基于无网格Galerkin法的连续体结构拓扑优化方法研究

Topology optimization of continuum structure based on element-free Galerkin methods

基于一种新型的数值计算方法—无网格伽辽金法(EFG);采用拓扑优化方法中的SIMP法,以节点相对密度为设计变量、结构柔量最小为目标函数,建立结构拓扑优化的数学模型;然后采用优化准则法,推导设计变量的迭代格式,分析其灵敏度,在拓扑优化设计中采用敏度过滤技术有效地遏制了点态棋盘格的产生;最后用Matlab软件编写了相应的计算程序,完成实例优化,并将结果与基于有限元法的优化结果相比较,证明了该方法的正确性和有效性。

Based on a new algorithm： Element-Free Galerkin method （EFGM）, using SIMP method, with the relative density of nodes as design variables and selected minimize compliance as objective function, a mathematical model for topology optimization is set. Then, an implicit iterative algorithm for design variables be established based on optimality criteria method, and algorithm of sensitivity is derived. Meanwhile, a sensitivity filtering method is using in topology optimization process, it is effectively to solve the nodes chess board problem. Finally, a topology optimization example is implemented by programming in MATLAB. Compared with the result which based on finite element method, proves the method proposed in this paper is validity.