PART II Design Optimization

Written by Changhyun, SON Chapter 5. Introduction to Design Optimization - 1

PART II

Design Optimization


CHAPTER 5CHAPTER 5

Introduction to Design OptimizationIntroduction to Design Optimization


What’s Design Optimization?What’s Design Optimization?

Design optimization is the creation of a design which :Design optimization is the creation of a design which :

Meets all specified requirementsMeets all specified requirements

Minimizes key items such as weight, size, stress, cost, and Minimizes key items such as weight, size, stress, cost, and

other factorsother factors

In short, is as effective as possibleIn short, is as effective as possible


Some DefinitionsSome Definitions

DesignDesign is the configuration of a part, product, or structure that is the configuration of a part, product, or structure that

enables a specified function to be performed.enables a specified function to be performed.

Optimum designOptimum design is a design in which a key aspect, such as is a design in which a key aspect, such as

weight, cost or performance, is improved to the greatest extent weight, cost or performance, is improved to the greatest extent

possible without compromising the intended function.possible without compromising the intended function.


Traditional Optimum DesignTraditional Optimum Design

Traditionally, an “optimum” design has often been costly and time Traditionally, an “optimum” design has often been costly and time

consuming to achieve. It’s usually pursued through a manual consuming to achieve. It’s usually pursued through a manual design process in which the engineer.design process in which the engineer.

Develops an initial designDevelops an initial design performs an analysis of the designperforms an analysis of the design evaluates the analysis resultsevaluates the analysis results modifies the designmodifies the design repeats steps 2 through 4 until an “optimum”design is obtained.repeats steps 2 through 4 until an “optimum”design is obtained.

The process is controlled by the engineer. Because of the expense The process is controlled by the engineer. Because of the expense and time involved in traditional “optimum” design, a “less than and time involved in traditional “optimum” design, a “less than optimum” design is often accepted in an economic trade-off.optimum” design is often accepted in an economic trade-off.


Initial DesignInitial Design

AnalysisAnalysis

ModificationModification EvaluationEvaluation

““Optimum” DesignOptimum” Design

Traditional Optimum DesignTraditional Optimum Design


Design OptimizationDesign Optimization

Design optimization is a programmed mathematical Design optimization is a programmed mathematical

technique that integrates this iterative design cycle into technique that integrates this iterative design cycle into

an automated process.an automated process.

The analysis, evaluation, and modification tasks are The analysis, evaluation, and modification tasks are

performed automatically, making it possible to obtain an performed automatically, making it possible to obtain an

“optimum” design more efficiently.“optimum” design more efficiently.

Resulting iterations can improve understanding of design Resulting iterations can improve understanding of design

behavior.behavior.


Initial DesignInitial Design

AnalysisAnalysis

ModificationModification EvaluationEvaluation

““Optimum” DesignOptimum” Design

Design OptimizationDesign Optimization


Specification of ANSYS Design OptimizationSpecification of ANSYS Design Optimization

ANSYS Design optimization employs approximation techniquesANSYS Design optimization employs approximation techniques

that permit optimization based on virtually any aspect of a design,that permit optimization based on virtually any aspect of a design,

not just cost or weight.not just cost or weight.

Any problem that can be solved by an ANSYS analysis can also beAny problem that can be solved by an ANSYS analysis can also be

included in ANSYS design optimization.included in ANSYS design optimization.

Full analysis capabilitiesFull analysis capabilities

APDL, ANSYS Parametric Design LanguageAPDL, ANSYS Parametric Design Language

Access to analysis results and database valuesAccess to analysis results and database values

Therefore, there is tremendous flexibility in the types of Therefore, there is tremendous flexibility in the types of

optimizationoptimization

problems that can be handled by the ANSYS program.problems that can be handled by the ANSYS program.


Design Optimization TechniqueDesign Optimization Technique

ANSYS offers a number of techniques for performing design ANSYS offers a number of techniques for performing design

optimization, including :optimization, including : Two automated optimization methodsTwo automated optimization methods

Tools for user-driven design studiesTools for user-driven design studies

Ability to program custom optimization logicAbility to program custom optimization logic

For most users, ANSYS optimization methods and tools are For most users, ANSYS optimization methods and tools are

sufficient to quickly help compute an optimal solution for a sufficient to quickly help compute an optimal solution for a

design.design.


Key ConceptsKey Concepts

In ANSYS, design optimization can be made an interactive In ANSYS, design optimization can be made an interactive process to seek an optimal design. The major steps involved process to seek an optimal design. The major steps involved are :are :

Create a functional analysis problem which parameterizesCreate a functional analysis problem which parameterizes

item that :item that : You wish to vary (design variables)You wish to vary (design variables) You wish to constrain (constrains)You wish to constrain (constrains) You wish to optimize (goal)You wish to optimize (goal) Are compared as resultsAre compared as results

Select an optimization technique.Select an optimization technique. Perform the optimization run.Perform the optimization run. Examine results.Examine results.


TerminologyTerminology

Some of the terminology we will use in creating automated Some of the terminology we will use in creating automated design optimization in ANSYS include :design optimization in ANSYS include :

- Design variables- Design variables

- State variables- State variables

- Objective function- Objective function

- Function minimization- Function minimization

- Design Space- Design Space

- Design Set- Design Set

- Feasible, infeasible, and best designs- Feasible, infeasible, and best designs


Design VariablesDesign Variables

Quantities varied in seeking an optimum design - for example, the thickness of a part. A design variable is a quantity which :

- Is independent of other quantities

- Will be changed during the optimization process

- Is constrained within a given range

Design variables in ANSYS optimization must be positive-valued quantities which are automatically changed, or can be set by the user.

Up to 60 design variables may be defined in ANSYS.


State VariablesState Variables

Quantities which set constraints on the design - for example,

a part can be deflect no more than 5 centimeters. A state

variable :

- Is a dependent variable

- Must have a minimum value, or a maximum value, or both

- Is a constraint, rather than the quantity you are optimizing


State Variables (Cont’d)State Variables (Cont’d)

State variables typically include results quantities such as stresses,

deflections, or any other analysis result. Up to 100 state variables may be defined in ANSYS. State variables typically are dependent on design variables.

Unlike design variables, which are independently varied, state variables

are dependent output quantities that are used to determine the

feasibility of a design, based on the specified constraints - for example, a

least-weight bridge structure which cannot sag more than 12 inches

when loaded.


Other terminologyOther terminology

Objective Function - A function you wish to optimize by modifying the design variables, such as weight, cost, or height.

In ANSYS, the objective function is a parameter which is always minimized.

Function Minimization - Successively modifying design variables to minimize the value of the objective function.

Design Set - The set of parameter values describing the state of the model, including design variable values.

ANSYS automatically retains database results corresponding to the last design set used in a design optimization run, and also retain the database for the best (minimum objective function) set.


Other terminology (Cont’d)Other terminology (Cont’d)

Design Space - A region defined by all possible feasible design sets.

Feasible Design - A design which meets all constraints, on both

design variables and state variables.

Infeasible Design - A design which violates at least one constraint.

Best Design - The design which attempts to minimize the objective

function and most closely meets all design constraints.

In problems where no design is feasible, ANSYS selects the design closestto feasible, not the design with the optimal objective function value, as best design.


A Sample Optimization ProblemA Sample Optimization Problem

Consider a beam model with a load on it :Consider a beam model with a load on it :

100 lbs

h

w

Design the beam height and width for the given loading Design the beam height and width for the given loading

condition such that the weight is minimized subject to an condition such that the weight is minimized subject to an

acceptable deformation at the beam end point.acceptable deformation at the beam end point.


A Sample Optimization ProblemA Sample Optimization Problem

The width w and height h are design variables - they must be positive, and can be varied to find an optimal design.

Deformation at beam endpoint () is a state variable - its result will depend on w and h, and it can be restricted within an allowable range of values. As a state variable, it is a response quantity.

The total area, represented as (w*h), which is directly proportional to the weight, is an objective function. It varies with changes in design variables, and is to be minimized.

Note that we are optimizing area rather than weight directly. The inclusion of a constant density value, which does not affect the optimization, would require the computation of a mass matrix during the analysis.


To Optimize the ProblemTo Optimize the Problem

Build initial model using ANSYS parameters for the width w Build initial model using ANSYS parameters for the width w and height h. Set another parameters “and height h. Set another parameters “deldel” to the retrieved ” to the retrieved end point nodal deformation value.end point nodal deformation value.

Modeling and analysis session will be saved, including Modeling and analysis session will be saved, including parameters, as an analysis file.parameters, as an analysis file.

In the optimization phase, w and h are defined as design In the optimization phase, w and h are defined as design variables, analysis result “variables, analysis result “deldel” is defined as a state variable, ” is defined as a state variable, and an additional parameter defined as the value (w*h) in and an additional parameter defined as the value (w*h) in the analysis file is used as the objective function.the analysis file is used as the objective function.


To Optimize the Problem (Cont’d)To Optimize the Problem (Cont’d)

After performing an optimization run in ANSYS, result values are

available for the last, and the “best” (e.g. minimum objective

function) solution encountered during the optimization run.

Values of w and h tried by the program, as well as area (w*h),

are available as design sets for later examination.


Methods and ToolsMethods and Tools

Optimization methods attempt an automated solution of an optimization Optimization methods attempt an automated solution of an optimization problem.problem.

Optimization tools can be employed by the user to help “get a feel” for Optimization tools can be employed by the user to help “get a feel” for

design space.design space.

The most general case of optimization, e.g. trying every possible The most general case of optimization, e.g. trying every possible

solution within the feasible design space, is virtually impossible solution within the feasible design space, is virtually impossible

for real problems.for real problems.

Approximations to this general case are sufficient for many Approximations to this general case are sufficient for many

problems. ANSYS offers several optimization tools and methods problems. ANSYS offers several optimization tools and methods

appropriate for different kinds of analysis problems. These appropriate for different kinds of analysis problems. These

methods and tools are discussed in more detail in Chapter 9.methods and tools are discussed in more detail in Chapter 9.


ANSYS Optimization MethodsANSYS Optimization Methods

Sub-problem Approximation MethodSub-problem Approximation Method - An approach based upon - An approach based upon

using an approximation of the objective function. Generally using an approximation of the objective function. Generally

efficient.efficient.

First Order MethodFirst Order Method - An approach based upon searching - An approach based upon searching

techniques using the gradients (e.g. rate of change) of techniques using the gradients (e.g. rate of change) of

dependent variables with respect to the design variables. dependent variables with respect to the design variables.

Generally more accurate.Generally more accurate.

User Method - Implementation of a user optimization function User Method - Implementation of a user optimization function

in subroutine form. These optimization methods seek minimum in subroutine form. These optimization methods seek minimum

for the objective function.for the objective function.


ANSYS Design Optimization ToolsANSYS Design Optimization Tools

Single Iteration Design ToolSingle Iteration Design Tool - Makes one pass through an ANSYS analysis - Makes one pass through an ANSYS analysis

using a specified design set. Facilitates user-driven “what if” studies.using a specified design set. Facilitates user-driven “what if” studies.

Random ToolRandom Tool - Generates several design sets using random variations of - Generates several design sets using random variations of

design variables.design variables.

Factorial ToolFactorial Tool - Scans all extreme points in design space. - Scans all extreme points in design space.

Gradient ToolGradient Tool - Uses gradient of objective function and state variables. - Uses gradient of objective function and state variables.

Sweep ToolSweep Tool - Sweeps design space one variable at a time. - Sweeps design space one variable at a time.

User Tool - Use of a user function in subroutine form.User Tool - Use of a user function in subroutine form.

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PART II Design Optimization