Optimum thickness design method for micro-shell structure embedded in 3D macrostructure

Abstract

In this study, we propose a multiscale thickness optimization method for designing micro-shell structure assuming that the macrostructure consists of multiple micro-shell structures. The micro-shell structures are connected to the macrostructure using the NIAH (Novel numerical implementation of asymptotic homogenization) method. The distributed thickness of the micro-shell structures is used as design variable. A squared error norm between actual and target displacements is minimized for controlling the displacements at arbitrary points of the macrostructure to the target values under the total volume constraint including the volume of the micro-shell structures. This design is formulated as a distributed optimization problem, and the thickness gradient function is theoretically derived. The derived sensitivity function is applied to the scalar-type H¹ gradient method to efficiently obtain the optimal thickness distribution of the micro-shell structures. Numerical examples demonstrate the effectiveness of the proposed method to optimize the thickness distribution of complex micro-shell structures.