考虑最小尺寸精确控制的 SIMP 和 MMC 混合拓扑优化方法

Topology optimization is an advanced design method, which has been successfully used to solve multidisciplinary optimization problems, but there are still many obstacles to the reliable use of topology optimization results in engineering manufacturing, such as tiny holes or boundary cracks and hinges in structural design. An effective means to solve the above problems is to consider the minimum size control of the structure in the topology optimization design stage. In the topology optimization method considering the minimum size control, the boundaries of the widely used solid isotropic material with penalization (SIMP) method optimization result are usually blurred and not smooth, and moving morphable component (MMC), which contains precise geometric information, has a strong dependence on the initial layout of components. This paper proposes a hybrid topology optimization method of the SIMP and MMC considering precise control of minimum size. The proposed method inherits the advantages of both and avoids their respective disadvantages. In this method, a mapping method from the SIMP optimization results to the initial layout of MMC components is firstly proposed, which uses the active contour without edges (ACWE) algorithm to obtain the topological boundary contour data of the SIMP and the geometric parameter matrix of the components. Secondly, the topological description function model of the multi-deformable component with the semicircular end is established by introducing three length variables of the component. Finally, a topology optimization model that considers the minimum size control of the structure is constructed with the component thickness variable as the constraint. The effectiveness of the proposed method is verified by the minimum compliance problem and the compliance mechanism problem. The numerical results show that, the proposed method can achieve precise control of the minimum size of the overall structure and obtain a globally smooth topological structure boundary only by setting the lower limit of the component thickness variable without additional constraints.