Topology optimization of micro structure of porous material to maximize dissipated energy by using homogenization method

Abstract

A topology optimization method to design micro structures of sound-absorbing poroelastic media utilizing the homogenization method based on an asymptotic expansion is proposed in this study. Design sensitivities of homogenized properties with respect to design variables defined on nodes of a microscopic finite element model are derived by using the homogenization method and the adjoint variable method. Then, design sensitivities of macroscopic objective function, which is dissipated power in this study, with respect to design variables defined on nodes of a microscopic finite element model are derived by using the adjoint variable method. The design variables are updated by using Method of Moving Asymptotes (MMA). Here, the design sensitivities both in microscopic and macroscopic scales are verified by a numerical examples.