三维弹塑性结构下限分析的边界元方法

刘应华; 张晓峰; 岑章志

三维弹塑性结构下限分析的边界元方法

清华大学工程力学系, 北京 100084

基金项目: 国家自然科学基金资助项目(19902007);全国优秀博士论文基金资助项目(200025)

详细信息

作者简介:
刘应华(1968- ),男,湖北潜江人,教授(E-mail:yhliu@mail.tsinghua.edu.cn).

中图分类号: O344.5
计量
- 文章访问数: 2752
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- 被引次数: 0
出版历程
- 收稿日期: 2001-11-02
- 修回日期: 2003-08-10
- 刊出日期: 2003-12-15

Lower Bound Limit Analysis of Three-Dimensional Elastoplastic Structures by Boundary Element Method

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P. R. China

摘要

摘要: 基于极限分析的下限定理,建立了用常规边界元方法进行三维理想弹塑性结构极限分析的求解算法.下限分析所需的弹性应力场可直接由边界元方法求得.所需的自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模拟,这些自平衡应力场基矢量由边界元弹塑性迭代计算得到.下限分析问题最终被归结为一系列未知变量较少的非线性数学规划子问题并通过复合形法进行求解.给出的计算结果表明该算法有较高的精度和计算效率.
- 边界元法 /
- 下限分析 /
- 自平衡应力场 /
- 非线性规划 /
- 复合形法
Abstract: Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three-dimensional elastoplastic structures was established using conventional boundary element method(BEM). The elastic stress field for lower bound limit analysis was computed directly by three-dimensional boundary element method(3-D BEM). The self-equilibrium stress field was constructed by the linear combination of several self-equilibrium "basis vectors" which can be computed by elastic-plastic incremental iteration of 3-D BEM analysis. The lower bound limit analysis problem was finally reduced to a series of nonlinear programming sub-problems with relatively few optimal variables. The complex method was used to solve the nonlinear programming sub-problems. The numerical results show that the present solution procedure has good accuracy and high efficiency.
- BEM /
- lower bound limit analysis /
- self-equilibrium stress field /
- nonlinear programming /
- complex method

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参考文献(10)

[1]	刘应华,岑章志,徐秉业.三维结构极限上限分析的有限元方法[J].清华大学学报,1996,36(3):47-53.
[2]	Maier G,Polizzotto C.A boundary element approach to limit analysis[A].In:Brebbia C A,Futagami T,Tanaka M Eds.Boundary Elements[C].Berlin:Springer-Verlag,1983,551-556.
[3]	Swedlow J L,Cruse T A.Formulation of boundary integral equations for three dimensional elastoplastic flow[J].Int J Solids Struct,1971,7(12):1673-1683.
[4]	Maier G,Novati G.Elastic-plastic boundary element analysis as a linear complementarity problem[J].Appl Math Modelling,1983,7(2):74-82.
[5]	Cen Z,Wang X,Du Q.A coupled finite element-boundary element method for three dimensional elastoplasticity analysis[A].In:Du Q Ed.On BEM in Eng'g[C].Beijing:Pergamon Press,1986,311-318
[6]	岑章志,王勖成,杜庆华.采用有限元-边界元耦合方法计算弹塑性应力[J].清华大学学报,1988,28(2):34-43.
[7]	Martin J B.Plasticity:Foundation and General Results[M].Cambridge,Mass:MIT Press,1975,379-526.
[8]	Zhang X,Liu Y,Cen Z.A solution procedure for lower bound limit and shakedown analysis by SGBEM[J].Acta Mechanica Solida Sinica,2000,14(2):118-129.
[9]	席少霖,赵凤治.最优化计算方法[M].上海:上海科学技术出版社,1983,370-377.
[10]	Borges L A,Zouain N,Huespe A E.Anonlinearoptimizationprocedureforlimitanalysis[J].Eur.J Mech,A/Solids,1996,15(3):487-512.