基于光滑有限元法的拓扑优化
首发时间:2014-01-22
摘要:本文研究了基于光滑有限单元法及节点密度法的拓扑优化问题的优化列式和算法。对于特定问题,光滑有限单元法(SFEM)较传统有限单元法(FEM)求解精度更高,同时在网格划分上更灵活。本文中,描述结构拓扑的密度场的离散独立于位移场网格。位移场的计算采用节点光滑有限单元法(NS-FEM),而结构拓扑采用基于节点密度设计变量插值构造的密度场进行描述,优化问题采用MMA算法求解。数值算例验证了该方法的正确性和有效性。
关键词: 计算固体力学 拓扑优化 光滑有限单元法 节点密度法 Shepard插值
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Topology Optimization Based on Smoothed Finite Element Methods
Abstract:By combining the SFEM with nodal density based design method, this paper studies the relevant topology optimization problem of continuum structures. Compared with conventional finite element method, for the particular problem, the SFEM achieves more accurate results and is more flexible in the domain discretization. In this paper, the density filed discretization is independent of the displacement field discretization. NS-FEM is used in the displacement field calculation, and the material layout is described by the density field which is constructed by interpolating the nodal density variables. The MMA algorithm is used in the optimization to update the design variables. Numerical examples demonstrate the validity and effectiveness of the proposed formulation.
Keywords: Computational Solid Mechanics Topology Optimization;Smoothed Finite Element Method;Nodal Density Method;Shepard Interpolation
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