An Introduction to Structural Optimization

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Springer Science & Business Media, Oct 14, 2008 - Technology & Engineering - 214 pages
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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.
 

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In my opinion, the best available book on Structural Optimization. I use it for my Topology Optimization class.

Contents

Introduction
2
Examples of Optimization of Discrete Parameter Systems
9
Basics of Convex Programming
35
Sequential Explicit Convex Approximations
57
Sizing Stiffness Optimization of a Truss
77
Sensitivity Analysis
96
TwoDimensional Shape Optimization
116
Stiffness Optimization of Distributed Parameter Systems
147
Topology Optimization of Distributed Parameter Systems
179
Answers to Selected Exercises
202
References
207
Index
209
Copyright

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