Discrete adjoint-based multi-material level set topology optimization

Abstract

The optimized designs obtained by level set topology optimization benefit from the crisp boundaries defined by a level set function. Moreover, the level set function maintains a signed distance property throughout the optimization process, contributing to numerical stability. This study proposes a novel multi-material structural design framework by extending the discrete adjoint sensitivity-based level set method. Previous works on level set topology optimization typically employ continuous adjoint-based sensitivity; however, its extension to multimaterial structure design is challenging due to discontinuous boundary sensitivities that necessitate additional regularization techniques. The proposed approach alleviates this issue by explicitly evaluating discrete adjointbased shape sensitivities at the boundary and offers advantages such as the accurate computation of shape sensitivities at boundary points without the need for regularization techniques. The accuracy and efficiency of the design sensitivities calculated using the proposed method are verified by solving topology optimization problems.