Introduction to Optimum Design

Introduction to Optimum Design

2nd Edition - May 5, 2004

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  • Author: Jasbir Arora
  • eBook ISBN: 9780080470252

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Description

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.

Key Features

  • 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

Readership

Engineering students and practitioners studying optimization and mechanical engineering design

Table of Contents

  • Jasbir S. Arora

    Dedication

    Preface

    Chapter 1: Introduction to Design

    1.1: The Design Process

    1.2: Engineering Design versus Engineering Analysis

    1.3: Conventional versus Optimum Design Process

    1.4: Optimum Design versus Optimal Control

    1.5: Basic Terminology and Notation

    Chapter 2: Optimum Design Problem Formulation

    2.1: The Problem Formulation Process

    2.2: Design of a Can

    2.3: Insulated Spherical Tank Design

    2.4: Saw Mill Operation

    2.5: Design of a Two-Bar Bracket

    2.6: Design of a Cabinet

    2.7: Minimum Weight Tubular Column Design

    2.8: Minimum Cost Cylindrical Tank Design

    2.9: Design of Coil Springs

    2.10: Minimum Weight Design of a Symmetric Three-Bar Truss

    2.11: A General Mathematical Model for Optimum Design

    Exercises for Chapter 2

    Chapter 3: Graphical Optimization

    3.1: Graphical Solution Process

    3.2: Use of Mathematica for Graphical Optimization

    3.3: Use of MATLAB for Graphical Optimization

    3.4: Design Problem with Multiple Solutions

    3.5: Problem with Unbounded Solution

    3.6: Infeasible Problem

    3.7: Graphical Solution for Minimum Weight Tubular Column

    3.8: Graphical Solution for a Beam Design Problem

    Exercises for Chapter 3

    Chapter 4: Optimum Design Concepts

    4.1: Definitions of Global and Local Minima

    4.2: Review of Some Basic Calculus Concepts

    4.3: Unconstrained Optimum Design Problems

    4.4: Constrained Optimum Design Problems

    4.5: Postoptimality Analysis: Physical Meaning of Lagrange Multipliers

    4.6: Global Optimality

    4.7: Engineering Design Examples

    Exercises for Chapter 4

    Chapter 5: More on Optimum Design Concepts

    5.1: Alternate Form of KKT Necessary Conditions

    5.2: Irregular Points

    5.3: Second-Order Conditions for Constrained Optimization

    5.4: Sufficiency Check for Rectangular Beam Design Problem

    Exercises for Chapter 5

    Chapter 6: Linear Programming Methods for Optimum Design

    6.1: Definition of a Standard Linear Programming Problem

    6.2: Basic Concepts Related to Linear Programming Problems

    6.3: Basic Ideas and Steps of the Simplex Method

    6.4: Two-Phase Simplex Method-Artificial Variables

    6.5: Postoptimality Analysis

    6.6: Solution of LP Problems Using Excel Solver

    Exercises for Chapter 6

    Chapter 7: More on Linear Programming Methods for Optimum Design

    7.1: 7.1 Derivation of the Simplex Method

    7.2: Alternate Simplex Method

    7.3: Duality in Linear Programming

    Chapter 8: Numerical Methods for Unconstrained Optimum Design

    8.1: General Concepts Related to Numerical Algorithms

    8.2: Basic Ideas and Algorithms for Step Size Determination

    8.3: Search Direction Determination: Steepest Descent Method

    8.4: Search Direction Determination: Conjugate Gradient Method

    Exercises for Chapter 8

    Chapter 9: More on Numerical Methods for Unconstrained Optimum Design

    9.1: More on Step Size Determination

    9.2: More on Steepest Descent Method

    9.3: Scaling of Design Variables

    9.4: Search Direction Determination: Newton’s Method

    9.5: Search Direction Determination: Quasi-Newton Methods

    9.6: Engineering Applications of Unconstrained Methods

    9.7: Solution of Constrained Problems Using Unconstrained Optimization Methods

    Exercises for Chapter 9*

    Chapter 10: Numerical Methods for Constrained Optimum Design

    10.1: Basic Concepts and Ideas

    10.2: Linearization of Constrained Problem

    10.3: Sequential Linear Programming Algorithm

    10.4: Quadratic Programming Subproblem

    10.5: Constrained Steepest Descent Method

    10.6: Engineering Design Optimization Using Excel Solver

    Exercises for Chapter 10

    Chapter 11: More on Numerical Methods for Constrained Optimum Design

    11.1: Potential Constraint Strategy

    11.2: Quadratic Programming Problem

    11.2.1: Definition of QP Problem

    11.2.2: KKT Necessary Conditions for the QP Problem

    11.2.3: Transformation of KKT Conditions

    11.2.4: Simplex Method for Solving QP Problem

    11.3: Approximate Step Size Determination

    11.4: Constrained Quasi-Newton Methods

    11.4.1: Derivation of Quadratic Programming Subproblem

    11.4.2: Quasi-Newton Hessian Approximation

    11.4.3: Modified Constrained Steepest Descent Algorithm

    11.4.4: Observations on the Constrained Quasi-Newton Methods

    11.4.5: Descent Functions

    11.5: Other Numerical Optimization Methods

    Chapter 12: Introduction to Optimum Design with MATLAB

    12.1: Introduction to Optimization Toolbox

    12.2: Unconstrained Optimum Design Problems

    12.3: Constrained Optimum Design Problems

    12.4: Optimum Design Examples with MATLAB

    Chapter 13: Interactive Design Optimization

    13.1: Role of Interaction in Design Optimization

    13.2: Interactive Design Optimization Algorithms

    13.3: Desired Interactive Capabilities

    13.4: Interactive Design Optimization Software

    13.5: Examples of Interactive Design Optimization

    Exercises for Chapter 13

    Chapter 14: Design Optimization Applications with Implicit Functions

    14.1: Formulation of Practical Design Optimization Problems

    14.2 Gradient Evaluation for Implicit Functions

    14.3: Issues in Practical Design Optimization

    14.4: Use of General-Purpose Software

    14.5: Optimum Design of a Two-Member Frame with Out-of-Plane Loads

    14.6: Optimum Design of a Three-Bar Structure for Multiple Performance Requirements

    14.7: Discrete Variable Optimum Design

    14.8: Optimal Control of Systems by Nonlinear Programming

    Chapter 15: Discrete Variable Optimum Design Concepts and Methods

    15.1: Basic Concepts and Definitions

    15.2: Branch and Bound Methods (BBM)

    15.3: Integer Programming

    15.4: Sequential Linearization Methods

    15.5: Simulated Annealing

    15.6: Dynamic Rounding-off Method

    15.7: Neighborhood Search Method

    15.8: Methods for Linked Discrete Variables

    15.9: Selection of a Method

    Exercises for Chapter 15*

    Chapter 16: Genetic Algorithms for Optimum Design

    16.1: Basic Concepts and Definitions

    16.2: Fundamentals of Genetic Algorithms

    16.3: Genetic Algorithm for Sequencing-Type Problems

    16.4: Applications

    Exercises for Chapter 16*

    Chapter 17: Multiobjective Optimum Design Concepts and Methods

    17.1: Problem Definition

    17.2: Terminology and Basic Concepts

    17.3: Multiobjective Genetic Algorithms

    17.4: Weighted Sum Method

    17.5: Weighted Min-Max Method

    17.6: Weighted Global Criterion Method

    17.7: Lexicographic Method

    17.8: Bounded Objective Function Method

    17.9: Goal Programming

    17.10: Selection of Methods

    Exercises for Chapter 17

    Chapter 18: Global Optimization Concepts and Methods for Optimum Design

    18.1: Basic Concepts of Solution Methods

    18.2: Overview of Deterministic Methods

    18.3: Overview of Stochastic Methods

    18.4: Two Local-Global Stochastic Methods

    18.5: Numerical Performance of Methods

    Exercises for Chapter 18*

    Appendix A: Economic Analysis

    A.1: Time Value of Money

    A.2: Economic Bases for Comparison

    Exercises for Appendix A

    Appendix B: Vector and Matrix Algebra

    B.1: Definition of Matrices

    B.2: Type of Matrices and Their Operations

    B.3: Solution of n Linear Equations in n Unknowns

    B.4: Solution of m Linear Equations in n Unknowns

    B.5: Concepts Related to a Set of Vectors

    B.6: Eigenvalues and Eigenvectors

    B.7*: Norm and Condition Number of a Matrix

    Exercises for Appendix B

    Appendix C: A Numerical Method for Solution of Nonlinear Equations

    C.1: Single Nonlinear Equation

    C.2: Multiple Nonlinear Equations

    Exercises for Appendix C

    Appendix D: Sample Computer Programs

    D.1: Equal Interval Search

    D.2: Golden Section Search

    D.3: Steepest Descent Method

    D.4: Modified Newton’s Method

    References

    Bibliography

    Answers to Selected Problems

    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 9.1

    Chapter 10: 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 18: Global Optimization Concepts and Methods for Optimum Design 18.1

    Appendix A: Economic Analysis

    Appendix B: Vector and Matrix Algebra

    Appendix C: A Numerical Method for Solution of Nonlinear Equations

    Index

Product details

  • No. of pages: 752
  • Language: English
  • Copyright: © Academic Press 2004
  • Published: May 5, 2004
  • Imprint: Academic Press
  • eBook ISBN: 9780080470252

About the Author

Jasbir Arora

Jasbir Arora
Dr. Arora is the F. Wendell Miller Distinguished Professor, Emeritus, of Civil, Environmental and Mechanical Engineering at the University of Iowa. He was also Director of the Optimal Design Laboratory and Associate Director of the Center for Computer Aided Design. He is an internationally recognized expert in the fields of optimization, numerical analysis, and real-time implementation. His research interests include optimization-based digital human modeling, dynamic response optimization, optimal control of systems, design sensitivity analysis and optimization of nonlinear systems, and parallel optimization algorithms. Dr. Arora has authored two books, co-authored or edited five others, written 160 journal articles, 27 book chapters, 130 conference papers, and more than 300 technical reports.

Affiliations and Expertise

Department of Civil and Environmental Engineering & Department of Mechanical Engineering, University of Iowa, iowa City, IA, USA

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  • Mustafa Mon Jul 09 2018

    Great book

    This book gives you all the basic necceary info about optimization. Great Professor.