三维弹塑性结构下限分析的边界元方法  

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

作　　者：刘应华[1] 张晓峰[1] 岑章志[1] 

机构地区：[1]清华大学工程力学系,北京100084

出　　处：《应用数学和力学》2003年第12期1301-1308,共8页Applied Mathematics and Mechanics

基　　金：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)

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。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.

关 键 词：边界元法 下限分析 自平衡应力场 非线性规划 复合形法 

分 类 号：O344.5[理学—固体力学]