOLID, .3, , , , 1

, CAST, 1 , Y, SYM, 1 , YZ

PSOLID 1 1 0

Output

Figure 7-7 shows the topology optimized result with one die casting constraints. It is observed that the design material is added by “filling up” in the Y direction from the bottom. In addition, the design is symmetric about the YZ plane in the reference coordinate system CID=1.


Figure 7-7 Torsion Beam with One Die Casting Constraints in Y Direction


218

Example 6 - A Torsion Beam with Two Die Casting Constraints (topex5b.dat)A torsion beam (shown in Figure 7-5) is also used here to demonstrate two die casting manufacturability constraints.

Input

The input for two die casting constraints is similar to the one die option in Example 5. Here, the difference is that 2 are selected for the DIE field on the TOPVAR entry. The input data related to imposing two die casting constraints is given in Listing 7-6.


DESOBJ = 1DESGLB = 1SUBCASE 1$ Subcase name : Default SUBTITLE=Default ANALYSIS = STATICS SPC = 2 LOAD = 2$ Direct Text Input for this SubcaseBEGIN BULKDRESP1 2 Frmass FRMASSDRESP1 1 COMPL COMPDCONSTR 1 2 .3CORD1R 1 5 167 7PSOLID 1 1 0TOPVAR, 1 , TSOLID, PSOLID, .3 , , , , 1

, CAST, 1 , Y, 2, SYM , 1 , YZ

PSOLID 1 1 0

Output

Figure 7-8 shows the topology optimized result with two die casting constraints. It is observed that the design material grows from the splitting plane in opposite directions along the y-axis specified in the reference coordinate system CID=1. The splitting plane is determined by optimization and in this case corresponds to the


Figure 7-8 Torsion Beam with Two Die Casting Constraints in Y-Axis


220

Revised Optimizer Options

IntroductionMD Nastran 2006 has made MSCADS the default optimizer for the Design Optimization in Solution 200. This provides MSC with greater flexibility in maintaining and enhancing the optimization algorithm relative to the DOT optimizer that is licensed from Vanderplaats Research & Development, Inc. (VR&D) and has been the mainstay algorithm for many years. DOT is still available as an option that requires explicit selection by the user. MSCADS is MSC.Software’s version of the ADS (Automated Design Synthesis) code, a public domain FORTRAN program developed by Dr. G. N. Vanderplaats while he was on the faculty of the Naval Postgraduate School under a contract from the Navy and NASA/Langley. Dr. Srinivas Kodiyalam provided MSC.Software with his enhanced version of the ADS source code at no cost.

The topology optimization of the previous section typically involves thousands of design variables (the simple MBB beam, for example, has 4800 independently designed elements). The MSCADS and DOT optimizers are intended for problems with much fewer design variables, with 3-4000 considered a practical upper limit. For this reason, MSC recommends that serious users of the topology optimization capability consider acquiring the Topology Optimization option, which contains the BIGDOT optimizer, also from VR&D. This code has been shown to be capable of handling tens of thousands of design variables while considering numerous constraints. At the same time, it must be stated that it is not strictly necessary to acquire the Topology Optimization option in order to apply topology optimization. A preliminary assessment of this capability on limited sized problems can be made using only the Design Optimization option. It is necessary in this case to explicitly select the MSCADS or DOT optimizer as outlined in the Input subsection below, in this case since the default when there are TOPVAR Bulk Data entries is to use BIGDOT.

BenefitsThe MSCADS optimizer provides numerous options for performing design optimization that can be explored. The BIGDOT optimizer not only enables performing practical topology optimization tasks but can also be used to perform standard shape and sizing optimization for design tasks with many thousands of design variables. This latter capability requires that both the Topology Optimization and the Design Optimization options be available.

InputThere are two ways to select the optimizer code. One way is by modifying an executive system parameter OPTCOD in the Runtime Configuration (RC) file as shown in Table 7-2.


The second way is by a new parameter OPTCOD added to the DOPTPRM Bulk Data entry that has options shown in Table 7-3. The parameter METHOD is used to select optimization methods.

Table 7-2 System Cell Summary

System Cell Number

System Cell Name Description and Default Value

413 OPTCOD Specifies which optimization code to be used

in SOL 200 (Default = 0)

0 – MSCADS (Design Optimization Option) and BIGDOT (Topology Optimization Option)

1 – DOT Optimizer

2 – BIGDOT Optimizer

Table 7-3 DOPTPRM Design Optimization Parameters

Name Description, Type, and Default Values

OPTCOD OPTCOD (Character; Default= Blank)

= Blank (taken from system cell number 413)

= "MSCADS" : MSCADS is used

= "DOT" : DOT is used

= "BIGDOT" : BIGDOT is used

METHOD Optimization Method: (Integer > 0; Default = 1)

= 1 Modified Method of Feasible Directions for both MSCADS and DOT

= 2 Sequential Linear Programming for both MSCADS and DOT

= 3 Sequential Quadratic Programming for both MSCADS and DOT

= 4 SUMT method for MSCADS

= IJK for user's specified MSCADS optimization strategy.


222

OutputThere are no outputs that are affected by optimizer selection with the exception that the optimizer output produced using the IPRINT parameter on the DOPTPRM entry is dependent on the method selected. In particular, the banner for the MSCADS code appears as:

M S C . A D S

E N H A N C E D A D S P R O G R A M

F O R

A U T O M A T E D D E S I G N S Y N T H E S I S

Guidelines and LimitationsThe optimization results from MSCADS are expected to be comparable to those from DOT. If this is not the case, the OPTCOD parameter can be used to invoke the DOT optimizer.

It is recommended that the Topology Optimization option be utilized for topology optimization and for sizing and shape optimization problems with thousands of design variables.

Sizing and shape cannot be combined with topology optimization in a single run.


Supporting Trust Region in SOL 200 for Adaptive Move Limits

IntroductionFormal approximate optimization is used in SOL 200 to find a new design without performing expensive and exact finite element analyses (Ref. 1, Chapter 2.7). However, move limits must be applied to define a restricted region on which an adequate approximate model can be created.

Convergence checks are made following each approximate optimization task. Currently, if the approximate optimization comes up with a design that an exact analysis shows is actually worse, it is assumed that the region defined by move limits are too generous and they are reduced. Using Trust Region Concepts, this simple update strategy can be improved in three fundamental ways:

1. A merit function is applied to provide a more quantitative measure of the quality of the approximation.

2. A provision is made to increase the move limits when the approximate optimization results are shown to be of high quality.

3. If the new design is judged to actually be worse, it is discarded and the approximate optimization task is performed again with tighter move limits.

BenefitsSince the move limits can be either reduced or increased in an adaptive fashion, it is expected that the quality of the approximate model will be enhanced. This should lead to more robust optimization result and faster convergence. In addition, rejecting a bad design should also smooth the design optimization process.

Theory

Concept of Trust Region

The main idea behind the Trust Region is to first compute a merit function that is a combination of the objective function and the maximum violated constraint value and then form a ratio of the exact reduction in a merit function to the predicted reduction in the merit function. The ratio can be written as follows, assuming a design task is a constrained minimization optimization task:

RatioMFp MFc–

MFp MFa–------------------------------=


224

where:

Notice that a merit function is the sum of objective and the product of penalty weight and the

maximum violated constraint . Subscripts c, p and a, indicate that the function is evaluated exactly at the current design cycle, evaluated exactly at the previous design cycle and evaluated approximately, respectively. The penalty weight plays an important role in a successful optimization task with Trust Region Method.

The magnitude of Ratio varies in the real interval of . The denominator is the predicted reduction in merit function while the numerator is the exact reduction in merit function. Since we consider the case of minimizing the objective, the denominator should always produce a positive number to indicate that the optimizer has done a good job.

Different Ratio values can measure the quality of the approximate model. For example, a negative Ratio (likely due to negative numerator) indicates that the approximate model is so bad that the exact merit function is greater than the previous exact. Thus reducing move limits is necessary. On the other hand, Ratio = 1 indicates the approximate model is very good that the predicted reduction is identical to the exact reduction and the move limits can be increased. In general, the following strategies are used to update move limits if:

1. Ratio < (say 0.01), reject the design, cut the move limits in half and repeat the approximate optimization task. For a minimization task, the reduction in the merit function must be greater than zero. A too small or negative Ratio indicates that the new design proposed by the approximate model either does not reduce the merit function, or the quality of the approximate model is very poor.

2. < Ratio < (say 0.25), accept the design, but cut the move limits in half for the next approximate design task. The ratio in this range indicates that quality of the approximate model is not good enough, or the current move limit is still too large.

3. < RATIO < (say 0.75), accept the design and do not adjust the move limits.

4. Ratio > , accept the design, but increase the move limits by 50%, up to a pre-specified upper value. The ratio approaching to 1 indicates that the approximate model I is accurately predicting the actual behavior. Therefore, the current move limits can be increased. In addition, although Ratio > 1 indicates that the approximate model is not particularly accurate, but it predicts in the right direction so that larger move limits can also be used.

Creating the Constrained Merit Function

For the unconstrained minimization tasks, the merit function is simply the objective. For constrained minimization tasks, the second term on the right hand side of the merit function accounts for violated constraints. Since Ratio is computed using three merit functions, according to Ref. 2, the approximate

The current exact merit function

The previous exact merit function

The approximate merit function.

MFc Φc= PW maxgc⋅+

MFp Φp= PW+ maxgp⋅MFa Φa= PW+ maxgc⋅

Φ( )g( )

∞ ∞,–( )

η1

η1 η2

η2 η3

η3


optimization problem should also be solved in the same fashion to minimize the merit function that is

formed by the objective and the corresponding 2nd term. A capability to transform an approximate optimization task to a feasible design was implemented and can be readily used here to satisfy this consistency requirement. Notice that the algorithm of Ref. 3 computes the penalty weight,

, where is the starting objective at the beginning of the approximate optimization job,

while here PW is obtained with a single number (See Penalty Weight Section).

Penalty Weight

Penalty Weight (PW) is used to form the merit function. The penalty weight plays an important role in a successful optimization task with Trust Region Method. It is problem dependent. The larger it becomes, the more the maximum violated constraint is penalized. There are two ways to define PW: automatic and user specified. For the automatic way, PW = 10 * the initial objective from the initial design cycle. This is the default option. Alternatively, the user can provide his own through a Bulk Data Parameter, MXLAGM1 (See Input Section). Then, PW = 10.* MXLAGM1.

Rejecting a Design

If Ratio < , the current design will be rejected. When the flag is set, the subsequent design sensitivity

phase will be skipped and the approximate optimization job will be performed based on the previous good design with reduced move limits.

Input

New Parameters added to the DOPTPRM entry

TREGION Flag to invoke Trust Region method.

= 0 (Default) Don’t employ trust regions

= 1 turn Trust Region on

ETA1 ( ) the cutting ratio 1 (Default = 0.01), used by Trust Region Method.



UPDFAC1 Updating Factor 1 (Default = 2.0), used by Trust Region Method.

UPDFAC2 Updating factor 2 (Default = 0.5), used by Trust Region Method.

DPMAX Maximum fraction of change on designed property (Default = 0.5) , used by Trust Region Method.

DXMAX Maximum fraction of change on design variable (Default = 1.0), used by Trust Region Method.

PW Penal= Φo⋅ Φo

η1

η1

η2

η3


226

Bulk Data Parameter

PARAM,MXLAGM1,VALUE - Control parameter for Penalty Weight (Real, Default = 0.0).

Outputs

Special Printout from DOM12

If Trust Region method is invoked, DOM12 prints out additional information message as shown below. This message is printed out once every design cycle. The left column is design cycle number. It prints out Objective, Maximum violated constraint and merit function for exact current, exact previous and approximate. It further prints out Ratio together with numerator, denominator. It also prints out the final Update factor for move limits plus the rejecting status. Finally, it prints out current move limits for property and design variable ply penalty weight.

Marker Indicating a Rejected Design in Design History

A rejected design will be marked by adding symbol ‘R’ to the design cycle number shown in the Summary of Design Cycle History at the end of f06 file. Below is an example that shows design cycle 2 has been marked with ‘R’. This is because although this design produces a smaller objective but with the violated constraint. So the design is rejected. Design cycle 1 is used as the next starting design point.

DCYCL OBJECTIVE MAX-CONS MERIT-FUN NUMER DENOM RATIO UPFAC REJ-FLAG TTTT

2 PREV 6.893711E+00 2.133793E+01 1.477869E+03 5.0832E+02 5.0839E+02 9.9987E-01 2.0000E+00 0 TTTT CURR 9.935308E+00 1.392006E+01 9.695438E+02 TTTT

APPX 9.935904E+00 1.391907E+01 9.694761E+02 TTTT MOVEP,MOVP-MIN = 5.000000E-01 1.000000E-02 TTTT

MOVEX,MOVX-MIN = 1.000000E+00 5.000000E-02 TTTT

NDOFs(NDV-NACS)= 0 TTTT PENAL WEIGHT = 0.6894E+02 TTTT

*************************************************************** 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 16 NUMBER OF OPTIMIZATIONS W.R.T. APPROXIMATE MODELS 15

OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY --------------------------------------------------------------------------------------------------------------- OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT ---------------------------------------------------------------------------------------------------------------

INITIAL 6.614414E+02 1.102773E-01

1 5.987441E+02 5.987546E+02 -1.743120E-05 -4.438843E-04

2R 5.475672E+02 5.475823E+02 -2.764282E-05 2.106060E+00

3 5.626934E+02 5.627052E+02 -2.104267E-05 -3.308058E-04


Guidelines and Limitations1. All new parameters introduced in the DOPTPRM have their own defaults and are usually

adequate. If you want the optimization job to have more aggressive move limit, you may do so by reduce ETA3 and/or increase DPMAX and DXMAX or increase UPDFAC1. Conversely, you may increase ETA3 and/or reduce DPMAX, DXMAX and/or decrease UPDFAC1.

2. A non-zero MXLAGM1 is used to override the default Penalty Weight (PW). This parameter is problem dependent and may require some iteration to come up a good number. When the need arises to specify one, a general rule is to specify a bigger number (say 100. and larger) for the maximum constraint is grossly violated.

3. In some cases, it is possible that activating Trust Region in SOL 200 may produce less desirable result than a non-Trust Region job.

Examples The example (dtrustr2.dat) is a Stiffened Panel constrained optimization job taken from the testing problem library (d200x7.dat). It tries to minimize a weight response while satisfies stress and displacement constraints. The same job was run with and without Trust Region (TR). The Trust Region is invoked by specifying TREGION=1 on the DOPTPRM entry. In addition, the parameter MXLAGM1 is set to 10.

Figure 7-9 plots the objective history and DELX history with and without TR. The TR job converges at design cycle 15 (notice that plots count initial design cycle as 1 that is actually zero if counted in the f06) while the non-TR job converges at design cycle 27. Both has same final objective function with maximum feasible constraint at the tolerance of GMAX=0.5%. The fast convergence achieved by the TR job may be explained by the DELX history shown at the bottom of Figure 7-9. The non-trust region job uses a constant move limit (e.g., DELX=0.5) while the DELX in the trust region job is adaptively updated: between design cycles 2 and 6, DELX=1.0 and then reduced below 0.5 between design cycles 8 and 14. Finally, Figure 7-10 plots the maximum constraint values with and without TR. Listing 7-7 lists the summary of the design history.


228

Figure 7-9 Objective History of Example 2: Trust Region vs. Non-Trust Region

Figure 7-10 Max. Constraint History of Example 2: Trust Region vs. Non-Trust Region

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0 5 10 15 20 25 30

Design Cycle

Ob

ject

ive

0.00.51.01.52.02.53.03.54.04.55.05.56.0

Fra

ctio

n o

f M

ove

Lim

it

OBJ-TR OBJ-NTR DELX-TR DELX-NTR

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 5 10 15 20 25 30

Design Cycle

Max

imu

m C

on

stra

int

MaxC-TR MaxC-NTR


Listing 7-7 Table Summary of Objective and Maximum Constraints

References1. MSC.Nastran 2004 Design Sensitivity and Optimization User’s Guide, MSC.Software

Corporation, Santa Ana, CA., 2003

2. MSC.Nastran 2005 Release Guide, MSC.Software Corporation, Santa Ana, CA., 2004

3. Prof. L. Lasdon, private communication, Dec. 13, 2004.

INITIAL 5.784520E+00 1.291873E+00 1 8.610938E+00 8.610291E+00 7.509516E-05 6.616151E-01 2 6.194046E+00 6.193711E+00 5.412208E-05 5.258847E-01 3 7.550942E+00 7.550880E+00 8.146334E-06 2.141915E-01 4 7.982732E+00 7.982616E+00 1.451547E-05 9.803727E-02 5 7.912356E+00 7.912348E+00 1.084769E-06 6.846836E-02 6 7.772725E+00 7.772723E+00 1.840425E-07 5.525844E-02 7R 7.562489E+00 7.562516E+00 -3.657057E-06 6.685141E-02 8R 7.575960E+00 7.575985E+00 -3.398793E-06 6.633586E-02 9 7.943342E+00 7.943305E+00 4.622315E-06 1.302273E-02 10R 7.829101E+00 7.829069E+00 4.019795E-06 1.883844E-02 11 7.925030E+00 7.925027E+00 4.211797E-07 9.176641E-03 12 7.889203E+00 7.889194E+00 1.148394E-06 8.753594E-03 13 7.907179E+00 7.907176E+00 3.015218E-07 3.031719E-03 14 7.924466E+00 7.924470E+00 -5.415548E-07 3.125000E-06 15 7.924493E+00 7.924493E+00 0.000000E+00 -1.562500E-07


230

Support of Analysis Model Value Overriding Design Model Value

IntroductionIn SOL 200, when the value of an analysis model property is different from a design model value obtained by the relation defined on a DVxREL1 entry, the design model value overrides the analysis model value. The new PVAL option provides an alternate to allow the analysis model value to take the precedence over the design model value.

BenefitsProvides a flexible way for a sizing optimization job to start with either design model values or analysis model values.

InputThe PVAL option is applicable to three linear design property entries: DVPREL1, DVCREL1 and DVMREL1. To activate this option, specify the character input of “PVAL” on the COEF1 field on a DVPREL1 (DVCREL1, DVMREL1) entry.

OutputNone.

ExampleThe example shows designing a plate thickness. The plate thickness, 2.5, is defined on PSHELL 1 entry. First, the design entries without the PVAL option are given below. In this case, the design model value, 2.0 (the product of the initial design variable value, 1.0 and the coefficient, 2.0 on the DVPREL1 entry) will override the analysis model value. The comparison of analysis model value and design model value printed in the f06 file is shown here:

PSHELL 1 2 2.5DESVAR 1 THICK 1. 0.1 10.DVPREL1 1 PSHELL 1 T

1 2.0


Then, the DVPREL1 entry with the PVAL option is shown here with other two entries being kept the same. In this case, the design model value equals the analysis model property value, 2.5 obtained directly

from the 4th field of PSHELL 1 entry. The similar comparison of analysis model value and design model value is printed in the f06 file.

DVPREL1 1 PSHELL 1 T1 PVAL

Guidelines and Limitations1. The PVAL option only applies to the linear design property entries and is not applicable to

DVxREL2 entries.

2. When the PVAL option is used, only a single design variable can be referenced on a DVxREL1 entry and PVAL is applied to the COEF1 field. If a DVxREL1 entry references more than one design variable with the PVAL option, a user fatal error message will be issued.

----- 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 ------------------------------------------------------------------------------------------------------------------------------------------------------------ PSHELL 1 T 2.500000E+00 2.000000E+00 N/A N/A WARNING

----- 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 ------------------------------------------------------------------------------------------------------------------------------------------------------------ PSHELL 1 T 2.500000E+00 2.500000E+00 N/A N/A NONE


232


Ch. :

8 Miscellaneous Enhancements

Export of Static Loads, 234

Enhanced Participation Factor Results, 237

Total Strain Energy Output for Defined SETs, 249

Model Checkout Procedures - Method to Vary Material Properties, 252


234

Export of Static Loads

Introduction Functionality was added to MD Nastran to facilitate load transfer from one run to the next in three important ways:

1. MD Nastran can use Grid Point Force methodology to extract the load on a user defined free body. This load is output on a PG-like matrix that has an associated NAME, ID and optional label. A BGPDT data block is also produced that contains information on the grids associated with the free-body.

2. MD Nastran can export static loads from a load case defined in the current subcase.

3. MD Nastran can now import a load from a pre-defined database (including, but not limited to, loads produced using the previous steps) to be used in the formation of the load on a structure.

BenefitsThe design of complex structures frequently involves joint development with a system integrator and a number of subcontractors. The development of design loads is typically the task of the system integrator based on an analysis of the entire vehicle. It is then necessary to communicate the loads on the pieces of the structure to various subcontractors. The ability to extract the load on a free body is particularly useful in aeroelasticity, where the load can be a combination of applied, rigid aerodynamic and inertial loadings. The ability to export the statically applied load, or some portion of the load, is felt to be of benefit when it is desired to apply the same loading to different representations of the same structure.

InputThe ability to export a statically applied load is enabled by the new EXPORTLD Case Control command as described in the MD Nastran 2006 Quick Reference Guide. Typically, this is applied at the subcase level, but can be applied above the subcase level as well. In any case, the command results in a unique load vector (qualified by LOADID and LOADNAME) for each subcase. If a subset of grids is provided by identifying a SET Case Control command as part of the EXPORTLD command, only the loads on the grids associated with this grid are exported. A BGPDT (Basic Grid Point Data Table) is output with the load vector to identify the degrees of freedom associated with each of the rows in the vector.

The ability to export a free body load is done through the combination of the new FBODYLD Case Control command and the FBODYLD and FBODYSB Bulk Data entries. The FBODYLD Case Control command is used to point to the FBODYLD Bulk Data (via the NAMEi called out on the case control command) that defines the submodel for which the freebody load will be calculated and stored. The case control command also provides an optional load ID that can be associated with the load. The FBODYLD Bulk Data entry, in turn, points to a FBODYSB Bulk Data entry. The FBODYLD entry provides a label that is intended to identify the loading condition while the FBODYSB entry has a second label that is intended to identify the component. Both labels are optional. The FBODYSB entry identifies the grids

235CHAPTER 8Miscellaneous Enhancements

and elements that make up the free body and provides the ability to exclude certain types of grid point forces in creating the free body load.

The remarks for the EXPORTLD Case Control command indicate how the loads created with an EXPORTLD request can be used in a subsequent run using FMS statements such as:

ASSIGN loads1=’run1.MASTER’DBLOCATE datablk=(EXTLD,EXTBGP) WHERE(LOADNAME=’ALLCASES’), CONVERT(LOADID=LOADID+1000) LOGICAL=loads1…CENDLOADS=1001 $ Select external load with LOADID=1001, imported from previous run.

The EXTLD datablock contains the loads whereas the EXTBGP contains the grid point information that is used to match up the imported loads with the grid points. Clearly, it is necessary that the Grid ID’s have the same meaning in the two runs.

The import of a load created using the FBODYLD Case Control command is similar except it is now necessary to rename the datablocks created in the previous run to match those required for the import of these loads:

ASSIGN loads1=’fbrun1.MASTER’DBLOCATE datablk=(FBLPG/EXTLD,FBLBGPDT/EXTBGP) WHERE(LOADNAME=’fblcase’), CONVERT(LOADID=LOADID+1000) LOGICAL=loads1…CENDLOADS=1001 $ Select external load with LOADID=1001, imported from previous run.

OutputThe new commands produce limited output. The FBODYLD request does produce informational messages from a DBDICT statement that requests output on the presence of all FBLPG and FBLBGPDT data blocks along with qualifiers as to loadid, namei (from case control and the FBODYLD Bulk Data entry), submodel name from the FBODYSB entry and the labels from the two bulk data entries.

Examples (TPL: exptld/imptld, sysmod/fbody, sfsw/ffsw) There are three simple sets of test cases in the text problem library that demonstrate these new features, each with an export import pair. Exptld.dat exports the load applied to the center section of a flat plate while imptld.dat applies this load to a model of only the center section of the plate. In this case, it is not necessary to dblocate the EXBGP datablock because the exported load is perfectly aligned with the reduced model. However, this is not a good practice in general.

Sysmod.dat is a SOL 101 run that creates a free body load on center section of the same small plate model used in the previous example. Note that the applied loads are excluded using an input of “A” on the XFLAG field of the FBODYSB Bulk Data entry. Only the element forces are used to create the load,


236

which is in equilibrium across the cutout. The fbody.dat file imports this load onto a model that is only the center section of the original model. It is necessary to constrain a corner of this “free body” to remove the rigid body motion. An examination of the .f06 results for this run shows that the SPC forces are negligible while the stresses agree well for the elements that are shared between the two models. The displacements do not agree, but this is to be expected because they displacements for the small model are relative to the artificially constrained model.

Sfsw.dat is a SOL 144 run that demonstrates the ability to ask for different free body loads is separate subcases and has multiple FBODYLD/FBODYSB pairs for different components of the familiar forward swept wing. The fuselage subsystem is selected for further analysis in the subsequent run and it is seen the FBODYSB entry with FUSELAGE in the NAMES field has the applied loads excluded using an ‘A’ in the XFLAG field. Ffsw.dat imports this load into a SOL 101 that only has a model of the fuselage and comparison of the results shows that the stresses in the bars that represent the fuselage agree well between the two runs.

Guidelines and LimitationsThe EXPORTLD command has utility in SOL 101. In SOL 144, only the applied loads are output with this command and these are typically zero.

The applied loads are typically excluded when using the FBODYSB Bulk Data entry so that only element forces remain at the grid points.

Import of loads has the following rules

• If a set of imported loads share a common LOADID value, then those loads will implicitly be added. The same holds true for imported loads and bulk data load sets that share a common ID.

• To explicitly combine load sets, the load IDs should be made unique. The LOAD Bulk Data entry can then be used to explicitly define the linear combination.

• Both standard exported loads (EXPORTLD) and free body loads (FBODYLD) can be imported and used together in a single run. It is up to the user to keep the load IDs unique between them.

• The BGPDT is used to link the exported loads to the grids points of the model to which they are applied. This means that the grid id’s for the loaded grids must be the same in the two models.


Enhanced Participation Factor Results

IntroductionNew Case Control commands PFMODE, PFPANEL and PFGRID have been implemented to request modal, panel and grid participation factors. These commands will replace the existing FLSPOUT and MCFRACTION Case Control commands.

A new, consistent output format is used for all types of modal and panel participation factors. This format is similar to the output format obtained with the MCFRACTION command. The output format of grid participation factors is similar to the output format of displacements.

In addition, the new implementation supports

• panel definition by referencing a set of grids, a set of elements or a set of properties.

• panel and grid participation factors in direct frequency response analysis (SOL 108).

Finally, an adjoint method is used to compute acoustic structural modal participation factors, acoustic panel participation factors and acoustic grid participation factors, resulting in significant performance improvements.

Benefits• The new case control commands and the new output formats provide a consistent user interface

to all kinds of participation factors that is easy to use.

• The following example shows significant reductions of computation times and IO when computing panel participation factors:

Problem Data Performance Data

3.3 mio. Structural Degrees of Freedom25000 Fluid Degrees of Freedom1022 Structural Modes45 Fluid Modes85 Subcases

Panel participation factors have been computed for 2 fluid grid points and 9 panels.

WO/Panel Part. W/Panel Part.

Elapsed Time (s) 22020 3960CPU Time (s) 9027 1332IO (GB) 24426 6415

These data refer to the computation of the participation factors only.


238

TheoryIn a linear structural dynamic analysis, the results at a degree of freedom considered are the sum of the contributions of the different modes, e.g., the accelerations at a degree of freedom considered are the sum of the accelerations due to the responses of the different structural modes. These contributions are called structural modal participation factors or modal contribution fractions. The degrees of freedom considered are called response degrees of freedom. Structural modal participation factors allow to identify the structural modes that have the largest influence on the response.

Likewise, in an acoustic analysis, the pressure at a grid point considered is the sum of the pressures due to the responses of the different fluid modes. These contributions are called acoustic fluid modal participation factors. Acoustic fluid modal participation factors allow to identify the fluid modes that have the largest influence on the response.

In a coupled analysis, the pressure at a response degree of freedom is the sum of the pressure due to the acoustic sources in a rigid cavity, and the pressure due to the acceleration of the fluid-structure interface, the so-called wetted surface. The pressure due to the acoustic sources in a rigid cavity is called the load participation factor.

The acceleration of the fluid-structure interface is the sum of the accelerations due to the responses of the different structural modes, obtained from a coupled analysis. These contributions are called acoustic structural modal participation factors. One acoustic structural modal participation factor equals the


pressure at the response degree of freedom if there are no acoustic sources, and if the acceleration of the wetted surface consists of the response of one mode only. Thus, the acoustic structural modal participation factors allow to identify the structural modes that have the largest influence on the pressure at the grid point considered. In the absence of acoustic sources within the cavity, the acoustic structural modal participation factors sum up to the total pressure at the response degree of freedom.

Modal participation factors, by their nature, are useful only in the low-frequency range where the resonance frequencies are well separated, and the response is dominated by a small number of modes. On the contrary, geometric participation factors are useful also at higher frequencies where the response has contributions from a large number of modes. There are two types of geometric participation factors, namely panel participation factors and grid participation factors.

A panel is a set of grid points of the wetted surface. The panel participation factor is that pressure at the grid point considered that results from the accelerations of the grid points of the panel only, with all other grid points of the wetted surface kept fixed. Thus, panel participation factors allow to identify the regions of the wetted surface that have the largest influence on the acoustic pressure at the grid point considered. Panel participation factors usually do not sum up to the total acoustic pressure. This is only the case if the panels do not overlap, and if their union equals the complete wetted surface.

The accelerations of the grid points of the panel are the sum of the accelerations due to the different structural modes. The pressure due to the accelerations at the grid points of the panel that are due to one mode only is called the acoustic panel modal participation factor. Acoustic panel modal participation factors sum up to the panel participation factors.

Finally, if the panels consist of one grid point only, acoustic grid participation factors are obtained. For each structural grid point of the wetted surface, there are six acoustic grid participation factors, i.e. the pressures at the response degree of freedom due to the accelerations of the six degrees of freedom of this grid point. The acoustic grid participation factors depend on the mesh size. Thus, their absolute value has no physical meaning. However, if the mesh of the wetted surface is of comparable size everywhere, the acoustic grid participation factors allow to quickly identify the regions that make the largest contribution to the acoustic pressure at the grid point considered, and thus help to define the panels.

Participation factors are complex quantities, summing up to the complex response. Thus, if they are divided by the response, they sum up to one. The participation factors divided by the response are called normalized participation factors. Normalized participation factors are complex quantities, too.

The real parts of the normalized participation factors sum up to one whereas the imaginary parts sum up to zero. Thus, the real part of a normalized participation factor is that part of the participation factor that is in phase with the total response, divided by the magnitude of the total response. It is called the modal fraction. The phase of a normalized participation factor is the phase of the participation factor relative to the total response.

If the modal fraction is multiplied by the magnitude of the total response, the projected participation factor is obtained. It is that part of the participation factor that is in phase with the total response. The projected participation factors sum up to the total magnitude.


240

InputComputation and output of modal participation factors is controlled by the PFMODE Case Control command:

ExamplesSET 20 = 25/T3, 33/T3PFMODE(STRUCTURE, STRUCTMP=ALL) = 20

Compute structural modal participation factors for z-translations at grid points 25 and 33

SET 20 = 11217SET 90 = 25., 30., 35.PFMODE(FLUID, STRUCTMP=ALL, FLUIDMP=ALL, SOLUTION = 90) = 20

Compute acoustic structural and fluid modal participation factors for pressure at grid point 11217 at excitation frequencies 25Hz, 30Hz and 35Hz.

Computation and output of panel participation factors is controlled by the PFPANEL Case Control command:

PFMODE STRUCTURE

FLUID

PRINT, PUNCH

PLOT

REAL or IMAG

PHASE , , ,

SORT sorttype=[ ] KEY sortitem=[ ] ITEMSALL

itemlist( )

= , , ,

FLUIDMP

ALL

mf

NONE

= STRUCTMP

ALL

ms

NONE

= , ,

PANELMP

ALL

setp

NONE

= SOLUTION

ALL

setf

NONE

= FILTER fratio=[ ], ,

NULL ipower=[ ] )setdof

NONE

=

,


ExampleSET 100 = 10., 12.SET 200 = 1222, 1223PFPANEL(SOLUTION=100, SORT=ABSD) = 200

Compute acoustic panel participation factors for pressure at grid points 1222 and 1223 at excitation frequencies 10Hz and 12Hz. Output is sorted according to descending modal fractions.

Computation and output of grid participation factors is controlled by the PFGRID Case Control command:

ExampleSET 20 = 11217SET 90 = 25., 30., 35.PFGRID(SOLUTION = 90) = 20

Compute acoustic grid participation factors for the pressure at grid point 11217 at excitation frequencies 25Hz, 30Hz and 35Hz.

Detailed descriptions of the PFMODE, PFPANEL and PFGRID Case Control Commands can be found in the Quick Reference Guide.

PFPANEL PRINT, PUNCH

PLOT

REAL or IMAG

PHASEPANEL

ALLsetp-----------

= , , ,

SORT sorttype=[ ] KEY sortitem=[ ] ITEMS ALL

itemlist( )

= , , ,

SOLUTIONALL

setf

NONE

= FILTER fratio=[ ] NULL ipower=[ ], ,

setdof

NONE

=

PFGRID PRINT, PUNCH

PLOT

REAL or IMAG

PHASEGRIDS

ALL

setg

=, ,

SOLUTION

ALL

setf

NONE

=

setdof

NONE

=


242

Panels are defined in the Bulk Data Section using PANEL Bulk Data entries which reference SET1 or SET3 Bulk Data entries.

• SET1 Bulk Data entries list the grid points of the panels.

• SET3 Bulk Data entries with option ELEM list the elements of the panels. The panels consist of all grid points associated to these elements.

• SET3 Bulk Data entries with option PROP list the property identifiers of the elements of the panels. The panels consist of all grid points associated to the elements with the property identifiers defined.

OutputOutput can be printed to the .f06 file, written to the .pch file or the .op2 file or stored in the database for later access by SimOffice.

Three different formats are used for printed output to the .f06 files. The format for modal participation factors is similar to the format obtained with the MCFRACTION command. The header contains the type of the participation factor, information on the grid point and degree of freedom considered, the total response, information on excitation frequency, subcase and load and information on the maximum modal response, the sort method and the filter. In case of acoustic panel modal participation factors, the header contains the name of the panel considered and the panel response instead of the total response.

The data are presented in ten columns:

The format for acoustic panel participation factors is the same as for modal participation factors, except that the first two columns contain the panel names.

Column Label Description

1 Mode Id Mode number

2 Natural Freq (Hz) Resonance frequency

3-4 Modal Response: Real / Imaginary Real and imaginary part of participation factor

5-6 Modal Response: Magnitude / Phase Magnitude and phase of participation factor

7 Projection Magnitude Projected participation factor: That part of the participation factor that is in phase with the total response

8 Relative Phase Phase of participation factor relative to total response

9 Modal Fraction Real part of normalized participation factor

10 Scaled Response Magnitude Projected participation factor divided by largest magnitude of all participation factors


Load participation factors are included in the acoustic structural modal participation factors and the acoustic panel participation factors, with a mode number of 0 and a panel name –LOAD-. Acoustic structural modal participation factors, together with the load participation factor, sum up to the total response.

Acoustic grid participation factors use the output format of complex displacements. Both real and imaginary part or magnitude and phase format are available. There is one output per excitation frequency and fluid grid point.

Example

The numbers printed indicate the normalized acoustic pressure at the selected grid point due to the accelerations at the corresponding degrees of freedom.

GuidelinesThe amount of output produced may be very large. This is especially true for acoustic panel mode participation factors and for acoustic grid participation factor (e.g., the number of data produced for acoustic panel modal participation factors equals the number of subcases times the number of excitation frequencies times the number of response degrees of freedom times the number of panels times the number of structural modes). Consequently, output should be limited to a small number of excitation frequencies and to a small number of response degrees of freedom.


244

LimitationsIn the current version, acoustic participation factors are not computed correctly in case of direct enforced motion.

ExampleThe example shows the acoustic analysis of a cabin. The cabin is excited by four forces at the corners of the seat. The result of interest is the pressure at the driver’s ear.

The frequency response of the pressure shows a peak at 37Hz. To investigate this peak, acoustic fluid and structure modal participation factors and panel participation factors are requested at a frequency of 37Hz.

Panels are defined for the front window, the rear wall, the left and the right side, the top and the bottom.

Input Data

$ Participation Factor Test Problem: Cabin$$ Coupled Modal Frequency Response Analysis$$ Participation Factor Example - Cabin


$$ Illustrates use of$ o Acoustic Fluid Modal Participation Factors$ o Acoustic Struct. Modal Part. Factors$ o Acoustic Panel Part. Factors$ o Acoustic Grid Part. Factors $$ =======================================================$SOL 111 DIAG 8 CEND$ECHO=SORT(EXCEPT,CBEAM,CQUAD4,CHEXA,CPENTA,GRID)AUTOSPC(NOZERO) = YES$METHOD(STRUCTURE)=1 METHOD(FLUID) =2 $FREQ = 100DLOAD = 200 $SET 1 = 11217 SET 20 = 11217SET 90 = 37.$


246

DISP(PHAS) = 1$PFMODE(FLUID, STRUCTMP=ALL, FLUIDMP=ALL, SOLUTION=90, SORT=ABSD) = 20PFPANEL(SOLUTION=90, SORT=ABSD) = 20$OUTPUT(XYPLOT) XPAPER=29. YPAPER=21. XGRID=YES YGRID=YES XTITLE = Frequency YTITLE = Pressure XYPLOT DISP RESPONSE / 11217(T1)$BEGIN BULK$$ Request OP2 for PATRANPARAM, POST, -1 $$ Define Structural DampingPARAM, G, 0.02 $$ Define Fluid DampingPARAM, GFL, 0.002 $$ Define Reference Pressure for dB (in Pa)PARAM, PREFDB, 2.8284-5 $PARAM, GRDPNT, 0 $ Request Weight Output$$ Structural and Acoustic Modes up to 300HzEIGRL, 1,,300. EIGRL, 2,,300. $$ Frequency Range: 25Hz to 100Hz by Steps of 5HzFREQ1, 100, 25., 5., 15$ Additional Frequencies around Resonance FrequenciesFREQ4, 100, 25., 100., 0.01, 5$$ Excitation ForcesRLOAD1, 200, 210,,, 220DAREA, 210, 1, 3, 1., 7, 3, 1.DAREA, 210, 29, 3, 1., 35, 3, 1.TABLED1, 220 , 0., 1., 1000., 1., ENDT$$ Nonmatching Fluid-Structure InterfaceACMODL, DIFF $$ Include Structural and Acoustic ModelINCLUDE 'cabin_structure.bdf'INCLUDE 'cabin_fluid.bdf'$


$ Panels$SET3, 101, ELEM, 127, THRU, 162, 667, THRU, 738SET3, 201, ELEM, 37, THRU, 72, 739, THRU, 810SET3, 301, ELEM, 331, THRU, 384SET3, 401, ELEM, 25, THRU, 36, 73, THRU, 126SET3, 501, ELEM, 271, THRU, 294, 601, THRU, 612SET3, 601, ELEM, 1, THRU, 24, 455, THRU, 478, , 497, THRU, 562$PANEL, LEFT, 101, RIGHT , 201, FRONT, 301, REAR, 401PANEL, TOP , 501, BOTTOM, 601$ENDDATA

Acoustic Structural Mode Participation Factors:


248

Acoustic Panel Participation Factors:

The acoustic structural mode participation factors show that the largest contribution comes from the 7th structural mode which has a resonance at 37.2Hz. The acoustic panel participation factors show that the rear wall and the bottom make the largest positive contribution whereas all remaining panels make negative contributions.


Total Strain Energy Output for Defined SETs

IntroductionTotal Strain Energy output can now be requested for user defined element SETs.

InputsA new Case Control command, SETP described below is introduced for defining the list of element SETs, which are referenced by the ESE – Element Strain Energy Output request.

Process Sets are used to define lists of SET identifications to be processed individually for data recovery:

FormatsSETP n = i1[,i2,i3 THRU i4 EXCEPT i5,i6,i7,i8 THRU i9]

ExamplesSET 77=5SET 88=5, 6, 7, 8, 9, 10 THRU 55

Remarks:1. A SETP command may be more than one physical command. A comma at the end of a physical

command signifies a continuation command. Commas may not end a set. THRU may not be used for continuation. Place a number after the THRU.

2. Set identification numbers following EXCEPT within the range of the THRU must be in ascending order.

SETP Process Set Definition

Describer Meaning

n SETP identification number. Any SETP may be redefined by reassigning its identification number. SETPs specified under a SUBCASE command are recognized for that SUBCASE only. (Integer > 0)

SET Identification numbers. If no such identification number exists, the request is ignored. (Integer > 0)

EXCEPT Set identification numbers following EXCEPT will be deleted from output list as long as they are in the range of the set defined by the immediately preceding THRU. An EXCEPT list may not include a THRU list or ALL.


250

In SET 88 above, the numbers 77, 78, etc., are included in the set because they are outside the prior THRU range.

3. SETP usage is limited to the EDE, EKE, and ESE Case Control Commands.

ExampleA small example (see setp01.dat in the examples folder) is shown below to show usage of the SETP command. Note only essential entries are shown.

id msc, setp $ TIME 6SOL 101CENDSPC=1setp 100 = 1 thru 43set 1 = 1set 2 = 2set 3 = 3set 4 = 4set 5 = 5set 6 = 6set 7 = 7set 8 = 8set 9 = 9..SUBCASE 1001LOAD=101ese = 100SUBCASE 1002LOAD=102ese = 100BEGIN BULKCQUAD4 1 1 1 2 9 8 CQUAD4 2 1 2 3 10 9 CQUAD4 3 1 3 4 11 10 CQUAD4 4 1 4 5 12 11 CQUAD4 5 1 5 6 13 12 CQUAD4 6 1 6 7 14 13 CQUAD4 7 1 8 9 16 15 CQUAD4 8 1 9 10 17 16 CQUAD4 9 1 10 11 18 17 ..ENDDATA


Output Example

An excerpt of the element strain energy output for the example is shown below:0 SUBCASE 1001 E L E M E N T S T R A I N E N E R G I E S ELEMENT-TYPE = QUAD4 * TOTAL ENERGY OF ALL ELEMENTS IN PROBLEM = 4.593646E+00 SUBCASE 1001 * TOTAL ENERGY OF ALL ELEMENTS IN SET 1 = 2.973878E-030 ELEMENT-ID STRAIN-ENERGY PERCENT OF TOTAL STRAIN-ENERGY-DENSITY 1 2.973878E-03 0.0647 1.631036E+00

TYPE = QUAD4 SUBTOTAL 2.973878E-03 0.0647 0 SUBCASE 1001 E L E M E N T S T R A I N E N E R G I E S ELEMENT-TYPE = QUAD4 * TOTAL ENERGY OF ALL ELEMENTS IN PROBLEM = 4.593646E+00 SUBCASE 1001 * TOTAL ENERGY OF ALL ELEMENTS IN SET 2 = 1.778719E-030 ELEMENT-ID STRAIN-ENERGY PERCENT OF TOTAL STRAIN-ENERGY-DENSITY 2 1.778719E-03 0.0387 5.811762E-01

TYPE = QUAD4 SUBTOTAL 1.778719E-03 0.0387


252

Model Checkout Procedures - Method to Vary Material Properties

IntroductionA new feature has been introduced that provides users with a simple means to evaluate the mass and thermal load characteristics of a structure. The feature is intended primarily for linear static analysis runs that are being used to validate aspects of the finite element model prior to embarking on more expensive production static and dynamics analyses. It allows the user to temporarily modify the material density and thermal expansion coefficient fields of material property bulk data entries. To implement the feature, the new MODEL_CHECK Executive Control statement and several NASTRAN Statement keywords have been introduced. Use of the feature causes the affected material property fields to be temporarily modified during the run. All results will be based on the temporary values of the material properties. The material property data stored on the Material Property Table data block is not modified and retains the original values supplied on the bulk data entries.

BenefitsThe introduction of this new feature simplifies the procedure typically used to evaluate the mass and thermal load characteristics of a finite element model. This procedure usually involves preparation, usage and storage of a duplicate set of bulk data material property entries that have the material density and thermal expansion coefficient values set to the values desired for model checkout purposes. When the model is undergoing checkout procedures, the production set of bulk data material property entries is replaced by the alternate set of bulk data material property entries. Creating and switching between the two sets of data for production and checkout runs is tedious and prone to errors. The material property update options of the MODEL_CHECK statement improve user productivity by reducing the need to create, maintain and substitute different sets of material properties needed for model check purposes.

Method and TheoryThere is no additional theory introduced by this feature. Finite element matrix generation and stress recovery operations use material properties in exactly the same manner as without this feature. The only difference is the actual value of the material property itself. The method is equally simple. As material property data is referenced, a check is made to see whether MODEL_CHECK is active for temporary material property updates. If it is, the appropriate entry of the material property data (mass density and/or thermal expansion coefficient(s)) is set to the user-specified value. All subsequent computations use the updated value.

InputsThis feature is activated using the new MODEL_CHECK Executive Control statement. The MODEL_CHECK statement features keywords that allow a value to be temporarily assigned to the


material density and thermal expansion coefficients. The general format of the statement used to change material properties to a specified value is:

MODEL_CHECK [ MAT_DENSITY=value, ] [ MAT_TECO=value, ] [ MAT_TEIJ=value ]

The complete description of the MODEL_CHECK statement can be found in Executive Control Statement Descriptions (p. 108) in the MD Nastran Quick Reference Guide.

OutputsThe MODEL_CHECK material property update feature produces no printed output other than an informational message summarizing the updates that will take place.

Guidelines and Limitations• MODEL_CHECK is ignored in RESTARTs

• Material property updates will take effect for all MAT1, MAT2, MAT3, MAT8 and MAT9 Bulk Data entries present in the input.

• Material properties stored on the Material Property Table (MPT) data block are those present on the bulk data material property entries.

• Post-processing of results could reference in-consistent data since the results are based upon different material property data than is present in the bulk data.

Demonstration ExampleA simple example is presented that demonstrates the material property update feature. The example consists of several disjoint models and is not intended to be representative of any production model. The MODEL_CHECK statement is used to temporarily set all material densities and thermal expansion coefficients to 0.0. This results in model mass contributions from only the CONM2 element and the non-structural mass as well as results for the temperature load case (subcase 3) being null.

Example Input Data$$***********************************************************************$$VERSION: 2004+$TEST DECK NAME: varmat01a.dat (Baseline Model w/MODEL_CHECK)$ Density is not temperature dependent.$ Thermal expansion coefficient is not temp. dependent$ MODEL_CHECK command present.$$PURPOSE:$ Demonstrate usage of the new MODEL_CHECK Executive Control Statement$ Note that non-structural mass cannot be modified using this command.$$DESCRIPTION:


254

$ The model consists of$ 1) CONM2 eid 3001 contributing mass.$ 2) ROD eid 101 referencing MAT1 materials$ 3) QUAD4 eid 3301 w/ PSHELL referencing MAT1 materials$ 4) QUAD4 eid 3313 w/ PSHELL referencing MAT1 and MAT2 materials$ 5) QUAD4 eid 3321 w/ PCOMP referencing MAT8 materials$ 6) HEXA eid 6701 w/ PSOLID referencing MAT9 materials$ 7) TRIAX6 id 5301 referencing MAT3 materials$$ A MODEL_CHECK executive command is used to modify material property$ data temporarily during the run. The command demonstrates$ 1) setting the material density to 0.0 via the OFF option$ 2) setting the material thermal expansion coefficients to 0.0 via$ the OFF option$ 3) continuation of MODEL_CHECK command$$EXPECTED RESULTS:$ 1) There should be an informational message indicating which of the$ material property data is being modified.$ 2) The grid point weight generator and element summary outputs should$ indicate mass for only the conm2 element and the non-structural$ masses of the rods and plates$ 3) results output for subcase 3 (temperature loading) should be 0.0$ since MODEL_CHECK is setting the alphas=0.0$ID MSC, varmatTIME 30 $SOL 101$$========================================================================$ temporarily set the density and thermal expansion coefficients for all$ materials to 0.0$model_check mat_density=off, mat_tecoeff=off,mat_teij=off$$========================================================================$CENDTITLE= VARIABLE MATERIAL TEST CASESUBTITLE = MSC V2005ECHO = SORTSPC = 12TEMP(MATE) = 1 SET 10002= 1 THRU 13999, 14399 THRU 16900 DISP=ALL ELFORCE=ALL OLOAD = ALL$ SPCF=ALL ESE=10002 SEFINAL=1 GPFO=10002$ELSUM(EID,PRINT) = ALL$SUBCASE 1LABEL = STATIC LOAD LOAD = 1 P2G=MATLOAD K2GG=MATK


SUBCASE 3LABEL = TURN ON TEMP LOADS TEMP(LOAD) = 2$BEGIN BULK$$ C O M M O N D A T A T O A L L P R O B L E M SPARAM, SNORM, 0.$CORD2C 1 0 3.0 -1.0 0.0 9.0 -1.0 0.0 +CORD2C+CORD2C 9.0 0.0 -1.0$CORD2R 2 0 0.0 -2.0 0.0 1.011234-2.0 0.0 +CORD2R+CORD2R 0.0 0.0 0.0$CORD2S 3 1 3.0 225.0 0.0 3.0 225.0 1.234567+CORD2S+CORD2S 3.0 -45.0 3.0$GRAV 3 1.0 1.0 1.0 1.0TEMPD 1 100.0TEMPD 2 200.0$MAT1 1 1. .8 .1 .05 .001 100. .01 +MAT11+MAT11 2.0 3.0 4.0MATT1 1 2 +MATT1+MATT1 4 5 6$MAT1 2 1.0E+7 0.3 .05 .001 100.0 .01 +MAT1-2+MAT1-2 1000. 2000. 3000.MATT1 2 +MATT1-2+MATT1-2 2 2$MAT2 22 1.0E+7 0.5E+6 0.5E+6 1.0E+7 0.5E+6 1.0E+7 .022 +MAT221+MAT221 .01 .02 .025 100.0 0.035MATT2 22 +MATT221+MATT221$MAT3 33 1.0E+7 1.0E+7 1.0E+7 .33 .33 .33 .00259 +MAT331+MAT331 2.4E+6 .001 .001 .001 100. .025MATT3 33 +MATT331+MATT331 $MAT8 3 1.E+7 1.E+7 .25 4.E+6 4.E+6 4.E+6 1.0 +MAT81+MAT81 1.-6 2.-6 1.E-4 1.E-3 1.E-4 +MAT82+MAT82 1.0$MAT9 9 1.E+7 1.E+7 +MAT91+MAT91 1.E+7 +MAT92+MAT92 5.1+3 5.1+3 5.1+3 .05 .001 +MAT93+MAT93 .002 .003 .004 .005 .006 100.0 .008MATT9 9 +MATT91+MATT91 +MATT92+MATT92 +MATT93+MATT93$TABLEM1 2 +TABLE-2+TABLE-2 0.0 1.0 150.0 1.0 150. 0.5 300. 0.5 +TABL-2+TABL-2 ENDT ENDTTABLEM2 3 100.0 +TABLE-3+TABLE-3 0.0 0.1 50.0 0.1 50.0 0.5 150.0 0.5 +TABL-3


256

+TABL-3 200.0 10.0 ENDTTABLEM3 4 100.0 2.0 +TABLE-4+TABLE-4 0.0 0.1 25.0 .1 25.0 2.0 75.0 2.0 +TABL-4+TABL-4 300.0 .00001 ENDTTABLEM4 5 100.0 100. 2.0 10.00 +TABLE-5+TABLE-5 2.0 ENDTTABLEM4 6 0.0 100. 0.0 100.00 +TABLE-6+TABLE-6 1.0 .25 ENDTTABLEM1 91 +TAB912+TAB911 0.0 0.01 150.0 0.05 150. 0.1 300. 0.2 +TAB912+TAB912 ENDTTABLEM1 92 +TAB921+TAB921 0.0 0.001 150.0 0.002 150. 0.003 300. 0.006 +TAB922+TAB922 ENDTTABLEM1 93 +TAB931+TAB931 0.0 1.0 150.0 1.0 150. 0.08 300. 0.1 +TAB932+TAB932 ENDT$PARAM, GRDPNT 0PARAM, NT 1PARAM, TINY 0.PARAM, AUTOSPC,YESPARAM, COMPARE,1 $ PROCESS SELECTED S.E., THEN ENTIRE MODEL, DMAP0PARAM, PNCHDB, 1 $ PUNCH FROM DATA BASE, DMAP0PARAM, NOELOP, 1 $ SUM OF FORCES. MG 21 OCT 1980$PARAM, NOGPF, -1 $ SUPPRESS GPFO OUTPUT. LOOK AT ELOP INSTEAD. MG$$ SPCS TO BE SELECTED FOR RF 1 THRU 12SPCADD 12 1 2$ SPCS TO BE SELECTED FOR RF 51,53 AND 59SPCADD 13 1 3$FREQ1 10 0.0 1.0 1RLOAD2 11 12 14TABLED1 14 +TABD4.1+TABD4.1-1.0 1.0001 2.0 1.0001 ENDT$$ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++$$ ROD ELEMENT NO. 1$CROD 101 101 101 102GRID 101 0 0.0 0.0 0.0GRID 102 0 1.0 0.0 0.0SPC1 1 123456 101SPC1 1 2356 102FORCE1 1 102 1.0 101 102MOMENT1 1 102 1.0 101 102DAREA 12 102 1 1.0 102 4 1.0PROD 101 1 1.0 2.0 0.1 0.5$$$+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++$$ QUAD4 ELEMENT NO. 33$CQUAD4 3301 3301 3301 3302 3303 3304 0.


GRID 3301 0 0.0 0.0 0.0GRID 3302 0 1.0 0.0 0.0GRID 3303 0 1.0 1.0 0.0GRID 3304 0 0.0 1.0 0.0SPC1 1 1256 3302 3303SPC1 1 123456 3301 3304FORCE 1 3302 0 1.0 0.0 0.0 1.0FORCE 1 3303 0 1.0 0.0 0.0 1.0DAREA 12 3302 3 1.0 3303 3 1.0PSHELL 3301 1 1.0 1 120.0 1 1.0 0.5 +QUAD41+QUAD41 0.2 -0.3$CQUAD4 3313 3313 3313 3314 3315 3316 382.5 +QUAD42+QUAD42 .63 .67 .53GRID 3313 3 3.0 90. 0. 3 123456GRID 3314 3 3.0 90. 60. 2 123456GRID 3315 3 3.0 40. 60. 1 4GRID 3316 3 3.0 30. 0. 0 5FORCE 1 3315 2 3.14159 0. 2.71828 0.DAREA 12 3315 3 1.73205PSHELL 3313 22 .618034 2 1 .30103 +QUAD43+QUAD43 0.$$ COMPOSITE TESTING , WITH STRAIN THEORY, ADDED 17JUN87, LNACQUAD4 3321 3321 3321 3322 3323 3324 0.GRID 3321 0 0.0 0.0 0.0 13456GRID 3322 0 10.0 0.0 6GRID 3323 0 10.0 10.0 0.0 6GRID 3324 0 0.0 10.0 0.0 123456FORCE 1 3322 0 1.+3 1.0 0.0 1.0FORCE 1 3323 0 1.+3 1.0 0.0 1.0DAREA 12 3322 3 1.0 3323 3 1.0PCOMP 3321 1. STRN +QUAD4C+QUAD4C 3 0.5 0. YES 3 0.5 0. YES$$+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++$$ HEXA ELEMENT NO.67$$CHEXA 6701 6701 6701 6702 6703 6704 6705 6706 +C6701+C6701 6707 6708GRID 6701 0 0.0 0.0 0. 0 456GRID 6702 0 0.0 .08 0. 0 456GRID 6703 0 0.0 .08 .1 0 456GRID 6704 0 0.0 0. .1 0 456GRID 6705 0 1.0 0. 0. 0 456GRID 6706 0 1.0 .08 0. 0 456GRID 6707 0 1.0 .08 .1 0 456GRID 6708 0 1.0 0. .1 0 456PSOLID 6701 9 0 2SPC1 1 123 6701 THRU 6704FORCE 1 6705 0 .25 0. 0. -1.FORCE 1 6706 0 .25 0. 0. -1.FORCE 1 6707 0 .25 0. 0. -1.FORCE 1 6708 0 .25 0. 0. -1.PLOAD4 1 6701 -125. 6701 6703$


258

$+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++$$ DUM1 ELEMENT NO. 53$$ADUM1,6,3,0,3,CTRIAX6 $CTRIAX6 5301 33 5301 5302 5303 5304 5305 5306 +TRIAX61+TRIAX6130.0GRID 5301 0 6.0 0.0 0.0 0 2456GRID 5302 0 6.0 0.0 2.0 0 2456GRID 5303 0 6.0 0.0 4.0 0 2456GRID 5304 0 4.238 0.0 3.0 0 2456GRID 5305 0 2.536 0.0 2.0 0 2456GRID 5306 0 4.238 0.0 1.0 0 2456SPC1 1 3 5302PLOADX 1 .0222139.03332095301 5302 5303$$+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++$$ CONM2 ELEMENT NO. 30$CONM2 3001 3001 0 1.0 1.0 1.0 1.0 +CONM21+CONM21 1.0 1.0 1.0 1.0 1.0 1.0GRID 3001 0 0.0 0.0 0.0SPC 1 3001 123456 0.0$$========================================================================$$ DMIG ELEMENT NO. 100$ NOTE:P.S. 3 ADDED 14-JAN-82GRID 10000GRID 10001 3DMIG MATK 0 6 2 0DMIG MATK 10000 3 10000 3 1.D6 + 10001 3 -1.D6DMIG MATK 10001 3 10001 3 1.D6DMIG MATLOAD 0 9 1 0DMIG* MATLOAD 1 +DMIG*DMIG 10000 3 1.DMIG* MATLOAD 2 +DMIG2*DMIG2 10000 3 0.$enddata

Example OutputThe printed output for the example problem consists of all of the output typically generated by a static analysis for the requests present in the case control section of the input and is not reproduced here. There is a small section of additional printed output generated in the Executive Control Echo region when the MODEL_CHECK material property options are used. The output summarizes the requested material property updates and is shown on the next several lines.


There is no other printed output generated that is peculiar to the material property update feature. All other output is typical printed output that is generated by the case control requests. For this example, the Grid Point Weight Generator output was requested via param,grdpnt,0 in the bulk data so that the mass of the structure could be verified as being produced by only the CONM2 element and the element non-structural mass.

$ MODEL_CHECK MAT_DENSITY=OFF, MAT_TECOEFF=OFF,MAT_TEIJ=OFF *************************************************************************************************************************************************************************************************************** ** THE PRESENCE OF THE MODEL_CHECK EXECUTIVE STATEMENT CAUSES THE FOLLOWING MATERIAL ** PROPERTY VALUES TO BE MODIFIED FOR EVERY MAT1, MAT2, MAT3, MAT8 AND MAT9 MATERIAL ** PROPERTY ENTRY PRESENT IN THE INPUT BULK DATA SECTION: ** MATERIAL DENSITY REVISED VALUE = 0.00000E+00 ** THERMAL EXP. DIRECT COEFF. REVISED VALUE = 0.00000E+00 ** THERMAL EXP. SHEAR COEFF. REVISED VALUE = 0.00000E+00 ** * **************************************************************************************************************************************************************************************************************


260