Micropore shape optimization of porous laminated shell structures

Abstract

In this study, we propose a multiscale shape optimization method for designing micropores in porous laminated shell structures. The shapes of the unit cells of the periodic micropores distributed in each layer of the laminated shell structure are optimized. The homogenization method is used to bridge the macrostructure and the periodic microstructures. A squared error norm is minimized for controlling the displacements at arbitrary points of the laminated shell structure to the target values under the total volume constraint including the microstructures. The equilibrium equation of the macrostructure and the homogenization equations of the unit cells are also used as the constraints. The shape optimization problem is formulated as a distributed-parameter optimization problem, and the shape gradient function is theoretically derived. The H1 gradient method is used for shape optimization of the unit cells of the micropores. The validity of the proposed method is confirmed by a numerical example for designing the optimal shapes of the micropores distributed in a laminated shell structure. With the proposed method, arbitrary stiff and compliant porous laminated shell structures can be created.