ENGLISH

Shape Optimization by the Homogenization Method

By Grégoire Allaire (auth.)

Book information

Publisher
Springer-Verlag New York
Year
2002
ISBN
978-1-4419-2942-6, 978-1-4684-9286-6
DOI
10.1007/978-1-4684-9286-6
Language
english
Format
PDF
Filesize
12 MB (12225735 bytes)
Series
Applied Mathematical Sciences 146
Edition
1
Pages
458\469
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Analysis;Mechanics;Engineering Design;Civil Engine

Description

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].

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