基于拓扑描述函数的结构拓扑优化设计  

Structural topology optimization using topological description function

作　　者：陈义保[1] 罗震[2] 钟毅芳[2] 

机构地区：[1]烟台大学机电汽车工程学院,烟台山东264005 [2]华中科技大学机械科学与工程学院,湖北武汉430074

出　　处：《华中科技大学学报（自然科学版）》2007年第1期102-105,共4页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家重点基础研究发展计划资助项目(2003CB716207);国家自然科学基金资助项目(50465001)

摘　　要：提出了一种基于水平集方法的结构刚度拓扑优化设计方法.该方法将结构的边界隐式地嵌入到一个高一维标量函数的零水平集模型中,通过一个Hamilton-Jacobi类型的偏微分方程来控制水平集函数的动态运动,从而间接地实现结构边界拓扑和形状的动态演化.偏微分方程中的法向运动速度依据优化目标函数的形状敏度分析结果建立.用有限元法和有限差分法相结合的方法分别实现弹性平衡方程和Hamilton-Jacobi方程的数值计算,并通过一个典型算例证明所研究方法的有效性.This paper presents a new scheme for stiffness topology optimization using topological description functions also named level set methods. Structural boundary is implicitly embedded in the level set function with a higher dimension as the zero-level set. Hamilton-Jacobi equation is applied to dominate the dynamic evolvement for the embedded level set function and further to control the movement of structural boundary with the flexibility of handing topology changes. In the Hamilton-Jacobi equation, a suitable normal velocity is derived according to the shape sensitivity analysis with respect to objective function. Finite element method and the finite difference approach are respectively applied to implement the numerical calculation of elastic equilibrium equation and Hamilton-Jacobi equation. The validity of the presented method is demonstrated by one typical example.

关 键 词：结构优化 拓扑优化 水平集方法 敏度分析 偏微分方程 

分 类 号：TH165[机械工程—机械制造及自动化]