基于隐含边界描述的连续体拓扑优化  

Continuum Structure Topology Optimization Based on Implicit Boundary Representation

作　　者：熊振华[1] 庄春刚[1] 丁汉[1] 

机构地区：[1]上海交通大学机械与动力工程学院,上海200240

出　　处：《上海交通大学学报》2007年第4期573-577,共5页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金项目(50305019);国家重点基础研究发展计划(973)项目(2005CB724100)

摘　　要：基于隐含边界描述的水平集方程推动几何边界,结合形状导数、拓扑导数等工具,实现了柔性目标函数的连续体结构拓扑优化设计.进一步通过引入Von Mises应力作为产生新拓扑结构的策略,给出了单独使用Von Mises应力开孔的算例.算例结果表明,基于隐含边界描述的连续体拓扑优化设计方法,它具有独特的处理拓扑变化能力及消除拓扑优化结果对网格和初始拓扑结构猜测的依赖性.这一类方法具有优秀的高维设计拓展能力,在工程实际和多材料设计等方面具有很好的应用前景.This paper introduced a continuum structure topology optimization method based on implicit boundary representation, such as level set method. This method combines level set method, shape derivative analysis and topology derivative to realize structural topology optimization. Furthermore, Von Mises stress was used as an index to generate new topologies. Two numerical examples were given which shows that this kind of method has superior ability to handle topological change during optimization and is very effective to make topology optimization process independent of initial topological guess and mesh size. At the same time, this method has the capability to easily handle higher dimensional problems. It has great potential usage in industrial practice and multi-material topological design.

关 键 词：隐含边界描述 水平集方法 拓扑优化 形状导数 拓扑导数 

分 类 号：TH122[机械工程—机械设计及理论]