2102 Topological optimum design using finite cover method incorporating level set boundary expressions

Abstract

In this paper, first, a topology optimization problem is formulated based on the level set method and a method for regularizing the optimization problem by the Tikhonov regularization method is explained. The reaction-diffusion equation that updates the level set function is then derived and an optimization algorithm, which uses the finite element method to solve the equilibrium equations and the reaction-diffusion equation when updating the level set function, is constructed. Next, the implementation of combining the level set-based topology optimization and the finite cover method is explained. Finally, a numerical examples is provided to demonstrate the effectiveness of the proposed method of topology optimization for minimum mean compliance problems.