マクロ構造の剛性最大化を目的とするマクロ構造とミクロ構造の同時形状最適化

抄録

In this study, we propose a concurrent shape optimization method for stiffness design of porous multiscale structures. The macrostructure is divided into several arbitrary domains, which have independent periodic microstructures. We optimize the shape of the macrostructure, the shapes of the voids distributed in the microstructures periodically and the boundary shapes of the interfaces between the domains. In order to bridge the macrostructure and the microstructures, the homogenized elastic moduli are calculated using the homogenization method, and applied to the elastic modulus of each domain in the macrostructure. The compliance of the macrostructure is minimized under the constraint conditions of the whole area of the macrostructure including the microstructures, the area of domains, the state equation of the macrostructure, and the homogenization equation of the microstructures. The sensitivity functions distributed on the design boundaries are derived using the material derivative of the Lagrange function. We use the H¹ gradient method to obtain the clear and smooth boundaries.