An effective phase field method for topology optimization without the curvature effects

In this paper, we will present a novel phase field based topology optimization method without the curvature effects. The original phase field based topology optimization method greatly simplifies griding, discretization, and handling of topological changes. However, the interface motion driven by curvature effects exists in the original phase field equation, which significantly affects the performance of structure. Furthermore, the existence of curvature effects also bring the ill-conditioned behavior of the normal vector. To overcome these shortcomings, we propose a modified phase field method with a nonlinear preconditioning process to eliminate the curvature effects. The method performs interface corrections on topological shapes through an anti-diffusive phase-field equation and imposes an adaptive preconditioning process to alleviate the problems of erroneous normal vector. The adaptive preconditioning method can capture more shape details for traditional topology optimization methods and offset the over-smooth effect of the phase field framework. We couple the finite element method and the finite difference method to solve the compliance minimization problem. The linearly stabilized splitting scheme is adopted to maintain the simplicity and stability of the algorithm. A series of comparative numerical examples are performed to show the feasibility and effectiveness of the proposed method. These examples demonstrate the superiority of our method compared to the original phase field method for topology optimization.