Shape Optimization by the Homogenization Method

This book offers a self-contained introduction to the theory and numerical developments of the homogenization method. It provides a detailed presentation of homogenization theory, focusing on its application to optimal design. It contains many new results not previously published as well as results that are well known but until now not adequately referenced in the literature. Numerical algorithms previously published only in journal form are now synthesized and systematically analyzed. This book is intended for an audience of researchers, engineers, and advanced graduate students in applied mathematics, mechanical engineering, and structural optimization. The more mathematically oriented reader can learn about homogenization and relaxation of optimal design problems, while the more practically inclined reader can be introduced to state-of-the-art numerical algorithms in structural optimization by the homogenization method.