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Shape Optimization by the Homogenization Method

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 nu...

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Bibliographic Details
Main Author: Allaire, Gregoire
Format: eBook
Language:English
Published: New York, NY Springer New York 2002, 2002
Edition:1st ed. 2002
Series:Applied Mathematical Sciences
Subjects:
Engineering Mathematics
Classical Mechanics
Mathematical Analysis
Engineering Design
Buildings / Design And Construction
Analysis
Civil Engineering
Engineering / Data Processing
Mechanics
Mathematical And Computational Engineering Applications
Building Construction And Design
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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

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