Vanderplaats-chap1

# Vanderplaats-chap1 - CHAPTER ONE 1BASIC CONCEPTS 1-1...

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1 CHAPTER ONE 1 BASIC CONCEPTS 1-1 INTRODUCTION The concept of optimization is basic to much of what we do in our daily lives. The desire to run a faster race, win a debate, or increase corporate profit implies a desire to do or be the best in some sense. In engineering, we wish to produce the “best quality of life possible with the resources avail- able.” Thus in “designing” new products, we must use design tools which provide the desired results in a timely and economical fashion. Numerical optimization is one of the tools at our disposal. In studying design optimization, it is important to distinguish between analysis and design. Analysis is the process of determining the response of a specified system to its environment. For example, the calculation of stresses in a structure that result from applied loads is referred to here as analysis. Design, on the other hand, is used to mean the actual process of defining the system. For example, structural design entails defining the sizes and loca- tions of members necessary to support a prescribed set of loads. Clearly, analysis is a sub-problem in the design process because this is how we eval- uate the adequacy of the design. Much of the design task in engineering is quantifiable, and so we are able to use the computer to analyze alternative designs rapidly. The purpose of numerical optimization is to aid us in rationally searching for the best design to meet our needs. While the emphasis here is on design, it should be noted that these methods can often be used for analysis as well. Nonlinear structural analysis is an example where optimization can be used to solve a nonlinear energy minimization problem.

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2 NUMERICAL OPTIMIZATION TECHNIQUES FOR ENGINEERING DESIGN Although we may not always think of it this way, design can be defined as the process of finding the minimum or maximum of some parameter which may be called the objective function. For the design to be acceptable, it must also satisfy a certain set of specified requirements called constraints. That is, we wish to find the constrained minimum or maximum of the objec- tive function. For example, assume we wish to design an internal-combus- tion engine. The design objective could be to maximize combustion efficiency. The engine may be required to provide a specified power output with an upper limit on the amount of harmful pollutants which can be emit- ted into the atmosphere. The power requirements and pollution restrictions are therefore constraints on the design. Various methods can be used to achieve the design goal. One approach might be through experimentation where many engines are built and tested. The engine providing maximum economy while satisfying the constraints on the design would then be chosen for production. Clearly this is a very expensive approach with little assurance of obtaining a true optimum design. A second approach might be to define the design process analyti- cally and then to obtain the solution using differential calculus or the calcu- lus of variations. While this is certainly an attractive procedure, it is seldom
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