optistruct manual 11

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OptiStruct Optimization

Analysis, Concept and Optimization

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HyperWorks 11.0 Release Notes

Trademark and Registered Trademark Acknowledgments Listed below are Altair HyperWorks applications. Copyright Altair Engineering Inc., All Rights Reserved for:

HyperMesh 1990-2011; HyperCrash 2001-2011; OptiStruct 1996-2011; RADIOSS 1986-2011; HyperView 1999-2011; HyperView Player 2001-2011; HyperStudy 1999-2011; HyperGraph 1995-2011; MotionView 1993-2011; MotionSolve 2002-2011; HyperForm 1998-2011; HyperXtrude 1999-2011; Process Manager 2003-2011; Templex 1990-2011; Data Manager 2005-2011; MediaView 1999-2011; BatchMesher 2003-2011; TextView 1996-2011; HyperMath 2007-2011; ScriptView 2007-2011; Manufacturing Solutions 2005-2011; HyperWeld 2009-2011; HyperMold 2009-2011; solidThinking 1993-2011; solidThinking Inspired 2009-2011; Durability Director 2009-2011; Suspension Director 2009-2011; AcuSolve 1997-2011; and AcuConsole 2006-2011.

In addition to HyperWorks trademarks noted above, GridWorks, PBS Gridworks, PBS Professional, PBS and Portable Batch System are trademarks of ALTAIR ENGINEERING INC., as is patent # 6,859,792. All are protected under U.S. and international laws and treaties. All other marks are the property of their respective owners.

HyperWorks 11.0 Proprietary Information of Altair Engineering, Inc.

II

Table of Contents OptiStruct Optimization

Analysis, Concept and Optimization

Table of Contents .................................................................................................................... II

Chapter 1: Introduction ............................................................................................ 1

1 HyperWorks Overview ............................................................................................... 1

1.1 HyperWorks Tool Descriptions ............................................................................... 2

1.2 OptiStruct Integration with HyperWorks .................................................................. 4

2 OptiStruct Overview .................................................................................................. 5

2.1 Finite Element Analysis .......................................................................................... 5

2.2 Multi-body Dynamic Analysis .................................................................................. 6

2.3 Structural Design and Optimization ........................................................................ 6

2.4 Case Studies .......................................................................................................... 9

2.4.1 Lightweight SUV Frame Development ................................................................. 9

2.4.2 Optimization Process of a Torsion Link .............................................................. 10

Chapter 2: Theoretical Background ...................................................................... 11

1 Optimization ............................................................................................................ 11

1.1 Design Variable .................................................................................................... 12

1.2 Response ............................................................................................................. 13

1.2.1 Subcase Independent Response ....................................................................... 13

1.3 Objective Function ................................................................................................ 20 1.4 Constraint Functions............................................................................................. 21

2 Gradient-based Optimization ................................................................................... 23

2.1 Gradient Method ................................................................................................... 24

2.2 Sensitivity Analysis ............................................................................................... 25

2.3 Move Limit Adjustments ....................................................................................... 29


III

2.4 Constraint Screening ............................................................................................ 29

2.4.1 Regions and Their Purpose ............................................................................... 31

2.5 Discrete Design Variables .................................................................................... 32

Chapter 3: HyperMesh Optimization Interface ..................................................... 33

1 Model Definition Structure ....................................................................................... 33

1.1 Input/Output Section ............................................................................................. 34

1.2 Subcase Information Section ................................................................................ 37

1.3 Bulk Data Section ................................................................................................. 37

2 Optimization Setup .................................................................................................. 38

2.1 Optimization GUI .................................................................................................. 38

2.2 Design Variable [ DTPL] ....................................................................................... 39 2.3 Responses [DRESP1] .......................................................................................... 40 2.4 Dconstraints [DCONSTR] ..................................................................................... 41 2.5 Obj. reference [DOBJREF] ................................................................................... 42 2.6 Objective [DESOBJ] ............................................................................................. 43 2.7 Table entries [DTABLE] ........................................................................................ 44 2.8 Dequations [DEQATN] ......................................................................................... 45 2.9 Discrete dvs [DDVAL] ........................................................................................... 46 2.10 Opti. control [DOPTPRM] ................................................................................... 47 2.11 Constr. Screen [DSCREEN] ............................................................................... 47 3 How to Setup an Optimization in HyperMesh .......................................................... 48

Chapter 4: Concept Design ................................................................................... 53

1 Topology Optimization ............................................................................................ 53

1.1 Homogenization method ....................................................................................... 54

1.2 Density method .................................................................................................... 54

Exercise 4.1 Topology Optimization of a Hook with Stress Constraints ...................... 57

Exercise 4.2 Topology Optimization of a Control Arm ................................................. 65


IV

Exercise 4.3: Pattern Repetition using Topology Optimization ....................................... 71

2 Topography Optimization ........................................................................................ 79

2.1 Design Variables for Topography Optimization ..................................................... 79

2.1.1 Variable Generation ........................................................................................... 80

2.1.2 Multiple Topography Design Regions ................................................................ 81

Exercise 4.4 Topography Optimization of a Slider Suspension ................................... 83

3 Free-size Optimization............................................................................................. 89

Exercise 4.5 Free-size optimization of Finite Plate with hole ...................................... 93

4 Design Interpretation - OSSmooth ......................................................................... 101

4.1 OSSmooth Input Data ........................................................................................ 103

4.2 Running OSSmooth ........................................................................................... 105

4.3 Interpretation of Topography Optimization Results ............................................. 106

4.4 Shape Optimization Results, Surface Reduction and Surface Smoothing ........... 107

Exercise 4.6 OSSmooth surfaces from a topologic optimization ............................... 109

Chapter 5: Fine-Tuning ........................................................................................ 111

1 Size Optimization .................................................................................................. 111

1.1 Design Variables for Size Optimization ............................................................... 112

Exercise 5.1 Size Optimization of a Rail Joint ........................................................... 113

Exercise 5.2 Discrete Size Optimization of a Welded Bracket .................................. 123

2 Shape Optimization ............................................................................................... 131

2.1 Design Variables for Shape Optimization ........................................................... 132

2.2 HyperMorph ....................................................................................................... 133

2.2.1 The Three Basic Approaches to Morphing ....................................................... 133

Exercise 5.3 Cantilever L-beam Shape Optimization ................................................ 135

Exercise 5.4 Shape Optimization of a Rail Joint ....................................................... 143

3 Free-shape Optimization ....................................................................................... 161

3.1 Defining Free-shape Design Regions ................................................................. 161

3.2 Free-shape Parameters ...................................................................................... 163


V

3.2.1 Direction type .................................................................................................. 163

3.2.2 Move factor ..................................................................................................... 164

3.2.3 Number of layers for mesh smoothing ............................................................. 164

3.2.4 Maximum shrinkage and growth ...................................................................... 165

3.2.5 Constraints on Grids in the Design Region ...................................................... 166

Exercise 5.5 Free-shape optimization Compressor Bracket ..................................... 169

Exercise 5.6 - Shape Optimization of a 3-D Bracket using the Free-shape Method .... 177

Appendix A ........................................................................................................... 187

Chapter 1: Introduction

HyperWorks 11.0 OptiStruct Optimization 1 Proprietary Information of Altair Engineering, Inc.

Chapter 1

Introduction

1- HyperWorks Overview HyperWorks, A Platform for Innovation, is an enterprise simulation solution for rapid design exploration and decision-making. As one of the most comprehensive CAE solutions in the industry, HyperWorks provides a tightly integrated suite of best-in-class tools for:

o Modeling

o Analysis

o Optimization

o Visualization

o Reporting

o Performance data management.

Based on a revolutionary pay-for-use token-based business model, HyperWorks delivers increased value and flexibility over other software licensing models.

Below we list the applications that are part of HyperWorks, for extra information about them go to www.altairhyperworks.com web page or go to HyperWorks online documentation.


OptiStruct Optimization 2 HyperWorks 11.0 Proprietary Information of Altair Engineering, Inc.

1.1 HyperWorks Tool Descriptions Finite Element Meshing and Modeling

HyperMesh Universal finite element pre- and post-processor

HyperCrash Finite element pre-processor for automotive crash and safety analysis

BatchMesher Geometry cleanup and auto-meshing in batch mode for given CAD files

Multi-body Dynamics Modeling

MotionView Multi-body dynamics pre- and post-processor

Solvers

RADIOSS Finite element solver for linear and non-linear problems

MotionSolve Multi-body dynamics solver

OptiStruct Design and optimization software using finite elements and multi-body dynamics

Post-processing and Data Analysis

HyperView High performance finite element and mechanical system post-processor, engineering plotter, and data analysis tool

HyperGraph Engineering plotter and data analysis tool

HyperGraph 3D Engineering 3-D plotter and data analysis tool

HyperView Player Viewer for visualizing 3-D CAE results via the Internet or desktop

Study and Optimization

HyperStudy Integrated optimization, DOE, and robustness engine

Data Management and Process Automation

Altair Data Manager A solution that organizes, manages, and stores CAE and test data throughout the product design cycle



Process Manager Process automation tool for HyperWorks and third party software; Processes can be created with the help of Process Studio.

Assembler A tool that enables CAE analysts to manage, organize, and control their CAE mesh data

Manufacturing Environments

Manufacturing Solutions A unified environment for manufacturing process simulation, analysis, and design optimization

HyperForm A unique finite element based sheet metal forming simulation software solution

HyperXtrude An hp-adaptive finite element program that enables engineers to analyze material flow and heat transfer problems in extrusion and rolling applications

Molding Provides a highly efficient and customized environment for setting up models for injection molding simulation with Moldflow

Forging Provides a highly efficient and customized environment for setting up models for complex three-dimensional forging simulation with DEFOM3D

Friction Stir Welding Provides an efficient interface for setting up models and analyzing friction stir welding with the HyperXtrude Solver

HyperWorks Results Mapper Process Manager-based tool that provides a framework to initialize a structural model with results from a forming simulation



1.2 OptiStruct Integration with HyperWorks OptiStruct is part of the HyperWorks toolkit, as described early this is a design and optimization software that is based on finite element and multi-body dynamics modeling of the structure or mechanical system. Analysis results are provided by RADIOSS analysis capabilities and the integration with MotionSolve.

The solvers consist of loosely integrated executables (see picture below). To the user the integration is seamless thru the run script provided. Based on the file naming convention the right executable or combination of executables is chosen.

Solver Overview

The pre-processing for OptiStruct is made using HyperMesh and the post-processing using HyperView and HyperGraph. HyperStudy is another HyperWorks tool that can be used with OptiStruct for Robust design, DOE and Optimization.

During the next sections the HyperWorks integration with OptiStruct will be showed in detail, and for more about it the user should go to our online documentation.



2 OptiStruct Overview OptiStruct is a finite element and multi-body dynamics software which can be used to design and optimize structures and mechanical systems. OptiStruct uses the analysis capabilities of RADIOSS and MotionSolve to compute responses for optimization.

The graphical interface for OptiStruct within HyperWorks allows you to perform complete modeling, optimization problem setup, job submission, and post-processing quickly and easily.

2.1 Finite Elements Analysis Different solution sequences are available for the analysis of structures and structural components, these include:

Basic analysis features

Linear static analysis.

Normal modes analysis.

Linear buckling analysis.

Thermal-stress steady state analysis

Advanced analysis features

Frequency response function (FRF) analysis o Direct

o Modal

Random response analysis

Transient response analysis

o Direct

o Modal

Transient response analysis based on the Fourier method

o Direct

o Modal

Non-linear contact analysis

Acoustic Analysis (Structure and Fluid) Fatigue Analysis (N and N)



Inertia relief analysis is available with static, frequency response, transient response, and non-linear gap analyses. All standard finite element types are available. All elements fulfill the usual patch tests as well as the full suite of MacNeal-Harder tests. OptiStruct can be used as a standalone finite element solver and it provides multi-threaded solutions on multi-processor computers.

2.2 Multi-body Dynamics Analysis Different solution sequences for the analysis of mechanical systems are available. These include:

o Kinematics

o Dynamics

o Static

o Quasi-static Systems with rigid and flexible bodies can be analyzed. Flexible bodies can be derived from any finite element model defined in OptiStruct. The multi-body solution sequence is the implemented as an integration of Altair MotionSolve.

Multi-body dynamics is an advanced analysis feature.

2.3 - Structural Design and Optimization Structural design tools include topology, topography and free sizing optimization. For structural optimization sizing, shape and free shape optimization are available.

In the formulation of design and optimization problems the following responses can be applied as objective or constraints: Compliance, frequency, volume, mass, moments of inertia, center of gravity, displacements, velocities, accelerations, buckling factor, stresses, strains, composite failure, forces, synthetic responses, and external (user defined) functions. Static, inertia relief, non-linear gap, normal modes, buckling, and frequency response solutions can be included in a multi-disciplinary optimization setup.

Topology: is a mathematical technique that optimized the material distribution for a structure within a given package space



Topologic optimization of a control arm

Topography: Topography optimization is an advanced form of shape optimization in which a design region for a given part is defined and a pattern of shape variable-based reinforcements within that region is generated using OptiStruct.

Topographic optimization of a plate

Free Size: is a mathematical technique that produces an optimized thickness distribution per element for a 2D structure.

Free-size optimization (Laminate total thickness)

Shape: is an automated way to modify the structure shape based on predefined shape variables to find the optimal shape.

Cantilever beam Shape optimization



Size: is an automated way to modify the structure parameters (Thickness, 1D properties, material properties, etc) to find the optimal design.

Size optimization (shell thickness and material properties)

Gauge: is a particular case of size, where the DV are 2D props (Pshell or Pcomp) Free Shape: is an automated way to modify the structure shape based on set of nodes that can move totally free on the boundary to find the optimal shape.

Free-shape optimization result for a cantilever beam

Composite shuffle: is an automated way to determine the optimum laminate stack sequence. DVs are the plies sequence of stacking. It is used for composite material only defined using PCOMP(G) or PCOMPP.

Laminate stack sequence optimization using composite shuffle



Topology, topography, free-size, size, shape and free-shape optimization can be combined in a general problem formulation.

All these optimizations methods will be discussed in detail on the next chapters.

2.4 Case Studies

2.4.1 Lightweight SUV Frame Development

OptiStruct Application



2.4.2 Optimization Process of a Torsion Link

OptiStruct Application

Chapter 2: Theoretical Background


Chapter 2

Theoretical Background

1 Optimization Optimization can be defined as the automatic process to make a system or component as good as possible based on an objective function and subject to certain design constraints. There are many different methods or algorithms that can be used to optimize a structure, on OptiStruct is implemented some algorithms based on Gradient Method, this method will be discussed in detail later on this book.

Models used in optimization are classified in various ways, such as linear versus nonlinear, static versus dynamic, deterministic versus stochastic, or permanent versus transient. Then it is very important that the user include a-priori all of the important aspects of the problem, so that they will be taken into account during the solution.

Mathematically an optimization problem can be stated as:

Objective Function: 0(p) min(max) (target) Subject to constraint Functions: i(p) 0 Design Space: pl pj pu where l is the lower bound and u is

the upper bound on the design variables

where:

0(p) and i(p) represent the system responses or a target value for system identification study, and pj represents the vector of design variables (p1,p2,,pn).



1.1 Design Variable Design Variables or DVs are system parameters that can vary to optimize system performance. For OptiStruct the type of parameter or DV defines the optimization type:

o TOPOLOGY: is a mathematical technique that optimized the material distribution for a structure within a given package space. DVs are defined as a fictitious density for each element, and these values are varied from 0 to 1 to optimize the material distribution.

o TOPOGRAPHY: Topography optimization is an advanced form of shape optimization in which a design region for a given part is defined and a pattern of shape variable-based reinforcements within that region is generated using OptiStruct

o FREE-SIZE: This is a special method designed by Altair to optimize 2D structure where the design variables are the thickness of each element. This method is very useful for aerospace structures where shear panels are preferable to truss structures.

o SHAPE: is an automated way to modify the structure shape based on predefined shape variables to find the optimal shape. DVs are used to modify the geometry shape of the component, on HyperMesh it is used HyperMorph to define this parameter.

o SIZE: is an automated way to modify the structure parameters to find the optimal design. DVs are any Scalar parameter (Thickness, 1D properties, material properties, etc) that affects the system response.

o GAUGE: Particular case of size optimization when the DV are PSHELL thickness.

o FREE-SHAPE: is an automated way to modify the structure shape based on set of nodes that can move totally free on the boundary to find the optimal shape. DVs are defined based a set of nodes.

o COMPOSITE SHUFFLE: is an automated way to determine the optimum laminate stack sequence. DVs are the plies sequence of stacking. It is used for composite material only defined using PCOMP(G) or PCOMPP.



1.2 Response Response for OptiStruct is any value or function that is dependent of the Design Variable and is evaluated during the solution.

OptiStruct allows the use of numerous structural responses, calculated in a finite element analysis, or combinations of these responses to be used as objective and constraint functions in a structural optimization.

Responses are defined using DRESP1 bulk data entries. Combinations of responses are defined using either DRESP2 entries, which reference an equation defined by a DEQATN bulk data entry, or DRESP3 entries, which make use of user-defined external routines identified by the LOADLIB I/O option. Responses are either global or subcase (loadstep, load case) related. The character of a response determines whether or not a constraint or objective referencing that particular response needs to be referenced within a subcase.

1.2.1 - Subcase Independent Response o Mass, Volume [ mass, volume]

Both are global responses that can be defined for the whole structure, for individual properties (components) and materials, or for groups of properties (components) and materials.

o Fraction of mass, Fraction of design volume [ massfrac, volumefrac] Both are global responses with values between 0.0 and 1.0. They describe a fraction of the initial design space in a topology optimization. They can be defined for the whole structure, for individual properties (components) and materials, or for groups of properties (components) and materials.

D

Di

f VVV

0

=

where: Vf : Volume fraction

DiV : Designable volume at current iteration; DV0 : Initial Designable volume;

0MMM if =

where: Mf : Mass fraction Mi : Total mass at current iteration; M0 : Total Initial mass;



If, in addition to the topology optimization, a size and shape optimization is performed, the reference value (the initial design volume in the case of volume fraction, or initial total mass in the case of mass fraction) is not altered by size and shape changes. This can, on occasion, lead to negative values for these responses. If size and shape optimization is involved, it is recommended to use Mass or Volume responses instead of Mass Fraction or Volume Fraction, respectively.

In order to constrain the volume fraction for a region containing a number of properties (components), a DRESP2 equation needs to be defined to sum the volume of these properties (components), otherwise, the constraint is assumed to apply to each individual property (component) within the region. This can be avoided by having all properties (components) use the same material and applying the volume fraction constraint to that material.

These responses can only be applied to topology design domains. OptiStruct will terminate with an error if this is not the case.

o Center of gravity [ cog ] This is a global response that may be defined for the whole structure, for individual properties (components) and materials, or for groups of properties (components) and materials.

o Moments of inertia [ inertia ] This is a global response that may be defined for the whole structure, for individual properties (components) and materials, or for groups of properties (components) and materials.

o Weighted compliance [ weighted comp ] The weighted compliance is a method used to consider multiple subcases (loadsteps, load cases) in a classical topology optimization. The response is the weighted sum of the compliance of each individual subcase (loadstep, load case).

== iTiiiiW wCwC fu2

1

This is a global response that is defined for the whole structure.

o Weighted reciprocal eigenvalue (frequency) [ weighted freq ] The weighted reciprocal eigenvalue is a method to consider multiple frequencies in a classical topology optimization. The response is the weighted sum of the reciprocal eigenvalues of each individual mode considered in the optimization.

[ ] 0uMK == iii

iw

wf with



This is done so that increasing the frequencies of the lower modes will have a larger effect on the objective function than increasing the frequencies of the higher modes. If the frequencies of all modes were simply added together, OptiStruct would put more effort into increasing the higher modes than the lower modes. This is a global response that is defined for the whole structure.

o Combined compliance index [ compliance index ] The combined compliance index is a method to consider multiple frequencies and static subcases (loadsteps, load cases) combined in a classical topology optimization. The index is defined as follows

+=

j

j

j

iiw

w

NORMCwS

This is a global response that is defined for the whole structure.

The normalization factor, NORM, is used for normalizing the contributions of compliances and eigenvalues. A typical structural compliance value is of the order of 1.0e4 to 1.0e6. However, a typical inverse eigenvalue is on the order of 1.0e-5. If NORM is not used, the linear static compliance requirements dominate the solution.

The quantity NORM is typically computed using the formula

minmaxCNF =

where Cmax is the highest compliance value in all subcases (loadsteps, load cases) and min is the lowest eigenvalue included in the index. In a new design problem, the user may not have a close estimate for NORM. If this happens, OptiStruct automatically computes the NORM value based on compliances and eigenvalues computed in the first iteration step.

o Von Mises stress in a topology or free-size optimization

Von Mises stress constraints may be defined for topology and free-size optimization through the STRESS optional continuation line on the DTPL or the DSIZE card. There are a number of restrictions with this constraint:

o The definition of stress constraints is limited to a single von Mises permissible stress. The phenomenon of singular topology is pronounced when different materials with different permissible stresses exist in a structure. Singular topology refers to the problem associated with the conditional nature of stress constraints, i.e. the stress constraint of an element disappears when the element vanishes. This creates another problem in that a huge number of reduced problems exist with solutions that cannot usually be found by a gradient-based optimizer in the full design space.



o Stress constraints for a partial domain of the structure are not allowed because they often create an ill-posed optimization problem since elimination of the partial domain would remove all stress constraints. Consequently, the stress constraint applies to the entire model when active, including both design and non-design regions, and stress constraint settings must be identical for all DSIZE and DTPL cards.

o The capability has built-in intelligence to filter out artificial stress concentrations around point loads and point boundary conditions. Stress concentrations due to boundary geometry are also filtered to some extent as they can be improved more effectively with local shape optimization.

o Due to the large number of elements with active stress constraints, no element stress report is given in the table of retained constraints in the .out file. The iterative history of the stress state of the model can be viewed in HyperView or HyperMesh.

o Stress constraints do not apply to 1-D elements.

o Stress constraints may not be used when enforced displacements are present in the model.

o Bead discreteness fraction [ beadfrac ] This is a global response for topography design domains. This response indicates the amount of shape variation for one or more topography design domains. The response varies in the range 0.0 to 1.0 (0.0 < BEADFRAC < 1.0), where 0.0 indicates that no shape variation has occurred, and 1.0 indicates that the entire topography design domain has assumed the maximum allowed shape variation.

Static Subcase o Static compliance [ compliance ]

The compliance C is calculated using the following relationship:

==

==

V

TT

T

dvKuu

fKufu

21

21

with21

C

or

C

The compliance is the strain energy of the structure and can be considered a reciprocal measure for the stiffness of the structure. It can be defined for the whole structure, for individual properties (components) and materials, or for groups of properties (components) and materials. The compliance must be assigned to a static subcase (loadstep, load case).



In order to constrain the compliance for a region containing a number of properties (components), a DRESP2 equation needs to be defined to sum the compliance of these properties (components), otherwise, the constraint is assumed to apply to each individual property (component) within the region. This can be avoided by having all properties (components) use the same material and applying the compliance constraint to that material.

o Static displacement [ static displacement ] Displacements are the result of a linear static analysis. Nodal displacements can be selected as a response. They can be selected as vector components or as absolute measures. They must be assigned to a static subcase (loadstep, load case).

o Static stress of homogeneous material [ static stress ] Different stress types can be defined as responses. They are defined for components, properties, or elements. Element stresses are used, and constraint screening is applied. It is also not possible to define static stress constraints in a topology design space (see above). This is a static subcase (loadstep, load case) related response.

o Static strain of homogeneous material [ static strain ] Different strain types can be defined as responses. They are defined for components, properties, or elements. Element strains are used, and constraint screening is applied. It is also not possible to define strain constraints in a topology design space. This is a subcase (loadstep, load case) related response.

o Static stress of composite lay-up [ composite stress ] Different composite stress types can be defined as responses. They are defined for PCOMP components or elements. Ply level results are used, and constraint screening is applied. It is also not possible to define composite stress constraints in a topology design space. This is a subcase (loadstep, load case) related response.

o Static strain of composite lay-up [ composite strain ] Different composite strain types can be defined as responses. They are defined for PCOMP components or elements. Ply level results are used, and constraint screening is applied. It is also not possible to define composite strain constraints in a topology design space. This is a subcase (loadstep, load case) related response.

o Static failure in a composite lay-up [composite failure ] Different composite failure criterion can be defined as responses. They are defined for PCOMP components or elements. Ply level results are used, and constraint screening is applied. It is also not possible to define composite failure criterion constraints in a topology design space. This is a subcase (loadstep, load case) related response.

o Static force [ static force ]



Different force types can be defined as responses. They are defined for components, properties, or elements. Constraint screening is applied. It is also not possible to define force constraints in a topology design space. This is a static subcase (loadstep, load case) related response.

Normal Modes Subcase o Frequency [ frequency ]

Natural frequencies are the result of a normal modes analysis, and must be assigned to the normal modes subcase (loadstep, load case).

Buckling Subcase o Buckling factor [ buckling ]

The buckling factor is the result of a buckling analysis, and must be assigned to a buckling subcase (loadstep, load case). A typical buckling constraint is a lower bound of 1.0, indicating that the structure is not to buckle with the given static load. It is recommended to constrain the buckling factor for several of the lower modes, not just of the first mode.

Frequency Response Subcase o Frequency response displacement [ frf displacement ]

Displacements are the result of a frequency response analysis. Nodal displacements can be selected as a response. They can be selected as vector components in real/imaginary or magnitude/phase form. They must be assigned to a frequency response subcase (loadstep, load case).

o Frequency response velocity [ frf velocity ] Velocities are the result of a frequency response analysis. Nodal velocities can be selected as a response. They can be selected as vector components in real/imaginary or magnitude/phase form. They must be assigned to a frequency response subcase (loadstep, load case).

o Frequency response acceleration [ frf acceleration ] Accelerations are the result of a frequency response analysis. Nodal accelerations can be selected as a response. They can be selected as vector components in real/imaginary or magnitude/phase form. They must be assigned to a frequency response subcase (loadstep, load case).

o Frequency response stress [ frf stress ] Different stress types can be defined as responses. They are defined for components, properties, or elements. Element stresses are not used in real/imaginary or magnitude/phase form, and constraint screening is applied. It is not possible to define stress constraints in a topology design space. This is a frequency response subcase (loadstep, load case) related response.



o Frequency response strain [ frf strain ] Different strain types can be defined as responses. They are defined for components, properties, or elements. Element strains are used in real/imaginary or magnitude/phase form, and constraint screening is applied. It is not possible to define strain constraints in a topology design space. This is a frequency response subcase (loadstep, load case) related response.

o Frequency response force [ frf force ] Different force types can be defined as responses. They are defined for components, properties, or elements in real/imaginary or magnitude/phase form. Constraint screening is applied. It is also not possible to define force constraints in a topology design space. This is a frequency response subcase (loadstep, load case) related response.

All FRF responses can be output as: All freq All evaluated points on the freq range. Vector = { iy } Freq = Argument value on a specific frequency f. Scalar = ( )fy sum Sum of all arguments. Scalar

=

=

m

iiy

1

avg Average of all arguments. Scalar mym

ii /

1==

ssq Sum of square of the arguments. Scalar =

=

m

iiy

1

2

rss Square root of sum of squares of the arguments. Scalar =

=

m

iiy

1

2

max Maximum value of arguments. Scalar = ( )iymax min Minimum value of arguments. Scalar = ( )iymin avgabs Average of absolute value of arguments. Scalar my

m

ii /

1

=

=

maxabs Maximum of absolute value of arguments. Scalar = ( )iymax minabs Minimum of absolute value of arguments. Scalar = ( )iymin sumabs Sum of absolute value of arguments. Scalar

=

=

m

iiy

1

o Fatigue [ fatigue ] It is the life or damage evaluated in a fatigue sequence for a group of elements or properties.

o Function [ function ] It is a generic equation defined using the dequations panel [DEQATN].



1.3 Objective Function The Objective function is a model response to be maximized or minimized. There are two ways to specify an objective in OptiStruct. Either a single response can be minimized or maximized or you can choose to minimize the maximum value, or maximize the minimum value, of a number of normalized responses.

In the first instance, where a single response is defined as the objective, a DESOBJ card must be included in the Subcase Information Section of the input file. The DESOBJ card references a response, (DRESP1 or DRESP2), which is defined in the Bulk Data Section of the input file. If the response, to which the DESOBJ card refers, is associated with a single subcase, the DESOBJ card must be placed within that subcase definition. If the response is associated with more than one subcase, the DESOBJ card must appear before the first SUBCASE statement.

Example: Objective is to minimize the value of the response with ID 1. DESOBJ(MIN) = 1

The second instance, where the objective references multiple responses, requires DOBJREF bulk data entries and MINMAX or MAXMIN subcase information entries. The DOBJREF cards reference responses (DRESP1 or DRESP2) and provide positive and negative reference values for these responses. Multiple DOBJREF cards may occur in the input file and they may or may not use the same Design Objective IDs. The reference values allow for normalization of different responses. The value of the response is divided by the appropriate reference value. When the value of the response is positive, the positive reference value is used. When the value of the response is negative, the negative reference value is used.

The MINMAX or MAXMIN cards reference the DOBJREF cards. If all DOBJREF cards use the same DOID, only one occurrence of MAXMIN or MINMAX is required. If different DOIDs are used on the DOBJREF cards, multiple occurrences of MINMAX and MAXMIN cards may be required, but a MINMAX statement cannot appear in the same input file as a MAXMIN statement. MINMAX or MAXMIN statements must appear before the first SUBCASE statement.

Example: Objective is to minimize the maximum of all DOBJREF's with DOID 1 and DOID 2. MINMAX = 1

MINMAX = 2

Example: Design objective for MINMAX (MAXMIN) problems - DOID 1 - references design response 10 in subcase 2 - negative reference value = -1.0, positive reference value = 1.0. $--(1)--$--(2)--$--(3)--$--(4)--$--(5)--$--(6)--$--(7)--



DOBJREF 1 10 2 1.0 1.0

1.4 Constraint Functions On all almost every engineering design there are constraints that need to be satisfied. These constraints can be defined as a lower bound or an upper bound on any response that is dependent of the design variable. To better understand it lets proposal a model where there are 3 constraints. A cantilever beam loaded with force F=24000 N. Where the cross-section parameters: Width b[20,40] and height h[30,90] can vary on their range to minimize the beam weight, subject to these constraint:

1) Max normal stress can not exceed the max value, 2) Max shear stress can not exceed the

max and 3) Height h should not be larger than twice the width b.

Mathematically this problem can be stated as:

Objective: min Weight(b,h)

Design Variables: bL < b < bU, 20 < b < 40

hL < h < hU, 30 < h < 90

Design Constraints: (b,h) = 6F/(bh2) max, with max = 70 MPa (b,h) =F/(bh) max, with max = 15 MPa h 2*b



This problem can be described graphically as showed below:

BEAM

0.010.020.030.040.050.060.070.080.090.0

100.0

0.00 10.00 20.00 30.00 40.00 50.00b (mm)

h (m

m)

Cantilever beam problem (Optimum (b=24.9, h=64.3) W = 8).

=70 =15

> 15

< 15

>70



2 Gradient-based Optimization OptiStruct uses an iterative procedure known as the local approximation method to solve the optimization problem. This approach is based on the assumption that only small changes occur in the design with each optimization step. The result is a local minimum. The biggest changes occur in the first few optimization steps and, as a result, not many system analyses are necessary in practical applications.

The design sensitivity analysis of the structural responses (with respect to the design variables) is one of the most important ingredients to take the step from a simple design variation to a computational optimization.

The design update is computed using the solution of an approximate optimization problem, which is established using the sensitivity information. OptiStruct has three different methods implemented: the optimality criteria method, a dual method, and a primal feasible directions method. The latter are both based on a convex linearization of the design space. Advanced approximation methods are used.

The optimality criteria method is used for classical topology optimization formulations using minimum compliance (reciprocal frequency, weighted compliance, weighted reciprocal frequency, compliance index) with a mass (volume) or mass (volume) fraction constraint. The dual or primal methods are used depending upon the number of constraints and design variables. The dual method is of advantage if the number of design variables exceeds the number of constraints (common in topology and topography optimization). The primal method is used in the opposite case, which is more common in size and shape optimizations. However, the choice is made automatically by OptiStruct.



2.1 Gradient Method This is an optimization algorithm that can be called Gradient descent method, or just Gradient Method. It is used to find a minimum of a function using the gradient value; the algorithm can be described as:

1. Start from a X0 point

2. Evaluate the function F(Xi) and the gradient of the function F(Xi) at the Xi. 3. Determine the next point using the negative gradient direction: Xi+1 = Xi - F(Xi). 4. Repeat the step 2 to 3 until the function converged to the minimum.

The picture below shows how this work:

This is a very simplified overview of this method, if the user needs more information it can be found on any Optimization text book

Gradient-based methods are effective when the sensitivities (derivatives) of the system responses, with respect to the design variables, can be computed easily and inexpensively.

The local approximation method is best suited to situations where:

Design Sensitivity Analysis (DSA) is available. The method is applied to linear static and dynamic problems integrated mostly with

FEA Solvers (i. e. OptiStruct). Gradient-based methods depend on the sensitivity of the system responses with respect to changes in design variables in order to understand the effect of the design changes and optimize the system.

For linear structural analysis codes, you can implement the derivatives of the structural responses using either finite difference or analytical methods (such as the Adjoint Method). Here, the responses are written as explicit algebraic equations with the needed continuity requirements and are easily differentiable.

X0

X1 X2

X3



For example, using first order finite difference method, you can calculate the gradient of i(p) as:

In finite element based structural optimization, you can state the linear static equation as KU = F, where K is the stiffness matrix and U is the displacement vector to be determined, and F is the applied force vector. Differentiating this with respect to the design variable X yields the following:

Rearranging terms gives the following equation:

You can obtain gradients of stresses and strains, etc, by chain rule differentiation.

2.2 Sensitivity Analysis The response quantity, g, is calculated from the displacements as:

The sensitivity of this response with respect to the design variable x, or the gradient of the response, is:

Two approaches to sensitivity analysis, the Direct and Adjoint variable method are possible. Given the equation of motion:

and its derivative with respect to design variable x,

one can calculate the sensitivity of the displacement vector u as:

Using this equation, the largest cost in the calculation of the response gradient is the forward-backward substitution required for the calculation of the derivative of the



displacement vector with respect to the design variable. This is called the direct method. One forward-backward substitution is required for each design variable.

If constraints are active in more than one load case, and the load is a function of the design variable (say body force or pressure loads for shape optimization), then the set of forward-backward substitutions must be performed for each active load case. If the loads are not a function of the design variables, but there are active load cases with multiple boundary conditions, then the set of forward-backward substitutions must be performed for each active boundary condition.

For the Adjoint variable method of sensitivity analysis, the vector (adjoint variable) a is introduced, which is calculated as:

Then the derivative of the constraint can be calculated as:

When the adjoint variable method for sensitivity analysis is used, a single forward-backward substitution is needed for each retained constraint. This forward-backward substitution is needed to calculate the vector a.

There are typically a small number of design variables in shape and size optimization (say 5 to 50) and a large number of constraints. The large number of constraints comes from stress constraints. If there are 20,000 elements, each with a single stress constraint, and 10 load cases, there are a total of 200,000 possible stress constraints.

There are typically a large number of design variables in topology optimization (between 1 and 3 per element) and a small number of constraints. Because stress constraints are not usually considered in topology optimization, it makes sense that the Adjoint variable method of sensitivity analysis be used for topology optimization (in order to reduce computational costs). For shape and sizing optimization, it is often beneficial to use the Direct method for sensitivity analysis. However, in some cases, when there are a large number of design variables and a small number of constraints, the adjoint variable method should be used. For example, in a topography optimization, the number of constraints that gradients need to be calculated for can be reduced using constraint screening. With constraint screening, constraints that are not close to being violated are ignored. Only constraints that are violated, or nearly violated, are retained. Also, if there are many stress constraints that are retained in a small region of the structure, say at a stress concentration, only a few of the most critical need to be retained.

The sensitivities of responses with respect to design variables can be exported to an Excel spreadsheet (see OUTPUT, MSSENS) or plotted in HyperGraph (See OUTPUT, HGSENS). For contouring in HyperView, the sensitivities of topology and gauge design variables can be exported to H3D format. (See OUTPUT, H3DTOPOL and OUTPUT, H3DGAUGE, respectively).



The Excel spreadsheet allows the modification of design variables and then computes approximated responses. This can be used to make design studies without running OptiStruct again. See the image below.

Example spreadsheet output showing that modification of field C10 yields approximate results in the lower right of the spreadsheet, identified by a border surround here.

File Creation This file is only created when size or shape optimization is performed. Output of this file is controlled by the SENSITIVITY and SENSOUT I/O options.

File Format The only values that can be changed in this file are those listed in the "New" column. All other values are either fixed or their calculation is fixed. When the .slk file is created, the values in the "New" column match those in the "Reference" column. These values may be adjusted, but should always remain within the design variable's bounds. Each size and shape design variable in the model is listed in the left-hand column of the sensitivity table. Information concerning a particular design variable is given in the row where its label is listed. The current value and the upper and lower bounds of the design variables are given in the columns, "Reference," "Lower," and "Upper" respectively.

Each referenced response in the model has its own column. These response columns are on the right-hand side of the sensitivity table. The calculated sensitivity of a response to changes in a design variable at the current iteration is given in the row corresponding to that design variable and the column corresponding to that response.

Beneath the list of design variables, in the left-hand column, are the headings "Response lower bound," "Response reference," and "Response upper bound". If a response is constrained, the constraint value will be given in either the "Response lower bound" or the "Response upper bound" row of the column corresponding to that response. The value given in the "Response reference" row is the calculated value of the response using the design variable reference values.



At the bottom of the left-hand column are the headings: "Response linear," "Response reciprocal," and "Response conservative". The response values in these rows are the predicted values of the responses for three different approximations. Initially, these values will match one another and the "Response reference" value for each response. This is because these are the predicted values of the response at the given variable settings, which initially are the same settings used to calculate the "Response reference" value. Once the design variable values in the "New" column are altered, these values will change.

The "Response linear" row predicts the response value using linear approximation. This is calculated as:

where:

1R is the predicted response value.

0R is the response reference value.

vnvv ,...,2,1 are the new values of the design variables.

000 ,...,2,1 vnvv are the reference values of the design variables.

dvndR

dvdR

dvdR

,...,

2,

1 are the sensitivities of the response to the design variables.

The "Response reciprocal" row predicts the response value using reciprocal approximation. This is calculated as:

where:

1R is the predicted response value.

0R is the response reference value.

vnvv ,...,2,1 are the new values of the design variables.

000 ,...,2,1 vnvv are the reference values of the design variables.

dvndR

dvdR

dvdR

,...,

2,

1 are the sensitivities of the response to the design variables.

The "Response conservative" row predicts the response value using a combination of the above approximations where linear approximation is used, when the sensitivity is positive, and reciprocal approximation is used when the sensitivity is negative. Therefore, if all sensitivities are positive, the conservative prediction will match the linear prediction. If all sensitivities are negative, it will match the reciprocal prediction, but if there is a mixture of positive and negative sensitivities for a given response then the conservative prediction will match neither the linear nor the reciprocal prediction.



The normalized values simply show the predicted response as a fraction of the response reference value.

2.3 - Move Limit Adjustments As the design moves away from its initial point in the approximate optimization problem, the approximate values become less accurate. This can lead to slow overall convergence, as the approximate optimum designs are not near the actual optimum design. Move limits on the design variables, and/or intermediate design variables, are used to protect the accuracy of the approximations. They appear as:

Small move limits lead to smoother convergence. Many iterations may be required due to the small design changes at each iteration. Large move limits may lead to oscillations between infeasible designs as critical constraints are calculated inaccurately. If the approximations themselves are accurate, large move limits can be used. Typical move limits in the approximate optimization problem are 20% of the current design variable value. If advanced approximation concepts are used, move limits up to 50% are possible.

Even with advanced approximation concepts, it is possible to have poor approximations of the actual response behavior with respect to the design variables. It is best to use larger move limits for accurate approximations and smaller move limits for those that are not so accurate.

Note that the same set of design variable move limits must be used for all of the response approximations. It is important to look at the approximations of the responses that are driving the design. These are the objective function and most critical constraints. If the objective function moves in the wrong direction, or critical constraints become even more violated, it is a sign that the approximations are not accurate. In this case, all of the design variable move limits are reduced. However, if the move limits become too small, convergence may be slowed, as design variables that are a long way from the optimum design are forced to change slowly. Therefore, the move limits on the individual design variables that keep hitting the same upper or lower move limit bound are increased. Move limits are automatically adjusted by OptiStruct.

2.4 - Constraint Screening During the optimization process at each iteration the objective function(s) and all constraints of the design problem are evaluated. Retaining all of these responses in the optimization problem has two potential disadvantages:

1. This can result in a big optimization problem with a large number of responses and design variables. Most optimization algorithms are designed to handle either a large number of responses or a large number of design variables, but not both.



2. For gradient-based optimization, the design sensitivities of these responses need to be calculated. The design sensitivity calculation can be very computationally expensive when there are a large number of responses and a large number of design variables.

Constraint screening is the process by which the number of responses in the optimization problem is trimmed to a representative set. This set of retained responses captures the essence of the original design problem while keeping the size of the optimization problem at an acceptable level. Constraint screening utilizes the fact that constrained responses that are a long way from their bounding values (on the satisfactory side) or which are less critical (i.e. for an upper bound more negative and for a lower bound more positive) than a given number of constrained responses of the same type, within the same designated region and for the same subcase, will not affect the direction of the optimization problem and therefore can be removed from the problem for the current design iteration.

Consider the optimization problem where the objective is to minimize the mass of a finite element model composed of 100,000 elements, while keeping the elemental stresses below their associated material's yield stress. In this problem, we have 100,000 constraints (the stress for every element must be below its associated material's yield stress) for each subcase. For every design variable, 100,000 sensitivity calculations must be performed for each subcase, at every iteration. Because design variable changes are restricted by move limits, stresses are not expected to change drastically from one iteration to the next. Therefore, it is wasteful to calculate the sensitivities for those elements whose stresses are considerably lower than their associated material's yield stress. Also the direction of the optimization will be driven primarily by the highest elemental stresses. Therefore, the number of required calculations can be further reduced by only considering an arbitrary number of the highest elemental stresses.

Of course there is trade-off involved in using constraint screening. By not considering all of the constrained responses, it may take more iterations to reach a converged solution. If too many constrained responses are screened, it may take considerably longer to reach a converged solution or, in the worst case, it may not be able to converge on a solution if the number of retained responses is less than the number of active constraints for the given problem.

Through extensive testing it has been found that, for the majority of problems, using constraint screening saves a lot of time and computational effort. Therefore, constraint screening is active in OptiStruct by default. The default settings consider only the 20 most critical (i.e. for an upper bound most positive and for a lower bound most negative) constraints that come within 50 percent of their bound value (on the satisfactory side) for each response type, for each region, for each subcase.

The DSCREEN bulk data entry controls both the screening threshold and number of retained constraints. Different DSCREEN settings are allowed for all of the response types supported by the DRESP1 bulk data entry. Responses defined by the DRESP2 bulk data entry are controlled by a single DSCREEN entry with RTYPE = EQUA. Likewise, responses defined by the DRESP3 bulk data entry are controlled by a single DSCREEN entry with RTYPE = EXTERNAL. It is important to ensure that DRESP2 and DRESP3 definitions that use the same region identifier use similar equations. (In order for constraint screening to work effectively, responses within the same region should be of similar magnitudes and



demonstrate similar sensitivities, the easiest way to ensure that is through the use of similar variable combinations). In order to reduce the burden on the user, it is possible to allow the screening criteria to be automatically and adaptively adjusted in an effort to retain the least number of responses necessary for stable convergence. Setting RTYPE=AUTO on the DSCREEN bulk data entry will enable this feature. Region definition is also automated with this setting. This setting is useful for less experienced users and can be particularly useful when there are many local constraints. However, there are some drawbacks; experienced users may be able to achieve better performance through manual definition of screening criteria, more memory may be required to run with RTYPE=AUTO, and manual under-retention of constraints will require less memory and may, therefore, be desirable for very large problems (even with compromised convergence stability and optimality).

2.4.1 Regions and Their Purpose In OptiStruct, a region is a group of responses of the same type.

Regions are defined by the region identifier field on the DRESP1, DRESP2, and DRESP3 bulk data entries used to define the responses. If the region identifier field is left blank or set to 0, then each property associated with the response forms its own region. The same region identifier may be used for responses of different types, but remember that because they are not of the same type they cannot form the same region.

Example 1 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

DRESP1 1 label STRESS PSHELL

SMP1

1

2 3

DRESP1 with ID 1 defines stress responses for all the elements that reference the PSHELL definitions with PID 1, 2, or 3. As no region identifier is defined, the stress responses for each PSHELL form their own regions. So, all of the stress responses for elements referencing PSHELL with PID1 are in a different region than all of the stress responses for elements referencing PSHELL with PID2, which in turn are in a different region than all of the stress responses for elements referencing PSHELL with PID3. If this response definition is constrained in an optimization problem, and the default settings for constraint screening are assumed, then 20 elemental stresses are considered for each of the three PSHELL definitions, i.e. 20 for each region, giving a total of 60 retained responses.

Example 2 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

DRESP1 2 label STRESS PSHELL 1 SMP1

1

2



(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) DRESP1 3 label STRESS PSHELL 1 SMP1

3

All of the stress responses defined in the DRESP1 entries above form a single region - notice the non-zero entries in field 6 (0 is equivalent to leaving it blank). Now, if these response definitions (which are of the same type (STRESS), with the same non-zero entry in field 6) are constrained in an optimization problem (assuming the default settings for constraint screening), then 20 elemental stresses are considered in total for the three PSHELL definitions because they form a single region.

2.5 Discrete Design Variables OptiStruct uses a gradient-based optimization approach for size and shape optimization. This method does not work well for truly discrete design variables, such as those that would be encountered when optimizing composite stacking sequences. However, the method has been adopted for discrete design variables where the discrete values have a continuous trend, such as when a sheet material is provided with a range of thicknesses. The adopted method works best when the discrete intervals are small. In other words, the more continuous-like the design problem behaves, the more reliable the discrete solution will be. For example, satisfactory performance should not be expected if a thickness variable is given two discrete values 0 and T.

It is known that rigorous methods such as branch and bound are very time consuming computationally. Therefore, we developed a semi-intuitive method that is targeted at solving relatively large size problems efficiently. It is recommended to benchmark the discrete design against the baseline continuous solution. This helps to quantify the trade-off due to discrete variables and to understand whether the discrete solution is reasonable. As local optima are always a barrier for none convex optimization problems, and discrete variables tend to increase the severity of this phenomenon, it could be helpful to run the same design problem from several starting points, especially when the optimality of a solution is in doubt.

It is also possible to mix these discrete variables with continuous variables in an optimization problem.

Discrete design variables are activated by referencing a DDVAL entry on a DESVAR card.

The DDVOPT parameter on the DOPTPRM card allows you to choose between a fully discrete optimization or a two phased approach where a continuous optimization is performed first, and a discrete optimization is started from the continuous optimum.

Chapter 3: Optimization Interface and Setup


Chapter 3

Optimization Interface and Setup

1 Model Definition Structure The input deck is formed per 3 different sections as shown on the following image:

Input deck example



1.1 Input/Output Section The I/O Section is the first part of a OptiStruct input file, it controls the overall running of the analysis or optimization. It controls for example the type, format, and frequency of the output, the type of run (analysis, check, or restart), and the location and names of input, output, and scratch files.

This is not a required section, if the user doesnt specify any I/O control this section will not be on the input deck, but OptiStruct has a default I/O setup that will generate these outputs:

1- ANALYSIS

o ASCII output

o .out This file is always created. It contains a report with comments on the solution process.

o .stat This file is always created. This file provides details on CPU and elapsed time for each solver module.

o HTML Reports

o .html This file is always created. This file contains a problem summary and results summary of the run.

o _frames.html This file is output when the H3D FORMAT is chosen. The file contains two frames. The top frame opens one of the .h3d files using the HyperView Player browser plug-in. The bottom frame opens the _menu.html file, which facilitates the selection of results to be displayed.

o _menu.html This file is output when the H3D FORMAT is chosen. This file facilitates the selection of the appropriate .h3d file, for the HyperView Player browser plug-in in the top frame of the _frames.html file, based on chosen results

o Model results



o .res The .res file is a HyperMesh binary results file.

o .h3d The .h3d file is a compressed binary file, containing both model and result data.

o HV session file

o .mvw The .mvw file is a HyperView session file that is linked with the h3d result file and can be open directly from HyperMesh using the HyperView button on OptiStruct or RADIOSS panel.

2- SIZE OPTIMIZATION

All the files generated on the ANALYSIS, with some small differences on:

o h3d results files:

o _des.h3d: This is the file to animate the Optimization history. The frequency on this file is defined by OUTPUT, DESIGN, ALL (Default = ALL).

o _s#.h3d: This file contains the analysis results for each loadcase. Optimization results can be written to the subcase files using DENSITY, SHAPE, or THICKNESS output requests

o HV session file:

o _hist.mvw: Design history output presentation for HyperGraph. It is linked with the

o ASCII files:

o .hist: Default it writes out: DVs, Obj., % max const. violation, all non-stress responses and all DRESP (2 and 3).

o .sh: Contain the Design Variable information to restart the optimization from the final iteration. It is controlled by SHRES.



o .desvar: It has the converged design variable values.

o .prop: Optimized property definition.

o .hgdata: Output history for HyperGraph. It is controlled by deshis = Yes (Default = Yes).

3- SHAPE OPTIMIZATION

All the files generated on SIZE optimization and more 2 ASCII files.

o ASCII files:

o .grid: Contain the node information translation for the final optimization iteration.

o .oss: It has the information to run OSSMOTH to generate the optimum topology for the model.

4- TOPOLOGY OPTIMIZATION

All the files generated on SIZE optimization, except the files .prop and .desvar and more 3 ASCII files:

o ASCII file:

o .oss: It has the information to run OSSMOTH to generate the optimum topology for the model.

o .HM.comp.cmf HyperMesh command file that can be used to isolate the elements in components based on the optimized density.

o .HM.ent.cmf HyperMesh command file that can be used to isolate the elements in sets based on the optimized density.

5- TOPOGRAPHY

All files generated on the SHAPE optimization.

6- GAUGE

All files generated on the SIZE optimization.

7- FREE-SHAPE

All files generated on the SHAPE optimization.

8- FREE-SIZE



All the files generated on TOPOLOGY optimization, except the file .hm.COMP.CMF.

9- COMPOSITE SHUFFLE

All the files generated on SIZE optimization, more 2 ASCII files:

o ASCII file:

o .prop: It has the information to run OSSMOTH to generate the optimum topology for the model.

o HTML Reports

o .shuf.html Laminate layout for the optimization iterations.

1.2 Subcase Information Section The Subcase or Case Control Section contains information for specific subcases. It identifies which loads and boundary conditions are to be used in a subcase. It can control output type and frequency, and may contain objective and constraint information for optimization problems. For more information on solution sequences, please see the table included on the Solution Sequences page of the help.

Descriptions for individual Subcase Control entries can be accessed on the online documentation.

1.3 Bulk Data Section The Bulk Data Section contains all finite element data for the finite element model, such as grids, elements, properties, materials, loads and boundary conditions, and coordinates systems. For optimization, it contains the design variables, responses, and constraint definitions. The bulk data section begins with the BEGIN BULK statement.



2 Optimization Setup The optimization cards can be divided in 2 groups according with the section on the input deck that this cards are localized.

o Subcase Information Entry DESGLB DESOBJ DESSUB DESVAR MINMAX or MAXMIN MODEWEIGHT MODTRAK NORM REPGLB REPSUB WEIGHT

o BULK Data Entry BEAD BMFACE DCOMP DCONADD DCONSTR DDVAL DEQATN DESVAR DLINK DLINK2 DOBJREF DOPTPRM DREPADD DREPORT DRESP1 DRESP2 DRESP3 DSCREEN DSHAPE DSHUFFLE DSIZE DTABLE DTPG DTPL DVGRID DVMREL1 DVMREL2 DVPREL1 DVPREL2

The complete descriptions of these cards are available at the online documentation.

2.1 Optimization GUI The optimization setup in HyperMesh can be made from 3 different areas:

Optimization Panel

Optimization Menu



Model Browser

2.2 Design Variable [ DTPL] To create and edit a design variable the user can chose one of the 3 options shown below:

Optimization panel Optimization Menu Model Browser

The procedure to create a design variable will be described later on each chapter as it define type of optimization that will be performed and have a different setup for each type.



2.3 Responses [DRESP1] To create and edit a response the user can chose one of the 3 options shown below:


This will open the response panel:

On this panel the user needs to:

1. Input a name to the response that needs to have less than 8 characters.

2. Choose the type of the response.

3. Choose where this response have to be evaluated:

a. If this is total or by entity. Ex. Mass, vol. etc

b. Choose the nodes/elements and the direction this will be evaluated. Ex. Static displacement

c. Exclude a group of elements that it should not be evaluated. Ex. Static Stress

d. For composite response the plies where it should be evaluated. Ex. Composite stress.

e. For FRF response choose between real, imaginary, magnitude and phase and the request (All freq; Freq =; sum; avg; ssq; rss; max; min; avgabs; maxabs; minabs; sumabs).

4. Define a region if necessary.

5. Create the response.



2.4 Dconstraints [DCONSTR] To create and edit a design constraint the user can chose one of the 3 options shown below:


This will open the constraints panel:


1. Input a name for this constraint

2. Select the response where this limits will be applied.

3. If this response is dependent of the loadstep, a yellow button will appear and the user need to select the appropriate loadsteps where this limits should be applied.

4. Create the constraint.



2.5 Obj. reference [DOBJREF] To create and edit an objective reference vector the user can chose one of the 3 options shown below:


This will open the objective reference panel:


1. Input a name for this reference vector

2. Select the response where these coefficients will be applied. The positive and negative value should be use together if the user is looking for the maximum or minimum absolute value, for example min(max(|S3|)). The most common usage is the positive reference. min(max(von Mises)).

3. Define if it is applied to all loadsteps or to specific ones.

4. Create the Objective reference vector.



2.6 Objective [DESOBJ] To create and edit an objective function the user can chose one of the 3 options shown below:


This will open the objective panel:


1. Select the response that will be optimized.

2. Define if the response will be minimized or maximized.

3. For MinMax or MaxMin response with multiple values the user needs to use the objective reference vector that can be created using the procedure described on the last section.



2.7 Table entries [DTABLE] To create and edit a list of constants the user can chose one of the 3 options shown below:


This will open the Table Entries panel:


1. Input the name and the value of all constants that can be used to define the generic functions and create them.



2.8 Dequations [DEQATN] To create and edit a function or design equation the user can chose one of the 3 options shown below:


This will open the Dequations panel:


1. Input the name for the function.

2. Input the mathematical expression for the function. Ex. F(x,y)=x**2+2+y. 3. Create the function.



2.9 Discrete DVs [DDVAL] To create and edit a Discrete Design Variable list the user can chose one of the 3 options shown below:


This will open the Discrete Design Variables panel:


1. Input the name for the list

2. Input the list values separated by comma or with X0, Xf and X to automatically generate it.

3. Create the list.



2.10 Opti. control [DOPTPRM] To add or edit the optimization parameters the user can chose one of the 2 options shown below:


This will open the Optimization Control Parameters panel:


1. Mark the parameter that needs to be modified and input the value for it.

2.11 Constr. screen [DSCREEN] To add or edit the optimization parameters the user can chose one of the 2 options shown below:


This will open the Constraint Screening panel:



( )

15 h 515 b 5

ton040.51

EMassfMin


1. Mark the response type that the solver will take a sub-group.

2. Define the threshold that is a reference value to compare with the normalized constraint to select the sub-group that will be monitored by the solver. if f >= threshold* and the N < max retained the response is add to the monitored list.

optistruct manual 11

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