In this study, we propose a novel multiscale shape optimization method for determining the optimal shape of microscopic structures composed of beams and shells. These microstructures are periodically embedded within a macroscopic structure and are connected to it using the NIAH (Novel Numerical Implementation of Asymptotic Homogenization) method to ensure mechanical consistency across different scales. In the proposed method, the shape of the microstructures is defined as a continuous design variable, and the objective is to match the actual displacement at arbitrary locations in the macrostructure to the given target displacement by minimizing the squared error norm between them. This design problem is formulated as a distributed optimization problem, and the shape gradient function is theoretically derived, enabling sensitivity analysis. The derived shape sensitivity function is applied based on the vector-type H1 gradient method, which ensures smoothness and numerical stability of the shape variables while efficiently determining the optimal shape of the microstructures.
SHINOJIMA et al. (Wed,) studied this question.