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An Introduction to Structural Optimization

  • Textbook
  • © 2009

Overview

Authors:
  1. Peter W. Christensen
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  2. Anders Klarbring
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  • Introductory text that covers all three basic classes of geometry optimization problems of mechanical structures: size, shape as well as topology optimization
  • The mathematics is kept at an elementary level
  • The algorithms are described in sufficient detail to enable readers to make their own implementations
  • The understanding of the material covered is facilitated by computer exercises using programs available at our home page
  • Includes supplementary material: sn.pub/extras

Part of the book series: Solid Mechanics and Its Applications (SMIA, volume 153)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Peter W. Christensen, Anders Klarbring
    Pages 1-7

  3. Examples of Optimization of Discrete Parameter Systems

    • Peter W. Christensen, Anders Klarbring
    Pages 9-34

  4. Basics of Convex Programming

    • Peter W. Christensen, Anders Klarbring
    Pages 35-55

  5. Sequential Explicit, Convex Approximations

    • Peter W. Christensen, Anders Klarbring
    Pages 57-75

  6. Sizing Stiffness Optimization of a Truss

    • Peter W. Christensen, Anders Klarbring
    Pages 77-95

  7. Sensitivity Analysis

    • Peter W. Christensen, Anders Klarbring
    Pages 97-115

  8. Two-Dimensional Shape Optimization

    • Peter W. Christensen, Anders Klarbring
    Pages 117-146

  9. Stiffness Optimization of Distributed Parameter Systems

    • Peter W. Christensen, Anders Klarbring
    Pages 147-177

  10. Topology Optimization of Distributed Parameter Systems

    • Peter W. Christensen, Anders Klarbring
    Pages 179-201

  11. Back Matter

    Pages 203-211
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Keywords

About this book

This book has grown out of lectures and courses given at Linköping University, Sweden, over a period of 15 years. It gives an introductory treatment of problems and methods of structural optimization. The three basic classes of geometrical - timization problems of mechanical structures, i. e. , size, shape and topology op- mization, are treated. The focus is on concrete numerical solution methods for d- crete and (?nite element) discretized linear elastic structures. The style is explicit and practical: mathematical proofs are provided when arguments can be kept e- mentary but are otherwise only cited, while implementation details are frequently provided. Moreover, since the text has an emphasis on geometrical design problems, where the design is represented by continuously varying—frequently very many— variables, so-called ?rst order methods are central to the treatment. These methods are based on sensitivity analysis, i. e. , on establishing ?rst order derivatives for - jectives and constraints. The classical ?rst order methods that we emphasize are CONLIN and MMA, which are based on explicit, convex and separable appro- mations. It should be remarked that the classical and frequently used so-called op- mality criteria method is also of this kind. It may also be noted in this context that zero order methods such as response surface methods, surrogate models, neural n- works, genetic algorithms, etc. , essentially apply to different types of problems than the ones treated here and should be presented elsewhere.

Reviews

From the reviews:

“This book represents a good introduction to structural optimization. It covers the main methods used for the optimization of discrete and distributed parametric systems. … Due to numerous practical examples, this book can be strongly recommended to young specialists and students in mechanical engineering.” (Sergiu T. Chiriacescu, Zentralblatt MATH, Vol. 1180, 2010)

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