Introduction to Optimum Design

Jasbir Singh Arora

• Publisher: Academic Press
• Year: 2004
• eBook ISBN: 9780080470252
• Edition: 2
• Topic: Technology & Engineering
• Subtopic: Applied Mathematics
• Index: Technology & Engineering

Optimization is a mathematical tool developed in the early 1960's used to find the most efficient and feasible solutions to an engineering problem. It can be used to find ideal shapes and physical configurations, ideal structural designs, maximum energy efficiency, and many other desired goals of engineering. This book is intended for use in a first course on engineering design and optimization. Material for the text has evolved over a period of several years and is based on classroom presentations for an undergraduate core course on the principles of design. Virtually any problem for which certain parameters need to be determined to satisfy constraints can be formulated as a design optimization problem. The concepts and methods described in the text are quite general and applicable to all such formulations. Inasmuch, the range of application of the optimum design methodology is almost limitless, constrained only by the imagination and ingenuity of the user. The book describes the basic concepts and techniques with only a few simple applications. Once they are clearly understood, they can be applied to many other advanced applications that are discussed in the text. - Allows engineers involved in the design process to adapt optimum design concepts in their work using the material in the text - Basic concepts of optimality conditions and numerical methods are described with simple examples, making the material high teachable and learnable - Classroom-tested for many years to attain optimum pedagogical effectiveness

1 Introduction to Design

Upon completion of this chapter, you will be able to:

• Describe the overall process of designing systems

• Distinguish between engineering design and engineering analysis activity

• Distinguish between the conventional design process and optimum design process

• Distinguish between the optimum design and optimal control problems

• Understand the notations used for operations with vectors, matrices, and functions

Engineering consists of a number of well established activities, including analysis, design, fabrication, sales, research, and the development of systems. The subject of this text—the design of systems—is a major field in the engineering profession. The process of designing and fabricating systems has been developed over centuries. The existence of many complex systems, such as buildings, bridges, highways, automobiles, airplanes, space vehicles, and others, is an excellent testimonial for this process. However, the evolution of these systems has been slow. The entire process has been both time-consuming and costly, requiring substantial human and material resources. Therefore, the procedure has been to design, fabricate, and use the system regardless of whether it was the best one. Improved systems were designed only after a substantial investment had been recovered. These new systems performed the same or even more tasks, cost less, and were more efficient.

The preceding discussion indicates that several systems can usually accomplish the same task, and that some are better than others. For example, the purpose of a bridge is to provide continuity in traffic from one side to the other. Several types of bridges can serve this purpose. However, to analyze and design all possibilities can be a time-consuming and costly affair. Usually one type has been selected based on some preliminary analyses and has been designed in detail.

The design of complex systems requires data processing and a large number of calculations. In the recent past, a revolution in computer technology and numerical computations has taken place. Today’s computers can perform complex calculations and process large amounts of data rapidly. The engineering design and optimization processes benefit greatly from this revolution because they require a large number of calculations. Better systems can now be designed by analyzing and optimizing various options in a short time. This is highly desirable because better designed systems cost less, have more capability, and are easy to maintain and operate.

The design of systems can be formulated as problems of optimization in which a measure of performance is to be optimized while satisfying all constraints. Many numerical methods of optimization have been developed and used to design better systems. This text describes the basic concepts of optimization methods and their applications to the design of engineering systems. Design process is emphasized rather than optimization theory. Various theorems are stated as results without rigorous proofs. However, their implications from an engineering point of view are studied and discussed in detail. Optimization theory, numerical methods, and modern computer hardware and software can be used as tools to design better engineering systems. The text emphasizes this theme throughout.

Any problem in which certain parameters need to be determined to satisfy constraints can be formulated as an optimization problem. Once this has been done, the concepts and the methods described in this text can be used to solve the problem. Therefore, the optimization techniques are quite general, having a wide range of applicability in diverse fields. The range of applications is limited only by the imagination or ingenuity of the designers. It is impossible to discuss every application of optimization concepts and techniques in this introductory text. However, using simple applications, we shall discuss concepts, fundamental principles, and basic techniques that can be used in numerous applications. The student should understand them without getting bogged down with the notation, terminology, and details of the particular a...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Jasbir S. Arora
• Dedication
• Preface
• Chapter 1: Introduction to Design
• Chapter 2: Optimum Design Problem Formulation
• Chapter 3: Graphical Optimization
• Chapter 4: Optimum Design Concepts
• Chapter 5: More on Optimum Design Concepts
• Chapter 6: Linear Programming Methods for Optimum Design
• Chapter 7: More on Linear Programming Methods for Optimum Design
• Chapter 8: Numerical Methods for Unconstrained Optimum Design
• Chapter 9: More on Numerical Methods for Unconstrained Optimum Design
• Chapter 10: Numerical Methods for Constrained Optimum Design
• Chapter 11: More on Numerical Methods for Constrained Optimum Design
• Chapter 12: Introduction to Optimum Design with MATLAB
• Chapter 13: Interactive Design Optimization
• Chapter 14: Design Optimization Applications with Implicit Functions
• Chapter 15: Discrete Variable Optimum Design Concepts and Methods
• Chapter 16: Genetic Algorithms for Optimum Design
• Chapter 17: Multiobjective Optimum Design Concepts and Methods
• Chapter 18: Global Optimization Concepts and Methods for Optimum Design
• Appendix A: Economic Analysis
• Appendix B: Vector and Matrix Algebra
• Appendix C: A Numerical Method for Solution of Nonlinear Equations
• Appendix D: Sample Computer Programs
• References
• Bibliography
• Answers to Selected Problems
• Index