Macropore shape optimization of porous laminated shell structures

Abstract

In this study, we propose a multi-scale shape optimization method to find the optimal macrostructure and microstructures that achieves the target displacement for a porous laminated shell structure. The displacement at any point of the laminated shell structure is controlled to the target value under the total volume constraint by minimizing the squared error. The equilibrium equation for the macrostructure and the homogenization equations for the unit cells are used as constraints. The shape optimization problem is formulated, and the shape gradient functions theoretically derived are applied to the H¹ gradient method. The homogenization method is used for connecting the macrostructure and the microstructures. With the H¹ gradient method for shape optimization, a smooth macrostructure and microstructure can be obtained.