OS 10.0 First Draft

HyperWorks 10.0 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 Elements Analysis ........................................................................................5

2.2 – Multi-body Dynamics 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 ...................................................................................22

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

1.4 – Optimization Cards...............................................................................................37

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

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

2.2 – Design Variable [ DTPL] .......................................................................................39

2.3 – Responses [DRESP1] ..........................................................................................39

2.4 – Dconstraints [DCONSTR].....................................................................................40

2.5 – Obj. reference [DOBJREF] ...................................................................................41

2.6 – Objective [DESOBJ] .............................................................................................42

2.7 – Table entries [DTABLE]........................................................................................43

2.8 – Dequations [DEQATN] .........................................................................................43

2.9 – Discrete dvs [DDVAL]...........................................................................................44

2.10 – Opti. control [DOPTPRM] ...................................................................................45

2.11 – Constr. Screen [DSCREEN] ...............................................................................45

3 – How to Setup an Optimization on HyperMesh .........................................................46

Chapter 4: Concept Design ...................................................................................51

1 – Topology Optimization ............................................................................................51

1.1 – Homogenization method.......................................................................................52

1.2 – Density method ....................................................................................................53


IV

Exercise 4.1 – Topology Optimization of a Hook with Stress Constraints ......................54

Exercise 4.2 – Topology Optimization of a Control Arm.................................................62

2 – Topography Optimization ........................................................................................67

2.1 – Design Variables for Topography Optimization.....................................................67

2.1.1 – Variable Generation...........................................................................................68

2.1.2 – Multiple Topography Design Regions ................................................................69

Exercise 4.3 – Topography Optimization of a Slider Suspension...................................70

3 – Free-size Optimization.............................................................................................74

Exercise 4.4 – Free-size optimization of Finite Plate with hole ......................................78

Chapter 5: Fine-Tuning ..........................................................................................85

1 – Size Optimization ....................................................................................................85

1.1 – Design Variables for Size Optimization.................................................................86

Exercise 5.1 – Size Optimization of a Rail Joint.............................................................87

2 – Shape Optimization .................................................................................................96

2.1 – Design Variables for Shape Optimization .............................................................97

2.2 – HyperMorph .........................................................................................................98

2.2.1 – The Three Basic Approaches to Morphing.........................................................98

Exercise 5.2 – Shape Optimization of a Rail Joint .......................................................100

3 – Free-shape Optimization .......................................................................................117

3.1 – Defining Free-shape Design Regions .................................................................117

3.2 – Free-shape Parameters......................................................................................119

3.2.1 – Direction type ..................................................................................................119

3.2.2 – Move factor .....................................................................................................120

3.2.3 – Number of layers for mesh smoothing .............................................................120

3.2.4 – Maximum shrinkage and growth ......................................................................121

3.2.5 – Constraints on Grids in the Design Region ......................................................122

Exercise 5.3 – Free-shape optimization Compressor Bracket .....................................125

Chapter 1: Introduction

HyperWorks 10.0 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 10.0 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 exercises 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, this include:

Basic analysis features

o Linear static analysis.

o Normal modes analysis.

o Linear buckling analysis.

o Thermal-stress steady state analysis

Advanced analysis features

o Frequency response function (FRF) analysis

o Direct

o Modal

o Random response analysis

o Transient response analysis

o Direct

o Modal

o Transient response analysis based on the Fourier method

o Direct

o Modal

o Non-linear contact analysis

o Acoustic Analysis (Structure and Fluid)

o Fatigue Analysis (σN and εN)

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. 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, 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: ψ0(p) ⇒ min(max) (target)

Subject to constraint Functions: ψi(p) ≤0

Design Space: pl ≤ pj ≤ pu where l is the lower bound and u is the

upper bound on the design variables

where:

ψψψψ0(p) and ψψψψi(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 V

VV

0

=

where:

Vf : Volume fraction D

iV : Designable volume at current iteration;

DV0 : Initial Designable volume;

0M

MM i

f =

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 fu

2

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 λ

λ 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

ii w

w

NORMCwSλ

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

minmaxλCNF =

where Cmax is the highest compliance value in all subcases (loadsteps, load cases) and λλλλmin 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 optimiz ation

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

σdvεKuu

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 mym

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 σσσσmax value,

2) Max shear stress can not exceed the ττττmax 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: σ (b,h) = 6F/(bh2) ≤ σmax, with σmax = 70 MPa

τ (b,h) =F/(bh) ≤ τmax, with τmax = 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 50.00

b (mm)

h (m

m)

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

σ=70 τ=15

ττττ > 15

ττττ < 15

σσσσ>70

σσσσ<70

W = 5

W = 7

W = 9

W = 11

FEASIBLE DOMAIN

UNFEASIBLE DOMAIN

OPTIMUM



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 - γ ∇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 ψi(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.

dvn

dR

dv

dR

dv

dR,...,

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.

dvn

dR

dv

dR

dv

dR,...,

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 shoed 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 doesn’t 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 <model_file_name>.out This file is always created. It contains a report with comments on the solution process.

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

o HTML Reports

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

o <model_file_name>_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 <model_file_name>_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 <model_file_name>.res The .res file is a HyperMesh binary results file.



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

o HV session file

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

o ASCII files:

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

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

o <model_file_name>.desvar: It has the converged design variable values.

o <model_file_name>.prop: Optimized property definition.

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

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

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

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

o HTML Reports

o <model_file_name>.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:

Optimization panel Optimization Menu

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:

Optimization panel Optimization Menu

This will open the Constraint Screening panel:



( )

15 h 5

15 b 5

ton040.51

≤≤≤≤

−≤ EMass

fMin


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 Φ to select the sub-group that will be monitored by the solver. if f >= threshold*Φ and the N < max retained the response is add to the monitored list.

3 – How to setup an optimization on HyperMesh Let’s proposal a very simple problem, a 2D cantilever beam that will be simulated using CBAR element with a PBARL property, the model properties are described below:

Optimization model description (2 D)

• Geometry:

o (L = 1000, h0 = 10, b0 = 10 mm)

• One load case: Normal Modes

o First mode

• Material STEEL:

o ρ = 7.8e-9 t/mm3 [RHO] Density o E = 210000 MPa [E] Young’s modulus o ν = 0.3 - [nu] Poisson’s ratio



Step 1 - Setup the Finite element analysis.

This model is already setup on a HyperMesh database, called beam.hm, and the input deck for it is showed below:

SUBCASE 1 SPC = 1 METHOD(STRUCTURE) = 2 BEGIN BULK GRID 1 0.0 0.0 0.0 GRID 2 1000.0 0.0 0.0 CBAR 1 1 1 20.0 1.0 0.0 PBARL 1 1 BAR + + 10.0 10.0 MAT1 1210000.0 0.3 7.80E-09 EIGRL 2 1 MASS SPC 1 1 1234560.0 SPC 1 2 3 0.0 ENDDATA

Step 2 - Define the Design Variables.

On main menu select Optimization > Create > Size Desvars:

This creates on the bulk data section:

DESVAR 1 b10.0 5.0 15.0 DESVAR 2 c10.0 5.0 15.0

Create a Design variable as showed above for b and c. Associate them with the Dimension 1 and Dimension 2 of the beam property as showed below:


DVPREL1 1 PBARL 1DIM1 0.0

+ 1 1.0

DVPREL1 2 PBARL 1DIM2 0.0

+ 2 1.0



Step 3 - Define the Responses.

On main menu select Optimization > Create > Response:

Create a Response as showed above f1 for first frequency and another response called Mass for the total mass on the model.


DRESP1 1 f1 FREQ 1 DRESP1 2 Mass MASS

Step 4 - Define the constraints.

On main menu select Optimization > Create > Constraints:

Create a Constraint CMass as showed below:

This creates on the Subcase Information section:

DESGLB 2


DCONSTR 1 2 5.00E-04

DCONADD 2 1

Step 5 - Define the Objective

On main menu select Optimization > Create > Objective:

Create a objective function Maximize f1 as showed below:

This creates on the Subcase Information section:

DESOBJ(MAX)=1



Step 6 - Run the Simulation.

On main menu select Application > OptiStruct:

Chose the directory where it should run:

FINAL SETUP

DESGLB 2 SUBCASE 1 SPC = 1 METHOD(STRUCTURE) = 2 DESOBJ(MAX)=1 BEGIN BULK DESVAR 1 b10.0 5.0 15.0 DESVAR 2 c10.0 5.0 15.0 DVPREL1 1 PBARL 1DIM1 0.0 + 1 1.0 DVPREL1 2 PBARL 1DIM2 0.0 + 2 1.0 DRESP1 1 f1 FREQ 1 DRESP1 2 Mass MASS DCONSTR 1 2 5.00E-04 DCONADD 2 1 GRID 1 0.0 0.0 0.0 GRID 2 1000.0 0.0 0.0 CBAR 1 1 1 20.0 1.0 0.0 PBARL 1 1 BAR + + 10.0 10.0 MAT1 1210000.0 0.3 7.80E-09 EIGRL 2 1 MASS SPC 1 1 1234560.0 SPC 1 2 3 0.0 ENDDATA



Chapter 4: Concept Design


Chapter 4

Concept Design

1 – Topology Optimization Topology Optimization is a mathematical technique that produces an optimized shape and material distribution for a structure within a given package space. By discretizing the domain into a finite element mesh, OptiStruct calculates material properties for each element. The OptiStruct algorithm alters the material distribution to optimize the user-defined objective under given constraints.

Example of a topology optimization

OptiStruct solves topological optimization problems using either the homogenization or density method. Under topology optimization, the material density of each element should take a value of either 0 or 1, defining the element as being either void or solid, respectively.



Unfortunately, optimization of a large number of discrete variables is computationally prohibitive. Therefore, representation of the material distribution problem in terms of continuous variables has to be used.

1.1 - Homogenization method

For the homogenization method, the material of the structure is represented as a porous continuum with certain periodic microstructure or layered composites of different ranks of densities. The homogenization method implemented in OptiStruct uses a material microstructure that contains periodic rectangular voids (hexahedral voids in 3-D). The design variables for each element are the breadth and depth of these rectangular voids and their orientations. These define the elasticity properties and the density of the material.

Using a normalized formulation, the density of an element may be determined by:

( )( )ba −−−= 0.10.10.1ρ

where (1.0 – a)(1.0 – b) represents the total volume of void in an element. It is easy to see that a=b=0 represents the state of void for this element, and a=1 or b=1 implies that the element is solid, i.e. filled with the 'real' material. Intermediate values of a and b represent fictitious material.

The void size variables are considered to be continuous variables varying between 0 and 1. The void orientation of each element is also a continuous variable, which is determined by the orientation of the principle strain. Note that while the real material is isotropic, the fictitious material of intermediate density is anisotropic.

1.2 - Density method

With the density method, the material density of each element is directly used as the design variable, and varies continuously between 0 and 1; these represent the state of void and solid, respectively. As with the homogenization method, intermediate values of density represent fictitious material.

With this method, the stiffness of the material is assumed to be linearly dependent on the density. This material formulation is consistent with our understanding of common materials. For example, steel, which is denser than aluminum, is stronger than aluminum. Following this logic, the representation of fictitious material at intermediate densities is more realistic under the density approach. An anisotropic representation of the semi-dense material is not consistent with the behavior of the real isotropic material, although it is more 'efficient' due to optimal material orientation.

In general, the optimal solution of problems, using both formulations (Homogenization and Density), involves large gray areas of intermediate densities in the structural domain. Such solutions are not meaningful when we are looking for the topology of a given material, and not meaningful when considering the use of different materials within the design space. Therefore, techniques need to be introduced to penalize intermediate densities and to force the final design to be represented by densities of 0 or 1 for each element. The penalization technique used for the density approach is the "power law representation of elasticity properties," which can be expressed for any solid 3-D or 2-D element as follows:



( ) KK pρρ =

where K and K represent the penalized and the real stiffness matrix of an element, respectively, ρ is the density and p the penalization factor which is always greater than 1.



Exercise 4.1: Topology Optimization of a Hook with Stress Constraints

In this exercise, a topology optimization is performed on a bracket-hook modeled with shell elements. The structural model with loads and constraints applied is shown in the figure below. The objective is to minimize the volume of the material used in the model subject to certain stress constraints. Topology optimization is performed to find the optimal material placement and reduce the volume. This optimization normalizes each element according to its density and lets you remove elements that have low density.

FEA model

The structural model is loaded into HyperMesh. The constraints, loads, subcases and material properties are already defined in the model. The topology design variables and the optimization problem set up will be defined using HyperMesh, and OptiStruct will be used to determine the optimal material layout. The results will then be reviewed in HyperView.

The optimization problem is stated as:

Objective function:

Minimize volume.

Constraints: Von Mises stress < 1.6 e 04.

Design Variables: The density of each element in the design space.



Step 1: Launch HyperMesh and Set the User Profile

1. Launch HyperMesh through the start menu.

The User Profiles dialog will appear by default.

2. Choose OptiStruct as the user profile by selecting the radio button beside it.

3. Click OK.

Step 2: Import the Finite Element Model File

The model file for this exercise, hook.fem.

1. Select the Import button .

An Import tab is added to your tab menu.

2. Make sure the Import type: is set to FE Model .

3. Make sure the File type: is set to Optistruct .

4. Click the Select files button.

5. Browse for your file and select it.

6. Click Open .

7. Click Import .

Step 3: Set a Front View

1. Press the v key on the keyboard to activate the view menu.

2. Select Front from the list.

3. Go to the forces panel.

4. Set the magnitude % to .5.

5. Go to the constraints panel.

6. Set the size to 1.0.

7. Click return .

8. Press f on the keyboard.



Step 4: Create the Design Variables for Topology Op timization

1. On Analysis page select the optimization panel.

2. Click the topology panel.

3. Select the create radio button.

4. Click props and select the check boxes by the Design and Base properties.

5. Click select .

6. Enter the name shells in the desvar= field.

7. Set the component type: switch to PSHELL .

8. Click create .

9. Select the parameters subpanel.

10. Toggle minmemb off to mindim= .

11. For mindim= , enter 0.3.

12. Under stress constraint: , toggle from none to stress= .

13. For stress= , enter 1.6e4.

14. Click update .

This value is the stress constraint for the model.

15. Click return twice to get back to the main menu.

Step 5: Create the Responses

A detailed description is available in the OptiStruct User's Guide, under Responses.

1. Select the optimization panel.

2. Click responses to go to the Responses panel.

3. Click response = and enter volume.

4. Click the response type: switch and select volume from the pop-up menu.

5. Ensure that the total/by entity toggle is set to total (this is the default).



6. Click create .

A response, volume , is defined for the total volume of the model.

7. Click return to go back to the optimization panel.

Step 6: Define the Objective Function

In this example, the objective is to minimize the volume response defined in the previous step.

1. Select the objective panel.

2. Click the switch in the upper left corner of the panel and select min from the pop-up menu.

3. Click response = and select volume from the response list.

4. Click create .

The objective function is now defined.

5. Click return to return to the optimization panel.

Step 7: Save the HyperMesh Database

1. Click the Save .hm File button .

A Save file... browser window pops up.

2. Select the directory where you would like to save the database and enter the name for the database, hook_opt.hm, in the File name: field.

3. Click save .

Step 8: Submit the Job to OptiStruct

1. From the Analysis page, select the OptiStruct panel.

2. Click save as… following the input file: field.

3. Select the directory where you would like to write the OptiStruct model file and enter the name for the model, hook_opt.fem, in the File name: field.

.fem is the suggested extension for OptiStruct input decks.

4. Click Save.



Note the name and location of the hook_opt.fem file displays in the input file: field.

5. Make sure the memory options: toggle is set to memory default .

6. Click the run options: switch and select optimization .

7. Make sure the export options: toggle is set to all .

8. Click OptiStruct .

This launches the OptiStruct job. If the job was successful, new results files can be seen in the directory where the OptiStruct model file was written. The hook_opt.out file is a good place to look for error messages that will help to debug the input deck if any errors are present.

Step 9: View an Isosurface Plot of the Density Resu lts

1. While still in the OptiStruct panel, click the green HyperView button.

HyperView launches and load the section file hook_opt.mvw that is linked with all the .h3d file generated by OptiStruct .

2. Click the iso Value toolbar button .

3. Select the Result type: Element densities (s) .

4. At the bottom of the GUI, click in the portion circled below to activate the Load Case and Simulation Selection dialog.

5. Selection the last iteration listed in the Simulation list.

6. Make sure that Show is set to above .

7. Click Apply .

8. Move the below Current value: slider to look at the element densities.

9. You can also enter a value of 0.3 in the Current value: field.



The isosurface post-processing feature is an excellent tool to use for viewing the density results from OptiStruct.

10. Click and move the slider bar (currently pointing to a value representing 0.3) for your density to change the isosurface.

You will see the isosurface in the graphics window interactively update when you change it to a new value. Use this tool to get a better look at the material layout and the load paths from OptiStruct.

11. Click Clear Iso .

Step 10: View the Element Stress Results

1. Click the Next Page toolbar button to move to the second page.

The second page, which has results loaded from the hook_opt_s19.h3d is displayed; this contains the linear static results for the 1st subcase.

2. Click the Contour toolbar button .

3. Select the first pull-down menu below the Result type: and select Element stresses .

4. Select the second pull down menu and select vonMises .

5. At the bottom of the GUI, click in the portion circled below to select the last Iteration.



7. Click Apply .

8. To better understand the whole simulation it is good to show all subcases on one page, it

can be done using the Page Layout button , where you choose the layout .

9. Use the Edit > Copy Window pull-down menu to copy the other subcase results from the pages 3,4 and 5 and past this on the respective window on the page 2 as showed below.

Stress results for all static sub case (Von Mises < 1.6e4)

Notice that there are some local regions where the stresses are still high; this is because topology stress constraints should be interpreted as global stress control or global stress target.

The functionality has some ways to filter out the artificial or local stresses caused by point loading or boundary conditions, but those artificial stresses will not be completely removed unless the geometry is changed by shape optimization.

Step 11: Query the Results of the Elements with Str esses Higher than 1.6e4

1. With the first window selected click on the Query toolbar button .

2. Under Elements , uncheck the options which are not needed and then click on Elements and choose By Contour .

3. Next to Method , choose By Contour .

4. Below value , enter >16000 and click Apply .



This would give a list of elements with the stress value above 16000; use the mask option to graphically find the elements above the stress value.

Query results table

Mask panel

Notes: The advantages of using stress based optimization over the classical minimize (compliance) subject to volume fraction constraint is that it eliminates the guessing of the right volume fraction. Additionally, it eliminates the need for compliance weighting bias for multiple subcases.

There might still be high local stress regions which can be improved more effectively with local shape and size optimization.



Exercise 4.2: Topology Optimization of a Control Ar m

The purpose of this exercise is to determine the best topology or the minimum mass for a control arm that is manufactured using a single draw mode. The arm needs to have a symmetric geometry because it will be used on both sides of the vehicle.

On the image below is already defined the finite element model that defines where the material can be removed or not. There are two different regions that are denominated Design (blue) that is where OptiStruct can remove material and Non-design (red) where this part will be mounted and can’t be changed.

The control arm can be considered totally fixed for all load cases as follow:

o NODE(3) X,Y and Z . (Bolted)

o NODE(4) Y and Z . (Cylindrical joint)

o NODE(7) Z. (Damp link)

This control arm needs to support 3 different load cases, and the design criterion for each load case is defined as strength constraints as:

1. Car turning on a intersection: corner = (0,1000,0) N Umax (2699) <= 0.02 mm

2. Car braking: brake = (1000,0,0) N Umax (2699) <= 0.05 mm

3. Car passing in a pothole: pothole (0,0,1000) N Umax (2699) <= 0.04 mm

Problem Setup

You should copy these Files: CONTROL_ARM.hm;



Step 1: Open the CONTROL_ARM.hm model on HyperMesh.

Step 2: Define 2 different PSOLID properties: desig n (1) and nondesign (2), both with material 1 and colors as showed on the compone nts.

We will create 2 different properties to isolate the Design space. All elements that will have the property design can be removed during the optimization process.

Model Browse tree after the properties creation

Step 3: Assign the properties to the components.

The property can be associated directly with the elements too, but on this case the easiest way is to associate the property with the component.

Step 4: Define 3 different loadsteps: Corner (1), B rake (2) and Pothole (2).

As was described on the beginning of this exercise, this part needs to perform well on 3 different load cases and as we can see below they have different direction. It makes necessary to define independent load cases for each one.

1. All load cases have the same constraints:

NODE(3) X,Y and Z . (Bolted)

NODE(4) Y and Z . (Cylindrical joint)

NODE(7) Z. (Damp link)

2. For corner (1) load step the force F = (0,1000,0) N applied on Node(2699)

3. For brake (2) load step the force F = (1000,0,0) N applied on Node(2699)

4. For pothole (3) load step the force F = (0,0,1000) N applied on Node(2699)



Model Browse after the load steps.

Step 5: Run the analyses and get the maximum displa cement for each loadstep.

It would take ~3 min, continue the exercise and later you should fill out the values below:

Corner (1) Total displacement (2699) = _________

Brake (2) Total displacement (2699) = _________

Pothole (3) Total displacement (2699) = _________

It is important to run an initial analysis to understand the model solution. If the responses are far from the desired values, the model need to be modified or the optimization problem redefined. It is very important at this point the user validate the problem and understand if the optimization setups that will be performed make sense.

Step 6: Define the topology design variable for the design region.

5. Define the symmetric manufacturing constraint 1-pln sym using as anchor node (1) and as first node (2).



6. Define the draw manufacturing constraint as single using as anchor node (6) and first node (5) and the nondesign property as obstacle.

Step 7: Define the volume response, call it volume.

Step 8: Define the displacement response on the bal l join node (2699), select total displacement, and call it DISP.

Step 6: Define the displacement constraint for each loadstep. Corner Umax (2699) <= 0.02 mm

Brake Umax (2699) <= 0.05 mm

Pothole Umax (2699) <= 0.04 mm



Step 7: Define the volume as objective function.

Step 8: Submit the optimization run.

Job submission panel (It should take ~ 1.5 h to complete)

Step 9: Open the results on HV and answer these que stions:

1. The solution converged to a feasible solution?

2. How much iteration it has take to converge and how much is the final volume of the part?

3. Plot the Iso-contour for the density on the last iteration, does it looks like a manufacturable part?

Design proposed by OptiStruct



2 – Topography Optimization

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.

The approach in topography optimization is similar to the approach used in topology optimization, except that shape variables are used rather than density variables. The design region is subdivided into a large number of separate variables whose influence on the structure is calculated and optimized over a series of iterations. The large number of shape variables allows the user to create any reinforcement pattern within the design domain instead of being restricted to a few.

2.1 - Design Variables for Topography Optimization

OptiStruct solves topography optimization problems using shape optimization with internally generated shape variables. One or more design domains are defined using the DTPG card. These cards must, in turn, reference PSHELL , PCOMP or DESVAR definitions. If a DESVAR definition is referenced, it must be a shape design variable, meaning that it must, in turn, be referenced by one or more DVGRID cards. If a PSHELL or PCOMP definition is referenced, OptiStruct generates shape variables using the parameters defined on the DTPG card, creating internal DVGRID data for the nodes associated with the PSHELL or PCOMP definitions. In both cases, the end result is that each DTPG card references a single shape variable. This shape variable then gets converted into topography shape variables.

Basic topography shape variables follow the user-defined parameters on the DTPG card (minimum bead width, and draw angle), they are circular in shape, and they are laid out across the design domain in a roughly hexagonal distribution . Each topography shape variable has a circular central region of diameter equal to the minimum bead width. Grids within this region are perturbed as a group, which prevents the formation of any reinforcement bead of less than the minimum bead width. Grids outside of the central circular region of the topographical variables are perturbed as the average of the variables to which they are nearest. This results in smooth transitions between neighboring variables. If two adjacent variables are fully perturbed, all of the nodes between them will be fully perturbed. If one variable is fully perturbed and its neighbor is unperturbed, the nodes in between will form a smooth slope connecting them at an angle equal to the draw angle. The spacing of the variables is determined by the minimum bead width and the draw angle in such a way that no part of the bead reinforcement pattern forms an angle greater than the draw angle.

Pattern grouping options link topographical variables together in such a way that the desired reinforcement patterns are formed. Linear, planar, circular, radial, etc. shaped reinforcements are controlled by single variables, ensuring that the reinforcements follow the desired pattern. One-plane, two-plane, three-plane and cyclical symmetry pattern grouping options also use a similar approach to ensure that symmetry is created in the solution.

Although topography optimization is primarily a tool for creating bead type reinforcements in shell elements, it can accommodate solid models as well. Many pattern



grouping options (such as planar and cylindrical) are intended to be used with solid models since they effectively reduce 3-D problems into 2-D ones.

2.1.1 – Variable Generation

There are three methods of automatically generating shape variables for topography optimization using the DTPG card. The first two, element normal and draw vector , are performed entirely in OptiStruct. The third (user-defined ) requires that the input data contain one or more shape design variables that are used as the design domain.

Element normal

This method is the easiest one to use. When norm is entered for the draw direction, the normal vectors of the elements are used to define the draw vector for the shape variables. This method is especially effective for curved surfaces and enclosed volumes where the beads are intended to be drawn normal to the surface.

Beads created using the element normal

method of determining draw vector.

Draw vector

This method allows you to define the draw vector that is used for generating the shape variables. The X, Y, and Z components of the draw vector in the nodal coordinate system are entered. This method is useful when all beads must be drawn in the same direction. Note that the draw angle may not be maintained while using this method.

Beads created using the Draw vector method of determining draw vector.



User-defined

This method allows you to set up the vectors and heights for the topography optimization. A DESVAR card is referenced in place of a PSHELL or PCOMP card. All of the grids with DVGRID cards associated with that DESVAR card are considered part of the design domain. The DESVAR and DVGRID entries are redefined to reflect the minimum bead width and draw angle parameters that have been set by the user. The vectors and magnitudes of the displacement vectors on each DVGRID card for each grid are retained, so these entries must be left blank on the DTPG card. This allows you to create a design domain in which each node can have its own draw vector and draw height. For more information about it see the example Using Topography Optimization to Forge a Design Concept O ut of a Solid Block.

Example of Topography optimization using DVGRID direction

2.1.2 – Multiple Topography Design Regions

OptiStruct generates topography shape variables for each design domain defined by a DTPG card. It allows for overlapping of design domains. A grid that is in more than one design domain will be a part of shape variables for each design domain. For automatically generated bead variables, the draw height is divided by the number of bead variables acting on that grid. Thus, if a grid is a part of two DTPG cards that have draw heights of 3.0mm and 5.0mm, the draw heights become 1.5mm and 2.5mm. If this is not desired, simply make sure that no grid is in more than one design domain. In cases where two design components touch each other and the design domains are not user-defined (i.e. PSHELL or PCOMP definitions are referenced), a row of non-design elements needs to be inserted between them to prevent averaging. If the bead variables are user-defined (i.e. DESVAR definition is referenced), no averaging will be performed. It is assumed that the user intends to have the shape variables overlap, which will result in the grid deflection being cumulative between multiple influencing bead cards.

Bead Discreteness Fraction

The bead discreteness fraction is a response that can be used to control the amount of shape variation 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.



Exercise 4.3: Topography Optimization of a Slider S uspension

On this exercise we will look for the best stamped shape for a slider suspension, the objective function will be a combination of the compliance and the frequency, the objective is to have it as stiffer as possible for the static force, and a stiffer dynamic behavior on the lower frequencies, this function can be defined on OptiStruct as a combined weighted compliance and the weighted modes . The design has an extra constraint on the 7th mode that has to be higher than 12 Hz. The finite element model of the slider suspension contains already the force and boundary conditions and the 2 load cases defined frequency (1) and force (2).

Disk drive slider

Problem Statement

Perform combined topology and topography optimization on a disk drive slider suspension to maximize the stiffness and weighted mode. The lower bound constraint on the seventh mode is 12Hz.

Objective function: Minimize the combined weighted compliance and the weighted modes .

Constraints: 7th Mode > 12 Hz.

Design variables: Nodes topography.

Problem Setup

You should copy these Files: Slider.fem;



Step 1: Import the finite element model Slider.fem.

Step 2: Run the analyses and get the compliance for the 2nd loadstep and the mode values on the 1 st load step.

Extract the values:

Compliance = _________

f1 = _____(Hz) f2 = _____(Hz) f3 = _____(Hz) f4 = _____(Hz)

f5 = _____ (Hz) f6 = _____(Hz)

If you are using a second monitor, take advantage of your output file and copy the values using Ctrl C.

It is important to run an initial analysis to understand the model solution. If the responses are far from the desired values, the model need to be modified or the optimization problem redefined. It is very important at this point the user validate the problem and understands if the optimization setup that is going to be performed makes sense.

Step 3: Define the topography design variable for t he design region.

1. Create the DV named topo with this parameters:

a. props = 1pin .

b. minimum width = 0.4 mm

c. draw angle = 60 degree

d. draw height = 0.15 mm

e. draw direction = normal to elements.

f. Boundary skip : load & spc * OS will not move this nodes.

g. Upper Bound = 1.0 (x)

h. Lower Bound = 0.0 (x)



Step 4: Define the response to measure the 7 th mode, call it freq7 .

Step 5: Define the combined response comb to sum the compliance from the static analysis and the normalized modes from the m odal analysis.

1. This response type is compliance index .

2. The loadstep is the Static analysis.

3. For the model list set as on the table:

Mode Weight

1 1.0

2 2.0

3 1.0

4 1.0

5 1.0

6 1.0

4. Define the it as autonorm

Step 6: Define the constraint cfreq7 ⇒⇒⇒⇒ 7th mode > 12 Hz.

Step 7: Define min comb response as objective.


Job submission panel (It should take ~ 30 seconds to complete)



2. How much iteration it has take to converge and how much is part improved?

3. Plot the contour for the shape change on the last iteration, does it looks like a manufacturable part?



Design proposed by OptiStruct

If the student had finish the exercise and wants to try a more advanced setup, these are a small list of things that could improve this result:

1. Add a topology optimization on the same design space.

2. Add a symmetry plane to the topography and topology DVs.

3. Increase the Height to 0.2 mm.

4. Use OSSMOOTH to export the geometry.

5. Prepare a HV report to describe the optimization results.

6. Export the final shape and rerun an analysis to check the performance.



3 – Free-size Optimization The purpose of composite free-sizing optimization is to create design concepts that utilize all the potentials of a composite structure where both structure and material can be designed simultaneously. By varying the thickness of each ply with a particular fiber orientation for every element, the total laminate thickness can change ‘continuously’ throughout the structure, and at the same time, the optimal composition of the composite laminate at every point (element) is achieved simultaneously. At this stage, a super-ply concept should be adopted, in which each available fiber orientation is assigned a super-ply whose thickness is free-sized.

For a shell cross-section (shown below), free-size optimization allows thickness to vary freely between T and T0 for each element; this is in contrast to topology optimization which targets a discrete thickness of either T or T0.

Free size definition

In addition, in order to neutralize the effect of stacking sequence, the SMEAR option is usually a good choice for this design phase unless the user intended to follow through with the stacking preference of the super-ply laminate model.

Coupling between total Thickness and Laminate Families (%0 %45…)

To determine the optimum laminate OptiStruct uses the SMEAR technology that captures the stacking sequence effects:

o A = Stacking Sequence independent

o B = 0 (Symmetric)

o D = At2/12 - Stacking Sequence Independent

In OptiStruct, additional manufacturing constraints are available for free-sizing optimization. As a composite laminate is typically manufactured through a stacking and curing process, certain manufacturing requirements are necessary in order to limit undesired side effects emerging during this curing process. For example, one typical such constraint for carbon fiber reinforced composite is that plies of a given orientation cannot be stacked successively for more than 3 or 4 plies. This implies that a design concept that contains areas of predominantly a single fiber orientation would never satisfy this requirement. Therefore, to



achieve a manufacturable design concept, manufacturing requirements for the final product need to be reflected during the concept design stage. For the particular constraint mentioned above, for instance, the design concept would offer enough alternative ply orientations to break the succession of plies of the same orientation if the percentage of each fiber orientation is controlled (e.g. no ply orientation should drop below 15%). In addition, balancing of a pair of ply orientations could be useful for practical reasons. For example, balancing 45° and -45° plies would eliminate twisting of a plate bended along the 0 axis. In order to address these needs, the following manufacturing constraints are made available for composite free-sizing:

• Lower and upper bounds on the total thickness of the laminate.

• Lower and upper bounds on the thickness of individual orientations.

• Lower and upper bounds on the thickness percentage of individual orientations.



• Thickness balancing between two given orientations.

• Constant thickness of individual orientations.

Example: Cantilever plate

The cantilever plate is shown in the following figure. Base-plate thickness T0 is zero. The optimization problem is stated as: Minimize Compliance Subject to Volume fraction < 0.3

Cantilever Plate

The next figure shows the final results of topology and free-size optimization as performed on this plate, side by side. As expected, the topology result created a design with 70% cavity, while the free-size optimization arrived at a result with a zone of variable thickness panel.



Topology result Free-size result Compliance of both designs

It is not surprising to see that the free-size design outperforms the topology design in terms of compliance since continuous variation of thickness offers more design freedom.

It should be emphasized that free-size offers a concept design tool alternative to topology optimization for structures modeled with 2-D elements. It does not replace a detailed size optimization that would fine tune the size parameters of an FEA model of the final product.

To illustrate the close relationship between free-size and topology formulation, consider a 3-D model of the same cantilever plate shown previously. The thickness of the plate is modeled in 10 layers of 3-D elements.

Cantilever plate – 3-D model 3-D topology result

The topology design of the 3-D model shown above looks similar to the free-size results shown previously. This should not be surprising because when the plate is modeled in 3-D, a variable thickness distribution becomes possible under the topology formulation that seeks a discrete density value of either 0 or 1 for each element. If infinitely fine 3-D elements are used, a continuous variable thickness of the plate can be achieved via topology optimization. The motivation for the introduction of free-size is based on the conviction that limitations due to 2-D modeling should not become a barrier for optimization formulation. In regards to the 3-D modeling of shell, topology optimization is equivalent to the application of extrusion constraint(s) in the thickness direction of a 3-D modeled shell.

It is important to point out that while free-size often creates variable thickness shells without extensive cavity, it does not prevent cavity if the optimizer demands it. For the example already shown, we can see cavity in the free-size result in the 45 degree region, adjacent to the support, and in the upper and lower corners of the free end.

Free-size optimization is defined through the DSIZE bulk data entry that is supported in the HyperMesh optimization panel. Features available for free-size include: minimum member size control, symmetry, pattern grouping and pattern repetition, and stress constraints applied to von Mises stresses of the entire structure.

Involving both topology and free-size in the same optimization problem is not recommended since penalization on topology components creates a bias that could lead to sub-optimal solutions.



Exercise 4.4: Free-size Optimization of Finite Plat e with Hole

The exercise intends to describe the process of setup and post-process of a composite free-size optimization. The objective is to determine the minimum weight composite plate configuration. The plate can be formed with [0, 90, 45, -45] plies with, the initial design is 4 super plies with uniform thickness equal 12.7 mm. This plate needs to have a compliance lower or equal to 3000 Nmm, there are some manufacturing constraint that needs to be considered, the laminate thickness <= 40 mm, the ply thickness needs to be higher then 0.5 and lower then 12.7 mm, and the 45o and -45o plies need to be balanced.

Problem description

Model Information

On the left hand extreme is applied a uniform force of 60000 N the other extreme is fixed as showed on the image bellow.

• Geometry:

o (L = 457.2 mm, b = 152.4 mm, Thk = 12.7 mm/ply, diam. = 12.7 mm)

• One load case:

o Force = 60000 N

• Material:

E1 = 1.3e5MPa E2 = E3 = 9850 MPa υ12 = υ13 = 0.3 υ23 = 0.36 G12 = G13 = 3450MPa G23 = 3100MPa

Problem Setup

You should copy these Files: Finite_Plate_with_hole.hm;

F = 60000N Ux, Uz =0 All Nodes

Uz =0 Corner

Uy,Uz =0 Corner



Step 1: Open the HyperMesh database Finite_Plate_with_hole.hm.

This is 2D finite element model of a composite plate with 4 supper plies (0, 90, 45 and -45 degree) where each super ply has 12.7 mm of thickness. On the left rand side is applied a constant distributed force on all nodes where the sum is 60000 N.

For an isotropic linear material the normal stress far from the hole would be:

75.74.152*7.12*4

60000 ===Area

FSref MPa

It appear to be a simple model, and for an isotropic material this is true, but when this plate is a composite laminate with different angles this problem became much more complex. As we can see on the approximated diagram showed below for a single ply with the fiber align o different angles, the max stress values as showed bellow will be very dependent of the angle, and the concentration factor can be more than 6 times for example to a ply with 0o:

MAX Principal Stress

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

0.0 30.0 60.0 90.0 120.0 150.0 180.0

Theta

Sm

ax/S

ref

|Smax|/Sref(0o)|Smax|/Sref(90o)|Smax|/Sref(45o)|Smax|/Sref(-45o)

Stress variation around a hole for an infinite plate under constant stress.

The values on this plot may be used as reference to test if your mesh is refined enough to capture the concentration effect, to reproduce it your laminate may be formed with a unique ply angle. On our simple case the plies with different angles are mounted together to form a laminate and on it the concentration factor is even higher.

Step 2: Run the analyses.

Sref Sref θ



Step 3: Compare the stress values you have got with the values showed below:

S1 – Normal Stress on material fiber direction

Max stress on ply with angle zero.

Try to reproduce this curve on HyperGraph using the HV contour and Query to export the values. Your model has already sets to make it easy.

Hints: o Export the maximum principal S1 and the minimum principal S3 from HV. o Export the nodes coordinates from HV. (Stress_nodes ) o Determine the coordinate of a element mid node (lininterp ) [ElemX] X = NODE_NUM[0:178:1] Y=lininterp(NODE_NUM,X_node,x) [ElemY] X = NODE_NUM[0:178:1] Y=lininterp(NODE_NUM,Y_node,x)

o Determine the angle. (atan ) 90-atan(ElemX/ElemY)*180/PI o Use the logical function to get the maximum stress based on module of them.

SP1.y*((abs(SP1.y)-abs(SP3.y))>0)+SP3.y*((abs(SP1.y)-abs(SP3.y))<=0)



Now extract the optimization relative values:

1. Maximum strain for each ply:

o Ply 1 ( 0º ) = 9.66 x10-4 (mm/mm) Ply 2 (90º ) = 8.14 x10-4 (mm/mm)

o Ply 3 (45º ) = 9.63 x10-4 (mm/mm) Ply 2 (-45º ) = 1.23 x10-3 (mm/mm)

2. Total compliance = __4873_ Nmm

3. Total Volume = __3.53 x106 _ mm3

* If you are using a second monitor, take advantage of your output file and copy the values using Ctrl C.

It is important to run an initial analysis to understand the model solution. If the responses are far from the desired values, the model need to be modified or the optimization problem redefined. It is very important at this point the user validate the problem and understands if the optimization setup that is going to be performed makes sense. On the end of this exercise we will show some important aspects that the engineer should be careful to get a meaningful optimized result.

Step 4: Define the FREE SIZE design variable for th e design region.

It is a good procedure to save the HM database now with the optimization suffix. With it the user can always recover the analysis model for posterior studies.

FREE SIZE desvar definition

Step 5: Define the FREE SIZE design parameters.



Step 6: Define the total volume response.

Step 8: Define the total compliance response.

Step 9: Define the maximum compliance admissible.

Step 11: Define minimize the total volume as object ive.



Step 12: ADD the FREESIZE to SIZE output finite ele ment model.

This card will make OptiStruct on the end of the Free-size optimization export the input file with a predefined a size optimization. This file correspond to the second phase of composite optimization, to learn more about this the student should attend the HyperWorks composite training.


Job submission panel (It should take ~ 15 minutes to complete)

If time is a concern, there is a coarse mesh on the same directory that would take only a couple of minutes to run.


1. Have the solution converged to a feasible solution?

2. How much iteration it has taken to converge and how much is changed on volume?

3. Plot the contour of the thickness of each ply angle on the last iteration. Does it looks like a manufacturable part?

Ply thickness



4. On HyperMesh Import the model for size optimization and plot the plies.

0o plies shape

90o plies shape

45o and -45 o plies shape

Important remarks:

1. At the run directory exist a file called Finite_Plate_with_hole_optimization_sizing.#.fem that is the model prepared to size optimization with the plies already defined using PCOMPP-PLY-STACK approach.

2. It is important to remove the small segments or ill defined shapes to make it meaningful.

3. The best way to plot the layers is importing the size model on HyperMesh and using the mask function isolate the specific ply.

Chapter 5: Fine Tuning Design


Chapter 5

Fine Tuning Design

1 – Size Optimization OptiStruct has the capability of performing size optimization. Size optimization can be performed simultaneously with the other types of optimization.

In size optimization, the properties of structural elements such as shell thickness, beam cross-sectional properties, spring stiffness, and mass are modified to solve the optimization problem.

Defining size variables in OptiStruct is done very similarly to other size optimization codes. Each size variable is defined using a DESVAR bulk data entry. If a discrete design variable is desired, a DDVAL bulk data entry needs to be referenced for the design variable values. The DESVAR cards are related to size properties in the model using a DVPREL1 or DVPREL2 bulk data entry. Each DVPREL bulk data entry must reference at least one DESVAR bulk data entry to be active during the optimization. HyperWorks includes a pre-processor called HyperMesh that can be used to set up any number of size variables for the properties.

The following responses are currently available as the objective or as constraint functions:

Mass Volume Center of Gravity

Moment of Inertia Static Compliance Static Displacement

Natural Frequency Buckling Factor Static Stress, Strain, Forces

Static Composite Stress, Strain, Failure Index

Frequency Response Displacement, Velocity, Acceleration

Frequency Response Stress, Strain, Forces

Weighted Compliance Weighted Frequency Combined Compliance Index

Function



1.1 – Design Variables for Size Optimization

In finite elements, the behavior of structural elements (as opposed to continuum elements), such as shells, beams, rods, springs, and concentrated masses, are defined by input parameters, such as shell thickness, cross-sectional properties, and stiffness. Those parameters are modified in a size optimization. Some structural elements have several parameters depending on each other; like beams in which the area, moments of inertia, and torsional constants depend on the geometry of the cross-section.

The property itself is not the design variable in size optimization, but the property is defined as a function of design variables. The simplest definition, as defined by the design-variable-to-property relationship DVPREL1, is a linear combination of design variables defined on a DESVAR statement such that:

∑ ⋅+= ii CDVCp 0

where p is the property to be optimized, and Ci are linear factors associated to the design variable DVi.

Using the equation utility DEQATN, more complicated functional dependencies using even trigonometric functions can be established. Such design-variable-to-property relations are then defined using the DVPREL2 statement.

For a simple gage optimization of a shell structure, the design-variable-to-property relationship turns into

iDVt =

where the gage thickness t is identical to the design variable.

If a discrete design variable is desired, a DDVAL bulk data entry needs to be referenced on the DESVAR bulk data entry for the design variable values.



Exercise 5.1 – Size Optimization of a Rail Joint This exercise demonstrates how to perform a size optimization on an automobile rail joint modeled with shell elements. The structural model with loads and constraints applied is shown in the figure below. The deflection at the end of the tubular cross-member should be limited. The optimal solution would use as little material as possible.

Structural model of a rail joint.

The structural model, shown above, is loaded into HyperMesh. The constraints, loads, material properties, and subcases (loadsteps) are already defined in the model. Size design variables and optimization parameters are defined, and OptiStruct is used to determine the optimal gauges for the components. The results are then reviewed in HyperView.

The optimization problem for this tutorial is stated as:

Objective: Minimize volume.

Constraints: A given maximum nodal displacement at the loading grid point for two loading conditions.

Design variables: Gauges of the two parts.



Step 1: Launch HyperMesh, set the User Profile and Retrieve the File

1. Launch HyperMesh .

2. Choose the OptiStruct user profile dialog and click OK.

This loads the user profile. It includes the appropriate template, macro menu, and import reader, paring down the functionality of HyperMesh to what is relevant for generating models in Bulk Data Format for RADIOSS and OptiStruct. The User Profiles… GUI can also be accessed from the Preferences pull-down menu on the toolbar. Select the optimization panel on the Analysis page.

3. From the File pull-down menu on the toolbar, select Open… .

4. Select the joint_size.hm file.

5. Click Open .

Step 2: Create the Size Design Variables for Optimi zation

1. From the Analysis page, select the optimization panel.

2. Click on the size panel.

3. Make sure the desvar subpanel is selected using the radio buttons on the left-hand side of the panel.

4. Click desvar = and enter tube .

5. Click initial value = and enter 1.0 .

6. Click lower bound = and enter 0.1 .

7. Click upper bound = and enter 5.0 .

8. Make sure the move limit toggle is set to move limit default .

9. Make sure the discrete design variable (ddval) toggle is set to no ddval .

10. Click create .

A design variable, tube, has been created. The design variable has an initial value of 1.0, a lower bound of 0.1, and an upper bound of 5.0.

11. Repeat steps 4 through 10 to create the design variable rail using the same initial value, lower, and upper bounds.

A design variable, rail, has been created. The design variable has an initial value of 1.0, a lower bound of 0.1, and an upper bound of 5.0.

12. Select the generic property subpanel using the radio buttons on the left-hand side of the panel.

13. Click Name = and enter tube_th .



14. Click prop and select tube2 from the list of property collectors.

15. Make sure the toggle is set to Thickness T .

16. Click designvars .

The list of design variables appears.

17. Check the box next to tube .

Note the linear factor (value is box beside tube) automatically gets set to 1.000.

18. Click return .

19. Click create .

A design variable to property relationship, tube_th, has been created relating the design variable tube to the thickness entry on the PSHELL card for the property tube2.

20. Repeat steps 13 through 19 to create the design variable to property relationship rail_th relating the design variable rail to the thickness entry on the PSHELL card for the property tube1.

21. Click return to go to the optimization panel.

Step 3: Create the Volume and Static Displacement R esponse

A detailed description can be found in the OptiStruct User's Guide under Responses.

1. Enter the responses panel.

2. Click response = and enter volume .

3. Click the response type: switch and select volume from the pop-up menu.

4. Ensure the regional selection is set to total (this is the default).

5. Click create .

A response, volume, is defined for the total volume of the model.

6. Click response = and enter X_Disp .

7. Click the response type: switch and select static displacement from the pop-up menu.

8. Click nodes and select by id from the pop-up menu.

9. Enter 3143 (node at center of rigid spider at loading point) and press Enter .

10. Select dof1 and click create .

A response, X_Disp, is defined for the x-displacement of the node 3143.

11. Click response = and enter Z_Disp .

12. Click nodes and select by id from the pop-up menu.

13. Enter 3143 (node at center of rigid spider at loading point) and press Enter .



14. Select dof3 and Click create .

A response, Z_Disp, is defined for the z-displacement of the node 3143.


Step 4: Create Constraints on Displacement Response

A response defined as the objective cannot be constrained. In this case, you cannot constrain the response volume.

Upper bound constraints are to be defined for the responses X_Disp and Z_Disp.

1. Enter the dconstraints panel.

2. Click constraint = and enter Disp_X .

3. Check the box for upper bound = .


5. Click response = and select X_Disp from the list of responses.

A loadsteps button should appear in the panel.

6. Click loadsteps .

7. Check the box next to FORCE_X and click select .

8. Click create .

A constraint is defined on the response X_Disp. The constraint is an upper bound with a value of 0.9. The constraint applies to the subcase FORCE_X.

9. Click constraint = and enter Disp_Z .

10. Check the box for upper bound = .


12. Click response = and select Z_Disp from the list of responses.

13. Click loadsteps .

14. Check the box next to FORCE_Z and click select .

15. Click create .

A constraint is defined on the response Z_Disp. The constraint is an upper bound with a value of 1.6. The constraint applies to the subcase FORCE_Z.





In this example, the objective is to minimize the volume response defined in the previous section.

1. Click objective to enter the panel.

2. The switch in the left should be set to min .

3. Click response = and select volume from the response list.

4. Click create .

The objective function is now defined.


Step 6: Save the HyperMesh Database

1. Select the Files panel toolbar button.

2. Click save as… .

3. Select the directory where you would like to save the database and enter the name for the database, joint_sizeOPT.hm , in the File name: field.

4. Click save .

Step 7: Run the Optimization Problem

1. From the Analysis page, select the OptiStruct panel.

2. Click save as… .

3. Select the directory where you would like to write the model file and enter the name for the file name, joint_sizeOPT.fem , in the File name: field.

The .fem file name is used for OptiStruct input decks.

4. Click Save.

Note the name and location of the joint_sizeOPT.fem file displays in the input file: field.

5. Set the export options: toggle to all .


7. Set the memory options: toggle to memory default .

8. Click OptiStruct to run the optimization.

This launches the OptiStruct job. If the job was successful, new results files can be seen in the directory where the OptiStruct model file was written. The joint_sizeOPT.out file is a good place to look for error messages that will help to debug the input deck if any errors are present.



These are some important results files for Size Optimization :

Step 8: View the Size Optimization Results (gauge t hickness)

1. Once you see the message Process completed successfully in the command window, click the HyperView button.

HyperView will launch and the results will be loaded. A message window appears to inform about the successful loading of the model and result files into HyperView. Notice that all three h3d files get loaded, each into a different page in HyperView. Files joint_sizeOPT_des.h3d , joint_sizeOPT_s1.h3d , and joint_sizeOPT_s2.h3d get loaded in page 1, page 2, and page 3 respectively. The optimization iteration results (gauge thickness) are loaded in the first page. Note that the name of the page is displayed as Design History to indicate that the results correspond to optimization iterations.

2. Click Close to close the message window.

3. Click the Contour toolbar button.

4. Make sure the first pull-down list below Result type: is Element Thicknesses (s) .

5. Make sure the second pull-down list is on Thickness .

6. Make sure the field below Averaging method is None .

7. Set the last Load Case Simulation by clicking the status bar shown below.

8. Scroll down to the last iteration and choose the last for e.g.: Iteration [3] and click OK.

9. Click Apply .

A contoured image representing shell thickness should be visible. Each element in the model is assigned a legend color, indicating the thickness value for that element for the current iteration.



Thickness contour at last iteration

Step 9: View the Displacement Results

It is helpful to view the deformations of the model to determine if the boundary conditions have been met and also to see if the model is deforming as expected. These analysis results are available in pages 2 and 3.

1. Click the Next Page toolbar button to move to the second page.

The second page, which has results loaded from the file joint_sizeOPT_s1.h3d , is displayed. Note that the name of the page is displayed as Subcase 1 – FORCE_X to indicate that the results correspond to subcase 1.

2. Set the animation mode to Linear Static .


4. Select the first pull-down menu below Result type: and select Displacement [v] .

5. Select the second pull-down menu and select X.

6. Click on Apply .

The resulting contours represent the x component displacement field resulting from the applied loads and boundary conditions.

7. Click the Measure toolbar button.

8. Click Add to add a new measure group.

The Measure panel helps measure different results. Here, we will measure the displacement at node 3143 for which we have constrained the displacement.

9. Click the pull-down menu and select Nodal Contour as shown below.

10. Click on Nodes , which opens a new window to select nodes By ID .



11. Click By ID to open a new window.

12. Enter 3143 in the field next to Node ID and click Ok.

Displacement on X-direction for the X-Force load case at the first iteration

The x-displacement value for 3143 (center of rigid spider, where loading is applied) is shown in the graphic area. Note that the x-displacement is larger than the upper bound constraint, which was defined earlier, of 0.9.

13. At the bottom of the GUI, click on the name State Analysis or Iteration 0 ,

, to activate the Load Case and Simulation Selection dialog.

14. Select the last iteration by double clicking on the last Iteration #.

The contour now shows the x-displacement results for Subcase 1 (FORCE_X) and iteration 4, which corresponds to the end of the optimization iterations. Note that the x-displacement is now less than 0.9.

Displacement on X-direction for the X-Force load case at the last iteration

15. Click the Next Page button again to move to the third page.



The third page shows results loaded from the joint_sizeOPT_s2.h3d file. Note that the name of the page is displayed as Subcase 2 – Force_Z to indicate that the results correspond to subcase 2.


17. Select the first pull-down menu below Result type: and select Displacement [v] .

18. Select the second pull-down menu and select Z.

19. Click on Apply .

The resulting contours represent the z component displacement field resulting from the applied loads and boundary conditions.

20. Repeat steps 8 through 14 to measure and display the z-displacement value for node 3143.

Z Displacement for Z-Force load case at the last iteration


2. How much iteration it has take to converge and how much is the final volume of the part?

3. What are the resulting gauges for the rail and tube?



2 – Shape Optimization OptiStruct has the capability of performing shape optimization. In shape optimization, the outer boundary of the structure is modified to solve the optimization problem. Using finite element models, the shape is defined by the grid point locations. Hence, shape modifications change those locations.

Shape variables are defined in OptiStruct in a way very similar to that of other shape optimization codes. Each shape variable is defined by using a DESVAR bulk data entry. If a discrete design variable is desired, a DDVAL bulk data entry needs to be referenced for the design variable values. DVGRID bulk data entries define how much a particular grid point location is changed by the design variable. Any number of DVGRID bulk data entries can be added to the model. Each DVGRID bulk data entry must reference an existing DESVAR bulk data entry if it is to be a part of the optimization. The DVGRID data in OptiStruct contains grid location perturbations, not basis shapes.

DESVAR Card Image

ID LABEL XINIT XLB XUB DELXV

DESVAR 1 DV001 0.0 -1.0 1.0

DVGRID Card Image

DVID GID CID COEFF X Y Z

DVGRID 1 1032 0 1.0 1.0 0.0 0.0

The generation of the design variables and of the DVGRID bulk data entries is facilitated by the HyperMorph utility, which is part of the Altair HyperMesh software.

The following responses are currently available as the objective or as constraint functions:

Mass Volume Center of Gravity

Moment of Inertia Static Compliance Static Displacement

Natural Frequency Buckling Factor Static Stress, Strain, Forces

Static Composite Stress, Strain, Failure Index

Frequency Response Displacement, Velocity, Acceleration

Frequency Response Stress, Strain, Forces

Weighted Compliance Weighted Frequency Combined Compliance Index

Function



2.1 – Design Variables for Shape Optimization

In finite elements, the shape of a structure is defined by the vector of nodal coordinates (x). In order to avoid mesh distortions due to shape changes, changes of the shape of the structural boundary must be translated into changes of the interior of the mesh.

The two most commonly used approaches to account for mesh changes during a shape optimization are the basis vector approach and the perturbation vector approach. Both approaches refer to the definition of the structural shape as a linear combination of vectors.

Using the basis vector approach , the structural shape is defined as a linear combination of basis vectors. The basis vectors define nodal locations.

∑ ⋅= ii BVDVx

where x is the vector of nodal coordinates, BVi is the basis vector associated to the design variable DVi.

Using the perturbation vector approach , the structural shape change is defined as a linear combination of perturbation vectors. The perturbation vectors define changes of nodal locations with respect to the original finite element mesh.

Description of a shape design variable

Original location:

Perturbations (DVGRID):

Magnitude of perturbations (DESVAR):

Mesh nodal movement:

where X is the vector of nodal coordinates, X(0) is the vector of nodal coordinates of the initial design, ∆∆∆∆Xj is the perturbation vector associated to the design variable α.

The initial nodal coordinates are those defined with the GRID entity. The perturbation vectors are defined on the DVGRID statement, which is referenced by the design variable entity DESVAR.

},,,{ )0()0(3

)0(2

)0(1

)0(nxxxxX L=

},,,,{ 321 nxxxxX ∆∆∆∆=∆ L

},,,,{ 321 nααααα L=

∑=

∆+=n

jjj XXX

1

)0( α



If a discrete design variable is desired, a DDVAL bulk data entry needs to be referenced on the DESVAR bulk data entry for the design variable values.

Note:

In OptiStruct, only the perturbation vector approach is available. The DVGRID cards must contain perturbation vectors.

2.2 – HyperMorph

HyperMorph is a tool in HyperMesh to morph the shape of a finite element model in ways that are useful, logical and intuitive. It enables rapid shape changes on the FE mesh without severely sacrificing the mesh quality. This is a very powerful tool to automatic generate the shape design variable described above.

2.2.1 – The Three Basic Approaches to Morphing

The Domains and Handles Concept

This approach involves dividing the mesh into domains containing elements or nodes and placing handles at the corners of those domains. HyperMorph can automatically divide the mesh into logical domains or you can manually define your own domains and handles. When the handles are moved, the shape of the mesh changes according to the domain boundaries. The domains and handles approach also allows for parametric morphing of lengths, angles, radii, and arc angles as well as morphing the mesh to match geometric data and other meshes. The domains and handles approach is the most difficult approach to learn but it is also the most powerful. This approach is most useful for making detailed changes to any mesh (local domains) as well as general changes to space frame type meshes (global domains).

Morph Example using handles and domain concept

The Morph Volume Concept



This approach involves surrounding the mesh with one or more morph volumes, which are highly deformable six-sided prisms. A number of methods exist to create the morph volumes, including single and matrix creation as well as the interactive on-screen method. Morph volumes support tangency between adjoining edges and allow for multiple control points along their edges. Handles placed at the corners and along the edges of the morph volumes allow for the morphing of the morph volumes which in turn morphs the mesh inside the morph volumes. The morph volume approach is quick and intuitive and is most useful for making large scale changes to complex meshes.

Morph Example using morph volume concept

The Freehand Concept

This approach involves morphing by moving the nodes directly without the need to create any HyperMesh morphing entities. You define the nodes which will move, the nodes which will stay fixed, and the affected elements, which manually allows for rapid changes to any mesh. You have great flexibility in how the moving nodes are moved, such as translation, rotation, and projection to geometry as well as using a tool to "sculpt" the mesh into the desired shape. You are also able to turn node manipulations made in any panel, such as scaling or node projection, into morphs using the record sub-panel. The freehand approach is an ideal introduction to HyperMorph since it allows morphing without the creation of any HyperMesh morphing entities while employing the concepts of domains and handles. The freehand approach also allows for "customized" morphing, allowing the user to do virtually any kind of morphing.

At online documentation the user can find a complete description about HyperMorph and how this tool can be used to generate shape design variable to OptiStruct. Here for convenience we will use during the next exercise only the first approach.



Exercise 5.2 – Shape Optimization of a Rail Joint Shape optimization requires you to have knowledge of the kind of shape you would like to change in the structure. This may include finding the optimum shape to reduce stress concentrations to changing the cross-sections to meet specific design requirements. Therefore, you need to define the shape modifications and the nodal movements to reflect the shape changes. Shape optimization requires the use of two cards DESVAR and DVGRID. They can be defined using HyperMorph . Then these cards are included in the OptiStruct input file along with the objective function and constraints to run the shape optimization.

In this exercise you perform a shape optimization on a rail-joint. The rail-joint is made of shell elements and has one load case. The shape of the joint is modified to satisfy stress constraints while minimizing mass.

Rail joint

Problem Statement

Objective: Minimize mass

Constraint: Maximum von Mises stress of the joint < 200 MPa

Design variables: Shape variables



Step 1: Launch HyperMesh, Set the User Profile and Retrieve the File


2. Choose OptiStruct in the User Profile dialog and click OK.

This loads the user profile. It includes the appropriate template, macro menu, and import reader, paring down the functionality of HyperMesh to what is relevant for generating models in Bulk Data Format for RADIOSS and OptiStruct .

The User Profiles… GUI can also be accessed from the Preferences pull-down menu on the toolbar.

3. From the File pull-down menu on the toolbar, select Open… .

4. Select the rail_joint_original.hm file.

Step 2: Run the Baseline Analysis

This tutorial takes a long time to run (elapsed time of about 52 hours on a typical work station) because of the fine mesh of solid elements. For the sake of user convenience, the results file (carm_draw_symm_des.h3d ) is available from [email protected]. You can skip this section and directly load the results file in HyperView for post-processing. The following steps are given for the sake of completeness of this tutorial and as a helpful user reference.

1. From the Analysis page click on Radioss .

2. Click save as… , enter rail_joint_original.fem as the file name, and click Save.

4. 3. Set the export options: toggle to all.

4. Click the run options: switch and select analysis .

5. Set the memory options: toggle to memory default .

6. Let the options: field blank .

The message …Processing complete appears in the window at the completion of the job. OptiStruct also reports error messages if any exist. The file rail_joint_original.out can be opened in a text editor to find details regarding any errors. This file is written to the same directory as the .fem file.

7. Close the DOS window or shell and click return .

Step 3: View the Maximum von Mises Stress

This section describes how to view the results in HyperView which will be launched from within the OptiStruct panel of HyperMesh .



HyperView is a complete post-processing and visualization environment for finite element analysis (FEA), multi-body system simulation, video and engineering data.

1. Once you see the message Process completed successfully in the command window, click the HyperView button.

HyperView will launch and the results will be loaded. A message window appears to inform about the successful loading of the model and result files into HyperView.


3. Click the Contour toolbar button .

4. Select the first pull-down menu below Result type: and select Element Stresses [2D & 3D] (t) .

5. Select the second pull-down and select von Mises .

6. Click Apply .

Von Mises stress for the Initial Design

7. Take note of the Maximum von Mises Stress of the joint and close HyperView .

8. Back on HyperMesh click return to exit the panel.

Step 4: Display Node Numbers

1. From Tool page, select numbers panel.

2. Click nodes and select by sets .

3. Select node set by clicking the check box to the left of node .

4. Click select .

16 nodes are highlighted on screen.

5. Click on to display node IDs.



6. Click return .

Step 5: Build 2-D Domains on the Rail

1. In the Model Browser window expand the Component list.

2. Right click on the component PSHELL and click on Isolate .

All other components are turned off for ease of visualization.


4. Go to the HyperMorph panel, and select domains .

5. Toggle the radio button on the left to partitioning .

6. Verify that domain angle = 50 .

7. Verify that curve tolerance = 8.0000 .

8. Toggle back the radio button to create .

9. Click the switch (small triangle) and select 2D domains .

10. Toggle all elements to elems .

11. Click elems and select by sets from the pop-up window.

12. Check the boxes for rail_set1 and rail_set2 .

13. Click select .

14. Click create .

Rail domains



Step 6: Split the Circular Edge Domains Around the Opening of the Rail

The following steps show the procedure to split each of the two circular domains (as seen in the previous figure) into four curved edge domains.

1. Toggle the radio button to edit edges subpanel.

2. Verify the top selector is split .

3. Click domain and select the circular edge-domain passing through nodes 1300, 1305, 1311, 1316.

4. Click node and select node 1311 from the display. Refer to the previous figure.

5. Click split .

The circular domain is split at Node 1311 and a new handle is created at node1311.

6. Select the circular edge between node 1311 and the other handle.

The edge is highlighted.

7. Click node 1316 to split the domain.

8. Similarly (as in steps 6-7), split the curved edge at nodes 1305 and 1300, respectively. Refer to the previous figure.

A similar process is followed to split the circular domain using the four nodes on the other side of the rail.

9. Click domain and select the circular domain passing through nodes 931, 926, 937 and 942.

10. Click node and select node 931 on screen.

11. Click split .

12. Select the circular edge between node 931 and the other handle.

The edge is highlighted.

13. Click node 926 to split the domain.

14. Similarly (as in steps 11-14), split the curved edge at nodes 937 and 942, respectively.

The following figure shows the image after the circular edge domains are split.

Rail domains after the circular edge have been split



Step 7: Merge Edge Domains

Each circular domain on the rail has been split at four nodes and four new handles have been added to each circular domain. This operation results in five curved edge domains on each circular edge on the rail. The objective is to have only four domains. The following steps show the procedure to merge domains.

1. Toggle the left switch and select to merge edges.

2. Click the left domain below merge and select the outer red curve from node 926 to pre-existing handle (refer to previous figure).

3. Click the right domain and select the outer red curve from pre-existing handle to node 942.

4. Verify that retain handles is unchecked.

5. Click merge .

Notice the pre-existing handle is removed.

6. Repeat steps 1 through 5 to merge two edge domains between node 1316 and node 1300 on the other side of the rail.

Rail domains after few domains are merged

Step 8: Build 2-D Domains on the Tube

1. In the Model Browser window expand the Component .

2. Right click on the component PSHELL.1 and click Show .

3. Toggle back the radio button to create .

4. Make sure the switch (small triangle) is selected to 2D domains .



5. Click elems and select by sets from the pop-up window.

6. Check the boxes for elem_set1 .

7. Click select .

8. Click create .

9. Repeat steps 5 through 8 to create three more 2-D domains for elements in sets elem_set2 , elem_set3 , and elem_set4 respectively.

10. Click return and go back to the HyperMorph module.

Domains on Rail and Tube Joint

Step 9: Create Shapes

In this step, we create three shapes using the created domains and handles.

1. Click morph .

We use the alter dimensions feature in HyperMorph to modify the curvatures of selected edge domains.

2. Toggle to alter dimensions .

3. Toggle the right switch and select curvature .

4. Toggle center calculation and change the setting to by edges .

5. Toggle the switch below and select hold ends .

Holding two ends of a selected edge domain allows a change of curvature of the selected edge without altering its end points.

6. Leave the other settings with the defaults.

7. Under edges only , click domains and select red edge-domains as shown in the following figure. You might need to zoom in for easier picking operation.



8. Verify that a total of eight edge domains are selected and highlighted on screen.

Morph edge domains

9. Click curve ratio = and enter 20 .

10. Click morph .

A new curvature is applied to the selected eight edge domains. See the following figure below.

11. Toggle the radio button to save shape .

12. Click on shape = , enter the name sh1 .

13. Toggle as handle perturbation to as node perturbation .

14. Click on the color button and change the color of the shape vectors or leave the default color.

15. Click save .

Shape vectors (arrows) are created of the selected color.

16. Click undo all to prepare for the generation of the next shape.

17. Click the Model browse tab, right click on Shape and select Hide .



First shape variable, sh1.

18. Toggle the radio button to alter dimensions .

19. Under edges only , click reset .

This will clean up previous selection from buffer.

20. Click domains and select the red edge curves as shown the following figure.

Morph edge domains for the second shape.

21. Click morph .

A new curvature is applied to the selected eight edge domains. See the following figure below.



22. Toggle the radio button to save shape .

23. Click on shape = , enter the name sh2 .

24. Toggle as handle perturbation to as node perturbation .

25. Click on the color button and change the color of the shape vectors or leave the default color.

26. Click save .

Shape vectors (arrows) are created of the selected color.

27. Click undo all to prepare for the generation of the next shape.

28. Click the Model browse tab, right click on Shape and select Hide .

Refer to the following figure for the new shape changes.

Second shape variable, sh2.

29. Toggle the radio button to apply shapes .

In HyperMorph, a new shape can be created as a linear combination of existing shapes.

30. Click shapes and select both sh1 and sh2 .

31. Click Select .

32. Verify that the multiplier is 1.0.

33. Click apply .

34. Toggle the radio button to save shapes .

35. Click shape = and enter sh3 .

36. Make sure that the toggle is set to node perturbations .

The new shape sh3 includes influences from both sh1 and sh2 shapes as shown in the next figure.



37. Click save .

38. Click the Model browse tab, right click on Shape and select Hide ..

Do NOT click undo all at this moment because we will create one more shape based on this third shape change.

The third shape variable, sh3, converts the tube to a square cross-section

An additional shape variable is created using the shape created in the previous step.

39. In the Model Browser window, right click on the component PSHELL and click on Hide .

These components are turned off for ease of visualization.

40. Toggle the radio button to alter dimensions .

41. Under edges only , click reset .

This will clean up previous selection from buffer.

42. Switch the top selector from curve ratio to distance = .

This feature allows you to shorten the distance between selected domains.

42. Switch the end a: selector from two handles to nodes and handles .

43. Click node a and pick node as shown in the next figure.

44. Click node b and pick node as shown in the next figure.



Setup for the fourth shape variable, sh4

Once nodes a and b are selected, the distance between node a and node b is measured automatically and appears in distance = field.

The distance between node a and node b is about 43.

45. Click handles under node a and select the 8 handles shown by the downward pointing arrows in the previous figure.

To select, click the handles on the screen until they are highlighted.

46. Click handles under node b and similarly as in the previous step, select the 8 handles near the opposite face of the tube.

47. Toggle the bottom selector and select hold middle .

48. In the Model Browser window, right click on the component PSHELL and click on Show .

These components are turned on for ease of visualization

49. Click distance = and enter 20.

50. Click morph .

A rectangular shape appears to the joint as shown in the next figure.

51. Toggle the button to save shape .

52. Click shape = and enter sh4 .

53. Make sure that the toggle is set to node perturbations .

54. Click save .



55. Click undo all to restore the mesh to the baseline configuration.

56. Click the Model browse tab, right click on Shape and select Hide ..

57. Click return three times to go the main menu.

Fourth shape variable, sh4

Step 10: Define the Shape Design Variables and Revi ew by Animation


2. Click on the shape panel.

3. Make sure the radio button is set to desvar and create .

4. Toggle the switch to select multiple desvars .

5. Click shape = and select sh1 , sh2 , sh3 and sh4 .

6. Click select .

7. Click initial value = and enter 0.0 .

8. Click lower bound = and enter -1.0 .


10. Click create .

This creates four design variables with the same initial value, lower bound, and upper bound. HyperMesh automatically links the design variables to each shape respectively and assigns names to each design variable the same as its associated shapes.



12. Click animate .

13. Click on simulation = SHAPE – sh1 (1) .

14. Make sure that data type = is set to Perturbation vector .

15. Click modal to animate the first shape variable.

16. Click next and then animate to see the next shape variable, and so forth.

17. Click return three times to go back to the optimization panel.

Step 11: Create the Mass and Static Stress Response

1. Enter the responses panel.

2. Click response = and enter Mass.

3. Click on the response type switch and select mass from the pop-up menu.

4. Ensure the regional selection is set to total (this is the default).

5. Click create .

A response, mass, is defined for the total mass of the model.

6. Click response = and enter Stress .

7. Click on the response type switch and select static stress from the pop-up menu.

8. Click the props button and select the PSHELL.1 component which contains skin shells.

9. Do NOT select any element under excluding: .

10. Make sure that the toggle is selected to von Mises .

11. Toggle the bottom switch to select both surfaces .

12. Click create .

A response, Stress, is defined for the model.


Step 12: Define the Objective

1. Enter the objective panel.

2. The switch on the left should be set to min .

3. Click response= and select Mass .

4. Click create .

5. Click return to exit the optimization panel.



Step 13: Create Constraints on Stress Response

In this step we set the upper and lower bound constraint criteria for this analysis.

1. Enter the dconstraints panel.

2. Click constraint= and enter con .

3. Check the box for upper bound only.

4. Click upper bound= and enter 200 .

5. Select response= and set it to Stress .

6. Click loadsteps and check STEP.

7. Click select .

8. Click create .

9. Click return to the main menu.

Step 14: Define Control Cards Required for Shape Op timization

Without this control card defined, optimization gets terminated by quality check and you do not get the converged results.

1. From the Analysis page, click the control cards panel.

2. Click the Next button twice and chose the PARAM card.

3. Check the box next to CHECKEL .

4. Click the YES button under CHECKEL_V1 to change to NO.

5. Click Return twice.

Step 15: Run the Optimization Problem

1. From the Analysis page enter the OptiStruct panel.

2. Click save as… , enter rail_joint_opt.fem as the file name, and click Save.

3. Click export options: switch and select All .


4. Make sure the memory options: toggle is set to memory default .

5. Click OptiStruct to run the optimization.

The message …Processing complete appears in the window at the completion of the job. OptiStruct also reports error messages if any exist. The file carm_complete.out can be opened in a text editor to find details regarding any errors. This file is written to the same directory as the .fem file.



6. Close the DOS window or shell.

Step 16: Review the Shape Optimization Results

1. Once you see the message Process completed successfully in the command window, click the green HyperView button.

HyperView is launched and the results are loaded. A message window appears to inform about the successful loading of the model and result files into HyperView. Notice that all three .h3d files get loaded, each in a different page of HyperView.


Rail_joint_opt_des.h3d will be opened in page 1 and Rail_joint_opt.h3d will be opened in page 2 of HyperView.


Note the Result type: is Shape Change [v] ; this should be the only results type in the “file_name”_des.h3d file.

The second pull-down menu shows mag .

4. Click Apply to display the shape change.

Note the contour is all blue this is because your results are on the first design step or Iteration 0.

5. At the bottom of the GUI, click on the name Design <> Iteration 0 to activate the Load Case and Simulation Selection dialog.

6. Select the last iteration by double clicking on the last Iteration listed.

Each element of the model is assigned a legend color, indicating the density of each element for the selected iteration.

Shape optimization results are applied to the model.

Shape change converged (Scale 2x)



Step 17: View a Contour Plot of the Stress on Top o f the Shape Optimized Model

1. Click the Next arrow to move to page 2.


Note the Result type: is Element Stresses [2D & 3D] [t] .

The second pull-down menu shows von Mises .

3. At the bottom of the GUI, click on the name Subcase 1 (STEP) <> Model Step to activate the Load Case and Simulation Selection dialog.

4. Select the last iteration by double clicking on the last Iteration listed.

5. Click Apply .

The stress contour shows on top of the shape changes applied to the model. Verify that this value is around the constraint value specified.

Von Mises Stress for the last iteration (Max < 200 MPa)

Reviewing the Results

Is your design objective of minimizing the volume obtained? If not, can you explain why?

Are your design constraints satisfied?

Which shape has the most influence in this problem setup?

What is the percentage decrease in compliance?

Can size optimization be introduced to the joint?



3 – Free-shape Optimization Free-shape optimization uses a proprietary optimization technique developed by Altair Engineering Inc., wherein the outer boundary of a structure is altered to meet with pre-defined objectives and constraints. The essential idea of free-shape optimization, and where it differs from other shape optimization techniques, is that the allowable movement of the outer boundary is automatically determined, thus relieving users of the burden of defining shape perturbations.

Free-shape design regions are defined through the DSHAPE bulk data entry. Design regions are identified by the grids on the outer boundary of the structure (the edge of a shell structure or the surface of a solid structure). These grids are listed on the DSHAPE entry.

Free-shape optimization allows these design grids to move in one of two ways:

1. For shell structures; grids move normal to the surface edge in the tangential plane.

2. For solid structures; grids move normal to the surface.

During free-shape optimization, the normal directions change with the change in shape of the structure, thus, for each iteration, the design grids move along the updated normals.

3.1 – Defining Free-shape Design Regions

Ideally, free-shape design regions should be selected where it can be assumed that the shape of the structure is most sensitive to the concerned responses. For example, it would be appropriate to select grids in a high stress region when the objective is to reduce stress.

Free-shape design regions should be defined at different locations on the structure where it is desired for the shape to change independently. For solid structures, feature lines often define natural boundaries for free-shape design regions. Containing any feature lines inside a free-shape design region should be avoided unless the intention is to smooth the feature lines during an optimization. Likewise for a shell structure, sharp corners should not be contained inside a free-shape design region unless the intention is to smooth out such corners.

The DSHAPE card identifies the design region through the GRID continuation card, shown here:

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

GRID GID1 GID2 GID3 GID4 GID5 GID6 GID7 GID8 GID9 … …



2D - A free-shape design region is defined on the curved edge of the plate by selecting the edge grids; the grids are free to move in the normal direction on the tangential plane.

3D - A free-shape design region is defined on a surface of the solid structure by selecting the face surface grids; the grids are free to move normal to the surface.



3.2 – Free-shape Parameters

The five parameters that affect the way in which the free-shape design region deforms are the direction type, the move factor, the number of layers for mesh smoothing, the maximum shrinkage, and the maximum growth.

3.2.1 – Direction type

This provides a general constraint on the direction of the movement of the free-shape design region. It is defined on the PERT continuation line of the DSHAPE entry in the DTYPE field, as shown:

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

PERT DTYPE MVFACTOR NSMOOTH MXSHRK MXGROWTH

DTYPE has three distinct options:

1. GROW – grids cannot move inside of the initial part boundary.

2. SHRINK – grids cannot move outside of the initial part boundary.

3. BOTH – grids are unconstrained.

GROW SHRINK BOTH

Undeformed

Deformed



3.2.2 – Move factor

The maximum allowable movement in one iteration of the grids defining a free-shape design region is specified as:

MVFACTOR*mesh_size

where "mesh_size" is the average mesh size of the design region defined in the same DSHAPE card.

MVFACTOR is defined on the PERT continuation line of the DSHAPE entry. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)


The default value of MVFACTOR is 0.5. A smaller MVFACTOR will make free-shape optimization run slower but with more stability. Conversely, a larger MVFACTOR will make free-shape optimization run faster but with less stability.

MVFACTOR affects the maximum movement in one iteration.

Undeformed shape

Shape at iteration 1 with MVFACTOR = 0.5(default)

Shape at iteration 1 with MVFACTOR = 1.0

3.2.3 – Number of layers for mesh smoothing

With free-shape optimization, internal grids adjacent to those grids defining the design region are moved to avoid mesh distortion. The number of layers of grids to be included in the mesh smoothing buffer may be defined by the NSMOOTH field on the PERT continuation line of the DSHAPE entry.



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


The default value of NSMOOTH is 10. A larger NSMOOTH will give a larger smoothing buffer, and consequently will work better in avoiding mesh distortion; however, it will result in a slower optimization.

NSMOOTH=5, 5 layers of grids move along with the design boundary.

NSMOOTH=1, only 1 layer of grids move along with the design boundary.

3.2.4 – Maximum shrinkage and growth

The maximum shrinkage and growth provide a simple way to limit the total amount of deformation of the free-shape design region. These parameters are defined on the PERT continuation line of the DSHAPE entry. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)




The design region is offset to form two barriers; MXSHRK is the offset in the shrinkage direction and MXGROWTH is the offset in the growth direction. The design region is then constrained to deform between these two barriers.

Deformation space defined by the maximum growing/shrinking distance

3.2.5 – Constraints on Grids in the Design Region

It is possible to identify additional constraints on certain grids in free-shape design regions. Three types of constraints are available for specified grids as defined by CTYPE# on the GRIDCON continuation line of the DSHAPE entry:

1. FIXED – grid cannot move due to free-shape optimization.

2. VECTOR – grid is forced to move along the specified vector.

3. PLANAR – grid is forced to remain on a plane for which the specified vector defines the normal direction.

Note: VECTOR is used to constrain a grid to move along a line, thus it makes no difference by rotating the vector by 180 degrees.

Constraints are defined on the GRIDCON continuation line as follows:

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

GRIDCON GCMETH GCSETID1 / GDID1

CTYPE1 CID1 X1 Y1 Z1

GCMETH GCSETID2 / GDID2

CTYPE2 CID2 X2 Y2 Z2



Example showing CTYPE = VECTOR

This example demonstrates a simple case where it is necessary to use the "DIR" constraint type to force grids to move in a predefined direction.

A free-shape optimization is performed on a quarter model of a rectangular plate with a hole, shown here:

The curved edge is the free-shape design region. Without any constraints on the free-shape design region, the grids at the ends of the curved edge do not move exactly along the line of the straight edge, but move slightly outward, as shown here:

In order to prevent this phenomenon, the grids at the ends of the curved edge (shown in yellow below) are both constrained to move along the vector indicated by the red arrows.



Using these constraints - corner grids moving along the constrained direction - the grids at the ends of the curved edge now move as desired, along the line of the straight edge, as shown here:



Exercise 5.3 - Free-shape optimization Compressor Bracket

In this exercise, shape optimization on a solid model will be performed using the free-shape optimization method along with manufacturing constraints, such as symmetry and mesh barrier constraints. The objective of this optimization is to reduce the stress by changing the geometry of the model.

Problem Statement

Objective: Minimize mass

Constraint: Maximum von Mises stress of the joint < 62 MPa

Design variables: Shape variables normal to the node set selected



Step 1: Launch HyperMesh, Set the User Profile, and Retrieve the Model


2. Choose OptiStruct in the User Profile dialog and click OK.

This loads the user profile. It includes the appropriate template, macro menu, and import reader, paring down the functionality of HyperMesh to what is relevant for generating models in Bulk Data Format for RADIOSS and OptiStruct.

User Profiles… can also be accessed from the Preferences pull-down menu on the toolbar.

3. Select the File panel toolbar button .

4. Select the freeshape3d_mfg.hm file.

5. Click Open .

The freeshape3D_mfg.hm database is loaded into the current HyperMesh session, replacing any existing data. Note the location of freeshape3D_mfg.hm now displays in the file: field.

Step 2: Create Free-shape Design Variables (DSHAPE Cards)

1. From Analysis page click optimization .

2. Click free shape .

3. In the Create sub-panel, click on desvar= , and enter shape .

4. Click on nodes and select by sets check the box next to shape_nodes click on select.

Free-shape design space

5. Click create .



6. Click on the parameters subpanel and select the direction as grow , mvfactor at 0.5 and nsmooth as 10 and click update

5. Click return twice to exit the panel.

Step 3: Convert the existing shell elements to crea te the Barrier Mesh Face (BMFACE)

1. Go to the 2D page

2. Enter the elem types panel

3. Click on elems to get the extended entity list

4. Select by collector

5. Check the box next to barrier

6. On 2D& 3D subpanel click on CTRIA3 in the field next to tria3

7. Select BMFACE from the list of options

8. Click on CQUAD4 in the field next to quad4

9. Select BMFACE from the list of options

10. Click update

Step 4: Define the 1-Plane Symmetry Constraint

The manufacturing constraint options for free-shape are: (Draw direction constraint, Extrusion constraint, Pattern grouping: 1-plane symmetry constraint, Maximum growing/shrinking distance control, Side constraint, Mesh barrier constraint)

In this exercise we will define the 1-plane symmetry constraint and mesh barrier constraint.

1. From Analysis page click optimization .

2. Click free shape ; make sure that the desvar selected is shape .

3. Click on pattern grouping in the free shape panel.

4. Select the pattern type: 1-pln sym .

The 1-plane symmetry constraints in free-shape will produce symmetric designs regardless of the initial mesh, boundary conditions or loads. The plane of symmetry is defined by



specifying the anchor and the first nodes. The plane of symmetry will then be perpendicular to the vector from the anchor node to the first node and pass through the anchor node.

3. Click anchor node and input the node id= 2 and press ENTER.

This selects the node with the ID of 2.

4. Click first node and input the node id= 1.

This selects the node with the ID of 1.

5. Click the update button to update the design variables.

This completes the definition of the symmetry constraint.

Defining 1-plane symmetry

Step 5: Define the Mesh Barrier (sidecon) Constrain t

A mesh barrier constraint allows control on the total deformation extent of a design boundary/surface; mesh barrier will constrain the design boundary/surface to deform within the restricted design space and never penetrate the barrier.



The barrier should be constructed by shell elements with the smallest number of elements possible.

For this exercise, the mesh barrier was already created and the component name is barrier .

1. Click on sidecon in the free shape panel.

2. Click on desvar = and select shape .

3. Click on Barrier mesh: component= and select barrier from the list.

4. Click update .

5. Click return to go back to the main menu.

Mesh barrier component

Step 6: Define Responses for Optimization

1. Click on responses panel.

2. Enter Stress in the response= field.

3. Set the response type to static stress .

4. Switch from props to elems and click on elems button and click by sets .

5. Check the box next to stress and click select .

6. Choose von mises and click create .

7. Click response= and assign mass .



8. Set the response type: to mass .

9. Click create .


Step 7: Define Constraints for Optimization

1. Select the dconstraints panel.

2. Click constraint= and type the name stress .

3. Click response= select stress .

4. Activate upper bound = and assign a value 62 .

5. Click on loadsteps , activate ls2 , and click select .

6. Click create .

7. Click return .


1. Choose the objective panel.

2. Click the left-most toggle and select min .

3. Click response= and select mass .

4. Click create .

5. Click return twice to go back to the main menu.

Step 9: Define the SHAPE Card

Only displacement and stress results are available in the _s#.h3d file by default. In order to look at stress results on top of a shape change that was applied to the model in HyperView, a SHAPE card needs to be defined.

1. From the Analysis page, select the control cards panel.

2. Click the green next button three times and select SHAPE.

3. Set format to h3d and both TYPE and OPTION to ALL .

4. Click return twice to go back to the main menu.

Step 10: Launch OptiStruct

1. From Analysis page click OptiStruct .

2. Click save as… following the input file: field.



3. Select the directory where you would like to write the OptiStruct model file and enter the name for the model, freeshape3d_mfgopt.fem , in the File name: field.

4. Click Save.

Note that the name and location of the freeshape3d_mfgopt.fem file is displayed in the input file: field.

5. Set the export options toggle to all .

6. Click the run options switch and select optimization .

7. Set the memory options toggle to memory default .

8. Click OptiStruct .

This launches an OptiStruct run in a separate (DOS or UNIX) shell.

If the optimization was successful, no error messages are reported to the shell. The optimization is complete when the line Processing complete appears in the shell.

Step 11: View Shape Results

1. While in the OptiStruct panel of the Analysis page, click the green HyperView button.

Note that the message window pops up to indicate that freeshape3d_mfgopt_des.h3d and freeshape3d_mfgopt_s4.h3d are opened.

2. Click Close to close the window.

freeshape3d_mfgopt_des.h3d will be opened in page 1 and freeshape3d_mfgopt_s4.h3d will be opened in page 2 of HyperView.

3. Click the arrow to move to page 2.

4. From Graphics pull down menu click on Select Load Case .

This will bring up the Load Case and Simulation Selection dialog which is also accessible from the lower right portion of the status bar.

5. Select Iteration14 from beneath Simulation (load final iteration results).

6. Click OK.

7. Go to the Deformed panel .

8. Set the Result type: to Shape change(v) .

9. Click Apply .

Shape optimization results are applied to the model.



Step 12: View a Contour Plot of the Stress on Top o f the Shape Optimized Model

1. Go to the Contour panel and select Element Stresses (2D & 3D) (t) as the Result type: .

2. Select von Mises as the stress type .

3. Click on Elements and click By set and pick the set stress click on Add and close .

4. Click Apply .

Von Mises Stress contour on Final shape

1. Is your design objective of minimizing the mass obtained? If not, can you explain why?

2. Are your design constraints satisfied?

Documents

OS 10.0 First Draft