Shape Optimization by the Homogenization Method

Gregoire Allaire

• 19 oktober 2001
• 9780387952987

Samenvatting:

The topic of this book is homogenization theory and its applications to optimal design in the conductivity and elasticity settings. 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).



This book provides an introduction to the theory and numerical developments of the homogenization method. Its main features are: a comprehensive presentation of homogenization theory; an introduction to the theory of two-phase composite materials;a detailed treatment of structural optimization by using homogenization; a complete discussion of the resulting numerical algorithms with many documented test problems. It will be of interest to researchers, engineers, and advanced graduate students in applied mathematics, mechanical engineering, and structural optimization.