Equivalent Conversion Method of Gray-Scale Elements for SIMP in Structures Topology Optimization

Gray-scale elements grow in number in case of topology optimization for complicated continuum structures. In order to obtain a distinct topological configuration, an equivalent conversion method based on SIMP(solid isotropic microstructures with penalization) is proposed to eliminate all gray-scale elements. The method applies two basic algorithms. Firstly, the conversion-controlling algorithm converts the continuous distribution(0, 1) of material into a discrete one(0, 1) without any gray-scale element. Secondly, another algorithm called conversion-equivalence evaluation algorithm can achieve a strong equivalence, therefore the difference between the continuous distribution and the discrete distribution can be ignored. In this paper, the equivalent-conversion method is combined with the standard SIMP approach so that a distinct topological configuration can be directly drawn from the calculated result of structural optimization. The method is further investigated and realized with numerical examples in both 2D and 3D models to show its correctness and effectiveness. The results show that the mechanics properties of the structures can be kept or even improved and the gray-scale elements disappear.