基于蜂窝镶嵌网格的离散变量拓扑优化

Topology Optimization with Discrete Variables Based on Honeycomb Tessellation Mesh

针对基于传统四边形网格划分的SIMP连续变量拓扑优化方法存在的棋盘格、结构点连接导致的零刚度和中间密度等问题,提出基于蜂窝镶嵌网格有限元划分方法,采用离散变量拓扑优化算法,在二维平面上展开拓扑优化方法的深入研究;在蜂窝镶嵌网格法划分的基础上引入离散变量优化算法求解,使所提出的方法(HoneyDVTOP)结合两者的优势,获得结构清晰、边界简洁、不存在中间密度的拓扑优化结构;最后,使用所提出的方法对MBB梁进行不同网格规模下的拓扑优化实验。结果表明,根据所提出的方法与拓扑方法HoneyTop进行对比,在3种不同网格规模的MBB梁和悬臂梁力学模型下刚度性能分别提升4.34%、10.56%和19.84%以及8.70%、20.98%和26.99%。随着网格规模变大,刚度的提升效果愈加明显。

Aiming at the problems of checkerboard and zero-stiffness and intermediate density caused by the structural points connection in SIMP continuous variable topology optimization method based on traditional quadrilateral mesh partition,this paper proposes the honeycomb mesh finite element method,and uses discrete variable topology optimization algorithm to carry out in-depth research on the topology optimization method on a two-dimensional plane.The discrete variable optimization algorithm is introduced to solve the problem based on the HoneyDVTOP method,so that the proposed method(HoneyDVTOP)combines the advantages of the two methods to obtain a topology optimization structure with clear structure,simple boundary and no intermediate density.Finally,the proposed method is used to conduct experiments on the topology optimization of MBB beams with different grid sizes.The results show that compared with the topological method HoneyTop,the stiffness performance of the proposed method is improved by 4.34%、10.56%and 19.84%,and 8.70%、20.98%and 26.99%respectively under three different mesh sizes of MBB beam and cantilever beam mechanical models.As the size of the grid becomes larger,the improvement effect of the stiffness becomes more obvious.