Shape Optimization by the Homogenization Method

  • Grégoire Allaire

Part of the Applied Mathematical Sciences book series (AMS, volume 146)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Grégoire Allaire
    Pages 1-89
  3. Grégoire Allaire
    Pages 91-188
  4. Grégoire Allaire
    Pages 189-257
  5. Grégoire Allaire
    Pages 259-342
  6. Grégoire Allaire
    Pages 343-425
  7. Back Matter
    Pages 427-458

About this book


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].


algorithm analysis mathematical modeling mathematics mechanical engineering model modeling optimization quality simulation structure

Authors and affiliations

  • Grégoire Allaire
    • 1
  1. 1.Centre of Applied MathematicsEcole PolytechniquePaliseau CedexFrance

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2942-6
  • Online ISBN 978-1-4684-9286-6
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site
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