Micropore shape optimization of porous laminated shell structures

In this study, we propose a micropore shape optimization method for designing porous laminated shell structures. The homogenization method is used to bridge the macrostructure and the periodic microstructures. The shapes of the unit cells of the periodic micropores distributed in each layer of the laminated shell structure are optimized. A squared error norm is minimized for controlling the displacements at arbitrary points of the laminated shell structure to the target values under a total volume constraint. The equilibrium equation of the macrostructure and the homogenization equations of the unit cells are also used as constraints. The shape optimization problem is formulated as a distributed-parameter optimization problem; the shape gradient function is theoretically derived and applied to the H1 gradient method in order to obtain the optimal shape of the independent unit cells of the porous laminated structure. The validity of the proposed method is confirmed by several numerical examples for designing the optimal shapes of the micropores distributed in each layer of the laminated shell structure. Arbitrarily stiff and compliant porous laminated shell structures can be created with the proposed method. Moreover, we confirmed that the method can produce designs that can be implemented directly using additive manufacturing by preparing a 3D printed model of the optimized shell structure. The stiffness of the 3D printed models are tested and compared with the numerical results.