基于光滑有限元法的拓扑优化.doc

文档介绍：
基于光滑有限元法的拓扑优化#
郭学兵,索晓瑜,亢战**
(大连理工大学工业装备结构分析国家重点实验室,大连 116024)
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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
中图分类号:TU318
Topology Optimization Based on Smoothed Finite Element
Methods
GUO Xuebing, SUO Xiaoyu, KANG Zhan
(State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of
Technology,Dalian 116024)
Abstract: bining 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.
Key words: Computati