Variational Methods for Structural Optimization / Edition 1

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The challenge of this book is to bridge a gap between a rigorous mathe matical approach to variational problems and the practical use of algo rithms of structural optimization in engineering applications. The fou ndations of structural optimization are presented in a sufficiently si mple form to make them available for practical use and to allow their critical appraisal for improving and adapting these results to specifi c models. Special attention is paid to the description of optimal stru ctures of composites; to deal with this problem, novel mathematical me thods of nonconvex calculus of variation are developed. The exposition is accompanied by numerous examples.

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Product Details

  • ISBN-13: 9780387984629
  • Publisher: Springer New York
  • Publication date: 5/1/2009
  • Series: Applied Mathematical Sciences Series, #140
  • Edition description: 2000
  • Edition number: 1
  • Pages: 548
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.25 (d)

Table of Contents

List of Figures
1 Relaxation of One-Dimensional Variational Problems 3
2 Conducting Composites 35
3 Bounds and G-Closures 59
4 Domains of Extremal Conductivity 81
5 Optimal Conducting Structures 117
6 Quasiconvexity 145
7 Optimal Structures and Laminates 171
8 Lower Bound: Translation Method 213
9 Necessary Conditions and Minimal Extensions 239
10 Obtaining G-Closures 261
11 Examples of G-Closures 279
12 Multimaterial Composites 309
13 Supplement: Variational Principles for Dissipative Media 343
14 Elasticity of Inhomogeneous Media 359
15 Elastic Composites of Extremal Energy 393
16 Bounds on Effective Properties 419
17 Some Problems of Structural Optimization 459
References 495
Author/Editor Index 525
Subject Index 533
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