Concurrent shape optimization for macro- and micro-structure of 3D multiscale porous structure

Abstract

In this study, we present a 3D shape optimization method for designing micro- and macro-structures concurrently. We assume the macrostructure consists of several arbitrary subdomains, which have different periodic microstructures. The macro- and microstructures are bridged by the homogenized elastic tensors, which are calculated by applying the homogenization method to the unit cells of the microstructures. Defining the boundary shapes of the macro-, microstructures and the interface shapes between the subdomains as design variable, the compliance of the macrostructure is minimized. The volume of the macrostructure considering the whole holes in the microstructures is used as the constraint. The homogenization equations for the microstructures and the equilibrium equation for the macrostructure are also used as the constraint. This design problem is formulated as a distributed-parameter optimization problem, and the shape sensitivity functions are theoretically derived. The optimum boundaries of the macro- and microstructures are determined by the H¹ gradient method. The proposed method is applied to a numerical example to confirm the effectiveness of the proposed method.