THE HOMOGENIZATION METHOD FOR TOPOLOGY AND SHAPE OPTIMIZATION

This paper is devoted to an elementary introduction to the homogenization theory and its application to topology and shape optimization of elastic structures. It starts with a brief survey of periodic homogenization, H- or G-convergence, and the mathematical modeling of composite materials. Then, these notions are used for minimum compliance and weight design of elastic structures in two or three space dimension. Theoretical, as well as numerical, aspects of the homogenization method are investigated.

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