基于水平集方法与FreeFEM的弹性结构拓扑优化  

Structural Topology Optimization Based on the Level Set Method and FreeFEM

作　　者：詹阳烈[1] 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》2009年第11期1326-1331,共6页China Mechanical Engineering

基　　金：国家自然科学基金资助项目(50775146);国家重点基础研究发展计划资助项目(2005CB724100)

摘　　要：通过水平集方法隐含描述材料域几何边界,研究了快速的弹性结构拓扑优化算法。利用FreeFEM实现了拓扑优化过程中的弹性结构有限元分析,该过程采用了三角网格模型,然后利用接口函数输出求解水平集方程所需差分节点的位移。MATLAB软件利用获得的结构位移,构造驱动材料边界运动的速度场,通过循环迭代实现弹性结构的拓扑优化。数值算例结果表明,该方法能够提高基于隐式描述的拓扑优化的计算效率和计算精度。This paper presented a new procedure which can implement the structural topology optimization in a short time. This method was based on implicit representation of material boundary and employed the FreeFEM to realize the finite element analysis during the topology optimization process. The triangle mesh model was adopted for the elastic analysis and the node displacement was delivered to the MATLAB software by using interface function. Then the velocity field of optimization was computed in the MATLAB environment. The topology optimization of elasticity was obtained by iteration of finite element analysis and the boundary propagation. The numerical examples illustrate that the proposed algorithm can improve the computational efficiency and the numerical accuracy of structural topology optimization.

关 键 词：水平集方法 拓扑优化 隐含描述 FreeFEM 有限元分析 

分 类 号：TH122[机械工程—机械设计及理论]