Host: The Japan Society of Mechanical Engineers
Name : [in Japanese]
Date : November 26, 2020 - November 28, 2020
In this study, we propose a novel multiscale shape optimization method for designing the shapes of periodic microstructures using the homogenization method and the H1 gradient method. The compliance of a macrostructure is minimized under the constraint conditions of the total area of the unit cells of the microstructures distributed in the macrostructure. The shape optimization problem is formulated as a distributed-parameter optimization problem, and the shape gradient function is then theoretically derived. The shape gradient function is calculated with the two state and two adjoint equations related to the micro- and macro structures. Clear and smooth boundary shapes of the unit cells can be determined with the H1 gradient method. The homogenized elastic moduli of the updated unit cells are calculated and applied to the macrostructure. The proposed method is applied to a multiscale structure, in which the numbers of domains with the microstructures are varied and the optimal shapes of the unit cells and the compliances obtained are compared. The numerical results confirm the effectiveness of the proposed method for creating the optimal shapes of microstructures distributed in macrostructures.
