基于水平集方法和von Mises应力的结构拓扑优化  

Structural Topology Optimization Based on Level Set Method and von Mises Stress

作　　者：庄春刚[1] 熊振华[1] 丁汉[1] 

机构地区：[1]上海交通大学,上海200030

出　　处：《中国机械工程》2006年第15期1589-1595,共7页China Mechanical Engineering

基　　金：国家自然科学基金资助项目(50305019;50390063);国家重点基础研究发展计划资助项目(2005CB724100)

摘　　要：结合水平集方法和形状灵敏度分析,用梯度法实现柔性目标函数的结构拓扑优化设计。该方法通过基于隐含表示边界的水平集方程推动几何边界,引入von Mises应力准则作为产生拓扑结构的策略。给出了多孔结构初始化和没有初始化情况的算例,根据von Mises应力的大小开孔,产生新的拓扑结构。算例结果表明,根据von Mises应力的大小产生新拓扑的方法消除了拓扑优化结果对网格和初始拓扑结构猜测的依赖性,同时也弥补了水平集方法不能开孔的缺点。This paper combined Level Set method with shape sensitivity analysis to implement structural topology optimization. We used Level Set method to implicitly represent the geometric boundary of structure. And the new topologies were generated by introducing holes according to the magnitude of von Mises stress. In the context of topology optimization we gave two examples. One had initial design with multiple holes, and the other had no hole in the initial design domain. Numerical examples show that the coupling, which introduces holes according to the magnitude of von Mises stress, is effective for topology optimization. The proposed method makes the final result largely independent on the initial topological guess. At the same time, this method enhances the capability of Level Set method, which can not generate new holes in the design domain, at least for 2D topological optimization problem.

关 键 词：水平集方法 拓扑优化 灵敏度分析 形状导数 

分 类 号：TH122[机械工程—机械设计及理论]