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＜電子ブック＞
Shape Optimization by the Homogenization Method / by Gregoire Allaire
(Applied Mathematical Sciences. ISSN:2196968X ; 146)

版	1st ed. 2002.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	XVI, 458 p : online resource
著者標目	*Allaire, Gregoire author SpringerLink (Online service)
件　名	LCSH:Buildings -- Design and construction  全ての件名で検索 LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 LCSH:Mathematical analysis LCSH:Mechanics LCSH:Engineering design LCSH:Civil engineering FREE:Building Construction and Design FREE:Mathematical and Computational Engineering Applications FREE:Analysis FREE:Classical Mechanics FREE:Engineering Design FREE:Civil Engineering
一般注記	1 Homogenization -- 1.1 Introduction to Periodic Homogenization -- 1.2 Definition of H-convergence -- 1.3 Proofs and Further Results -- 1.4 Generalization to the Elasticity System -- 2 The Mathematical Modeling of Composite Materials -- 2.1 Homogenized Properties of Composite Materials -- 2.2 Conductivity -- 2.3 Elasticity -- 3 Optimal Design in Conductivity -- 3.1 Setting of Optimal Shape Design -- 3.2 Relaxation by the Homogenization Method -- 4 Optimal Design in Elasticity -- 4.1 Two-phase Optimal Design -- 4.2 Shape Optimization -- 5 Numerical Algorithms -- 5.1 Algorithms for Optimal Design in Conductivity -- 5.2 Algorithms for Structural Optimization The topic of this book is homogenization theory and its applications to optimal design in the conductivity and elasticity settings. Its purpose is to give a self-contained account of homogenization theory and explain how it applies to solving optimal design problems, from both a theoretical and a numerical point of view. The application of greatest practical interest tar­ geted by this book is shape and topology optimization in structural design, where this approach is known as the homogenization method. Shape optimization amounts to finding the optimal shape of a domain that, for example, would be of maximal conductivity or rigidity under some specified loading conditions (possibly with a volume or weight constraint). Such a criterion is embodied by an objective function and is computed through the solution of astate equation that is a partial differential equa­ tion (modeling the conductivity or the elasticity of the structure). Apart from those areas where the loads are applied, the shape boundary is al­ ways assumed to support Neumann boundary conditions (i. e. , isolating or traction-free conditions). In such a setting, shape optimization has a long history and has been studied by many different methods. There is, therefore, a vast literat ure in this field, and we refer the reader to the following short list of books, and references therein [39], [42], [130], [135], [149], [203], [220], [225], [237], [245], [258] HTTP:URL=https://doi.org/10.1007/978-1-4684-9286-6

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