PART II Design Optimization

1. PART II Design Optimization Written by Changhyun, SON

2. CHAPTER 5 Introduction to Design Optimization Written by Changhyun, SON

3. 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

4. Some Definitions Designis the configuration of a part, product, or structure that enables a specified function to be performed. Optimum designis 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

5. 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

6. Analysis Initial Design Modification Evaluation “Optimum” Design Traditional Optimum Design Written by Changhyun, SON

7. 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

8. Analysis Initial Design Modification Evaluation “Optimum” Design Design Optimization Written by Changhyun, SON

9. 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

10. 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

11. 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

12. 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

13. 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 positive-valued 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

14. 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

15. 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. Written by Changhyun, SON

16. 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

17. 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

18. 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. Written by Changhyun, SON

19. 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

20. 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. Written by Changhyun, SON

21. 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

22. 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

23. 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

24. 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