PART II
Design Optimization
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 1
CHAPTER 5
Introduction to Design Optimization
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 2
What’s Design Optimization?
Design optimization is the creation of a design which :

Meets all specified requirements

Minimizes key items such as weight, size, stress, cost,
and other factors

In short, is as effective as possible
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 3
Some Definitions
Design is the configuration of a part, product, or structure that
enables a specified function to be performed.
Optimum design is a design in which a key aspect, such as
weight, cost or performance, is improved to the greatest
extent possible without compromising the intended function.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 4
Traditional Optimum Design
Traditionally, an “optimum” design has often been costly and time
consuming to achieve. It’s usually pursued through a manual
design process in which the engineer.

Develops an initial design

performs an analysis of the design

evaluates the analysis results

modifies the design

repeats steps 2 through 4 until an “optimum”design is obtained.
The process is controlled by the engineer. Because of the expense
and time involved in traditional “optimum” design, a “less than
optimum” design is often accepted in an economic trade-off.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 5
Traditional Optimum Design
Analysis
Initial Design
Modification
Evaluation
“Optimum” Design
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Chapter 5. Introduction to Design Optimization - 6
Design Optimization

Design optimization is a programmed mathematical
technique that integrates this iterative design cycle into
an automated process.

The analysis, evaluation, and modification tasks are
performed automatically, making it possible to obtain an
“optimum” design more efficiently.

Resulting iterations can improve understanding of design
behavior.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 7
Design Optimization
Analysis
Initial Design
Modification
Evaluation
“Optimum” Design
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 8
Specification of ANSYS Design Optimization

ANSYS Design optimization employs approximation techniques
that permit optimization based on virtually any aspect of a design,
not just cost or weight.

Any problem that can be solved by an ANSYS analysis can also be
included in ANSYS design optimization.
 Full
analysis capabilities
 APDL,
ANSYS Parametric Design Language
 Access

to analysis results and database values
Therefore, there is tremendous flexibility in the types of
optimization
problems that can be handled by the ANSYS program.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 9
Design Optimization Technique

ANSYS offers a number of techniques for performing design
optimization, including :
 Two
automated optimization methods
 Tools
for user-driven design studies
 Ability

to program custom optimization logic
For most users, ANSYS optimization methods and tools are
sufficient to quickly help compute an optimal solution for a
design.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 10
Key Concepts
In ANSYS, design optimization can be made an interactive
process to seek an optimal design. The major steps involved
are :

Create a functional analysis problem which parameterizes
item that :

You wish to vary (design variables)

You wish to constrain (constrains)

You wish to optimize (goal)

Are compared as results

Select an optimization technique.

Perform the optimization run.

Examine results.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 11
Terminology
Some of the terminology we will use in creating automated
design optimization in ANSYS include :
- Design variables
- State variables
- Objective function
- Function minimization
- Design Space
- Design Set
- Feasible, infeasible, and best designs
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 12
Design 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 positivevalued quantities which are automatically changed, or can be
set by the user.

Up to 60 design variables may be defined in ANSYS.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 13
State 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
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 14
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.
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Chapter 5. Introduction to Design Optimization - 15
Other 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.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 16
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 closest
to feasible, not the design with the optimal objective function value, as
best design.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 17
A Sample Optimization Problem
Consider a beam model with a load on it :
100 lbs
h
w
Design the beam height and width for the given loading
condition such that the weight is minimized subject to an
acceptable deformation at the beam end point.
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Chapter 5. Introduction to Design Optimization - 18
A 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 (D) 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.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 19
To Optimize the Problem

Build initial model using ANSYS parameters for the width w
and height h. Set another parameters “del” to the retrieved
end point nodal deformation value.

Modeling and analysis session will be saved, including
parameters, as an analysis file.

In the optimization phase, w and h are defined as design
variables, analysis result “del” is defined as a state variable,
and an additional parameter defined as the value (w*h) in
the analysis file is used as the objective function.
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Chapter 5. Introduction to Design Optimization - 20
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.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 21
Methods and Tools
The most general case of optimization, e.g. trying every
possible solution within the feasible design space, is virtually
impossible for real problems.
Approximations to this general case are sufficient for many
problems. ANSYS offers several optimization tools and methods
appropriate for different kinds of analysis problems. These
methods and tools are discussed in more detail in Chapter 9.

Optimization methods attempt an automated solution of an optimization
problem.

Optimization tools can be employed by the user to help “get a feel” for
design space.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 22
ANSYS Optimization Methods

Sub-problem Approximation Method - An approach based
upon using an approximation of the objective function.
Generally efficient.

First Order Method - An approach based upon searching
techniques using the gradients (e.g. rate of change) of
dependent variables with respect to the design variables.
Generally more accurate.

User Method - Implementation of a user optimization function
in subroutine form. These optimization methods seek
minimum for the objective function.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 23
ANSYS Design Optimization Tools

Single Iteration Design Tool - Makes one pass through an ANSYS analysis
using a specified design set. Facilitates user-driven “what if” studies.

Random Tool - Generates several design sets using random variations of
design variables.

Factorial Tool - Scans all extreme points in design space.

Gradient Tool - Uses gradient of objective function and state variables.

Sweep Tool - Sweeps design space one variable at a time.

User Tool - Use of a user function in subroutine form.
Written by Changhyun, SON
Chapter 5. Introduction to Design Optimization - 24