郑娟^*， 龙述尧

（  湖南大学汽车车身先进设计制造国家重点实验室；  ）

摘要： 针对基于有限元法进行连续体结构拓扑优化时，需不断重构网格来处理网格畸变和网格移动，且存在数值计算不稳定等问题，提出了基于无单元Galerkin方法的渐进结构拓扑优化方法。基于应力准则，以结构最大Von Mises应力值为基准，确定删除阈值，对设计域内的节点进行评估，删除处于低应力状态的节点，致使结构达到最优。基于位移约束，建立高斯点的灵敏度分析公式，删除低灵敏度的高斯点，致使结构达到最优。通过经典的连续体结构拓扑优化算例证明了该方法的可行性和有效性。
关键词： 拓扑优化；连续体结构；无单元Galerkin方法；渐进结构优化方法；应力约束；位移约束

Zheng Juan^*， Long Shuyao

（  State Key Laboratory of Advanced Design and Manufacture for Vehicle Body，Hunan University；  ）

Abstract： While using finite element method to perform topology optimization of continuum structures，there exists the continuous mesh reconstruction problem in dealing with mesh distortion and moving，and the numerical computation is not stable．A new evolutionary topology optimization method based on element free Galerkin method is proposed. Considering the deletion criterion based on the stresses, the maximum Von Mises stress value of the structure is used as a benchmark, and the nodes in a low stress state are deleted, the structure to achieve the optimal. Considering the displacement constraint, the sensitivity analysis based on gauss points is derived and the gauss points with low sensitivity are deleted, the structure to achieve the optimal. The classical continuum structure topology optimization examples show that the method is feasible and efficient．

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