三维线弹性连续体的结构拓扑优化设计  

Structural Topology Optimization of Three-dimensional Linear Elasticity

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200240

出　　处：《中国机械工程》2007年第14期1703-1708,共6页China Mechanical Engineering

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

摘　　要：研究了基于水平集模型和SIMP方法的三维线弹性结构的拓扑优化方法,优化模型的目标是结构的柔度最小。引入水平集模型隐含描述具有复杂拓扑关系的三维线弹性结构的几何边界,以材料域的形状为变量进行灵敏度分析,构造水平集方程的速度函数,通过几何边界的演化获得结构的最优形状和拓扑。同时研究了基于SIMP方法的三维连续体结构的拓扑优化设计。对基于水平集模型和SIMP的拓扑优化方法的数值算例进行比较,结果表明,基于水平集的三维结构拓扑优化具有光滑的几何边界,数值算法稳定。An approach of topology optimization was investigated based on the level set model and the solid isotropic microstructure with penalization（SIMP） method for three--dimensional linear elas- ticity. The optimization model was the minimization of structural compliance. Since the level set method can naturally handle the propagation of geometric interface with complex topology and the geomet- ric characteristics of front interface can be easily computed by the level set function, this paper introduced the level set method for structural topology optimization of three--dimensional elastic continuum. We employed the level set model to implicitly represent the geometric boundaries of three-- dimensional structure with complex topology. The construction of the velocity function was realized by the shape sensitivity analysis and the optimal shape and topology was gradually obtained by the updating of the level set function. At the same time, we extended the algorithm of the SIMP method for three--dimensional structural topology optimization. By comparing the numerical examples of two approaches based on the level set model and the SIMP method, we can see that the level set model-- based approach has the smooth geometric boundaries. The numerical algorithm of the level set model --based topology optimization is stable.

关 键 词：水平集方法 隐式曲面 三维线弹性体 形状导数 拓扑优化 SIMP方法 

分 类 号：TH122[机械工程—机械设计及理论]