1. Introduction Chapter One

2. Training Manual January 30, 2001 Inventory #001449 1-2 Introduction Course Overview This Design Optimization course is designed to familiarize you with the optimization capabilities of ANSYS. It is intended for the ANSYS user who wishes to move from the question “How will my design perform” to “What is my design?” Although design optimization is applicable to all the multi- physics capabilities of ANSYS, this course will mainly use stress analyses to describe and illustrate the optimization procedures.

3. Training Manual January 30, 2001 Inventory #001449 1-3 Introduction...Course Overview Upon completing this course, you should have a basic understanding of how to: –create a parametric model –optimize the design –experiment with different designs –work with the optimization database –build a conceptual design

4. Training Manual January 30, 2001 Inventory #001449 1-4 Introduction...Course Overview In this first chapter, we will: A.Define design optimization and review some sample applications B.Learn some of the underlying terminology C.Find out some of the features of ANSYS design optimization D.Run a simple example

5. Training Manual January 30, 2001 Inventory #001449 1-5 Introduction A. Design Optimization What is Design Optimization? A procedure to create an optimum design. An optimum design performs the intended function and: a)meets all specified requirements - stress level, natural frequency, maximum temperature, etc. b)keeps the total weight (or total volume, cost, or other specified criterion) to a minimum. An I-beam, for example, is an optimum configuration to carry a bending load.

6. Training Manual January 30, 2001 Inventory #001449 1-6 Introduction...Design Optimization Powder metallurgy gear* The gear was optimized for minimum weight with a limit on maximum stress under load. A 27% weight reduction was achieved by changing a solid gear to one with voids. * Design Optimization of Powder Metallurgy Gears, Orbison et al, ANSYS Conference Proceedings

7. Training Manual January 30, 2001 Inventory #001449 1-7 Introduction...Design Optimization Oil cooled piston* This piston for a diesel engine was optimized for minimum temperature in critical areas of the piston crown. A 5% temperature reduction was achieved between the initial and final designs. * Design Optimization of an Oil Cooled Gallery Piston, Urbani et al, ANSYS Conference Proceedings

8. Training Manual January 30, 2001 Inventory #001449 1-8 Introduction...Design Optimization... Oil cooled piston

9. Training Manual January 30, 2001 Inventory #001449 1-9 Introduction...Design Optimization “Nut plate” of a lube system filter* The plate was optimized for minimum weight and to improve its dynamic and hydrostatic characteristics. A 17% reduction in weight (54 grams) was achieved by changing the shape of the plate. Also, maximum von Mises stress and maximum deflection reduced by 19% and 47%, respectively. * Optimization of a Parametric Structural Plate, Robbins et al, ANSYS Conference Proceedings

10. Training Manual January 30, 2001 Inventory #001449 1-10 Introduction...Design Optimization... “Nut plate” of a lube system filter Initial Design Final Design

11. Training Manual January 30, 2001 Inventory #001449 1-11 Introduction...Design Optimization Air starter turbine rotor* This air starter rotor for a diesel engine was optimized for minimum weight with a limit on maximum von Mises stress. * Design Optimization of an Air Starter Turbine Rotor, Owens et al, ANSYS Conference Proceedings The original, two-piece design (0.5 lb) was changed to a one-piece design (0.19 lb), achieving a weight reduction of 62%.

12. Training Manual January 30, 2001 Inventory #001449 1-12 Introduction...Design Optimization... Air starter turbine rotor

13. Training Manual January 30, 2001 Inventory #001449 1-13 Introduction...Design Optimization Shape optimization of a piston* The piston was optimized for minimum weight with a limit on maximum von Mises stress. A weight reduction of 35% (1.01 lb to 0.64 lb) was achieved. * Effective Use of Numerical Optimization in Structural Design, Vanderplaats, ANSYS Conference Proceedings

14. Training Manual January 30, 2001 Inventory #001449 1-14 Introduction B. Terminology A typical design optimization problem consists of three parts: 1. An item that is minimized or maximized. This is the objective function. Examples: –total weight or volume (usually minimized) –heat flow rate (usually maximized)

15. Training Manual January 30, 2001 Inventory #001449 1-15 Introduction...Terminology 2.Design characteristics that are varied to achieve the objective. These are the design variables. Examples: –thickness –height –fillet radius –yield stress –number of holes

16. Training Manual January 30, 2001 Inventory #001449 1-16 Introduction...Terminology 3.Conditions that the design must meet. These are the state variables. Examples: –limits on maximum stress –limits on maximum deflection –minimum first natural frequency –limits on maximum temperature –limits on maximum temperature gradient.

17. Training Manual January 30, 2001 Inventory #001449 1-17 200 ft 50 ft 20 lb/in Introduction...Terminology Consider, for example, the following optimization problem: Minimize the weight of a continuous-span truss bridge subject to a maximum member stress of 10,000 psi and a maximum deflection of 1 in. You are allowed to vary the member cross sections and the elevation of the bridge at mid-span.

18. Training Manual January 30, 2001 Inventory #001449 1-18 Introduction...Terminology Design variables (DVs) are –A1, A2, A3… the cross sectional areas of the horizontal, vertical, and diagonal members. –H1, H2… the elevation at quarter-span and mid-span. H1 H2 A1 A2 A3 State variables (SVs) are –SMAX  10,000 psi… maximum stress in all members. –DMAX  1.0 in… maximum deflection at all joints. Objective function is V, the total volume, to be minimized. H1

19. Training Manual January 30, 2001 Inventory #001449 1-19 Introduction...Terminology A design can now be defined as the model created by one set of DV values. For example, the initial design of the truss bridge could be the one defined by: –A1 = 2.0 in 2 –A2 = 2.0 –A3 = 2.0 –H1 = 0.0 in –H2 = 0.0

20. Training Manual January 30, 2001 Inventory #001449 1-20 Introduction...Terminology A feasible design is within all the DV and SV ranges. Generally, the DV’s are always inside their permitted range. An infeasible design is one that violates at least one constraint. –In the truss bridge example, if a given design causes one of the joints to deflect more than 1.0 in, it is an infeasible design. –ANSYS can achieve an optimum design even if the initial design is infeasible. SV DV SV max SV min DV min DV max feasible infeasible

21. Training Manual January 30, 2001 Inventory #001449 1-21 Introduction...Terminology The best design is one that has the lowest objective function value and most closely meets all the constraints. –If no feasible designs are available, the best design is one that most closely meets all the constraints, not the one with the lowest objective function value. The design domain (or design space) is the region defined by all possible feasible designs.

22. Training Manual January 30, 2001 Inventory #001449 1-22 Introduction C. Optimization Features in ANSYS ANSYS design optimization allows you to do the following: Optimize the design –Two optimization methods, or algorithms, allow you to start with an initial design and let ANSYS “hone in” on the optimum. –You can even incorporate your own user optimization* algorithm. * Not covered in this course

23. Training Manual January 30, 2001 Inventory #001449 1-23 Introduction...Optimization Features in ANSYS Explore the design domain –Optimization tools allow you to experiment with different, “what- if” type designs and create initial design sets for the optimizers. –You can generate random designs, sweep through a range of DV values, run sensitivity studies, and even run a design of experiments using the factorial tool.

24. Training Manual January 30, 2001 Inventory #001449 1-24 Introduction...Optimization Features in ANSYS You can optimize virtually any aspect of your design, not just shape parameters. Examples: –Minimize deflection variations by finding the best support points. –Determine the “best” film transfer coefficient for efficient cooling.

25. Training Manual January 30, 2001 Inventory #001449 1-25 Introduction...Optimization Features in ANSYS Optimization is entirely based on parameters (APDL, discussed later). –DVs, SVs and the objective function must be defined as parameters. You can use results from a combination of analysis types. –For example, both maximum stress (from a stress analysis) and natural frequency (from a modal analysis) can be specified as state variables in a single optimization run.

26. Training Manual January 30, 2001 Inventory #001449 1-26 Introduction...Optimization Features in ANSYS A finite element analysis is not necessary. –You can minimize any function as long as it is defined as a parameter. –For example, “Determine the optimum speed of travel to minimize the cost of a 50-mile trip, subject to a one-hour limit on travel time.” Here, cost is the objective function, speed is the DV, and travel time is the SV.

27. Training Manual January 30, 2001 Inventory #001449 1-27 Introduction...Optimization Features in ANSYS Optimization begins with building a parametric model of the initial design and creating an analysis file. Analysis File Explore the Design Domain Optimize the Design Initial Design Parametric Model & Loading Solution Parametric Results

28. Training Manual January 30, 2001 Inventory #001449 1-28 Introduction...Optimization Features in ANSYS Additional Optimization Techniques in ANSYS –Shape Optimization (conceptual design) Known as topological optimization, this allows you to apply loads on a basic shape and let ANSYS determine the shape that can provide the maximum stiffness for those loads – Probabilistic Design Predicts variations in design performance

29. Training Manual January 30, 2001 Inventory #001449 1-29 Introduction...Optimization Features in ANSYS The next five chapters explain how to use these optimization features: –Chapter 2 describes how to create the initial design (the parametric model) and the analysis file. –Chapters 3 and 5 cover how to optimize the design. –Chapters 4 and 6 describe details of how to explore the design domain. Chapter 7 gives an introduction to probabilistic design Finally, Chapter 8 covers how to build a conceptual design (topological optimization).

30. Training Manual January 30, 2001 Inventory #001449 1-30 Introduction D. Workshop This workshop introduces you to design optimization by solving the trip cost minimization problem mentioned earlier. Determine the optimum speed of travel to minimize the cost of a 50-mile trip, subject to a one-hour limit on travel time. See your Design Optimization Workshop Supplement for details.