Topology optimization using a reaction-diffusion equation

This paper presents a structural topology optimization method based on a reaction-diffusion equation. In our approach, the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction-diffusion equation. The distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction-diffusion equation, so free generation of new holes is allowed without the use of the topological gradient method. Our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model. The evolution of the density field is based on the implicit finite element method. As numerical examples, compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method's effectiveness and utility.