Topology Optimization Method Using SIMP Combined with Evolutionary Deletion of Elements

Solid isotropic microstructures with penalization (SIMP) can be used to solve the continuum topology optimization problem. Due to the existence of sensitivity or density filtering in SIMP, gray-scale elements will appear in the optimization results, which affects the clarity of the structure. In order to solve this problem, SIMP combined with evolutionary deletion of elements is proposed using the idea of evolutionary structural optimization. A process of evolutionary deletion of elements is added into SIMP method, elements deletion threshold is determined by the average element density and reduction factor. Sigmoid function is introduced to define a reduction factor which contains two parameters, so that the gray-scale elements can be gradually removed during the process. After discussing the influence of parameters on the reduction factor, the range of parameters is determined by taking the MBB beam as an example. SIMP combined with element evolutionary deletion is applied to numerical examples such as MBB beam and cantilever beam, it is proved that the method can be combined with sensitivity filtering, density filtering, and Heaviside projection, which shows good applicability. In addition, this method suppresses the gray-scale elements in the SIMP method effectively, and improves the efficiency.