弹塑性结构安定下限分析的无网格局部Petrov-Galerkin法  

A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR STATIC SHAKEDOWN ANALYSIS OF ELASTO-PLASTIC STRUCTURES

作　　者：陈莘莘[1] 刘应华[1] 岑章志[1] 

机构地区：[1]清华大学航天航空学院工程力学系,北京100084

出　　处：《力学学报》2009年第5期713-721,共9页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(19902007);全国优秀博士论文专项基金(200025)资助项目~~

摘　　要：将基于Voronoi结构的无网格局部Petrov-Galerkin法与减缩基技术相结合,建立了一种安定下限分析的新方法.为了克服移动最小二乘近似难以准确施加本质边界条件的缺点,采用了自然邻近插值构造试函数.通过引入基准载荷域上载荷角点的概念,消除了安定下限分析中由时间参数所引起的求解困难.利用减缩基技术,将安定分析问题化为一系列未知变量较少的非线性规划子问题.在每个非线性规划子问题中,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,而这些自平衡应力场基矢量可应用弹塑性增量分析中的平衡迭代结果得到.算例结果证明了提出的分析方法的有效性.Shakedown analysis is an important branch of plasticity and can provide a theoretical basis for engineering designs and safety assessments. Based on the static theorem of shakedown analysis, a novel numerical method is developed to perform lower bound shakedown analysis by means of meshless local Petrov-Galerkin method （MLPG） with the Voronoi cells and the reduced-basis technique. The natural neighbour interpolation is employed instead of the moving least squares approximation to construct trial functions. The natural neighbour interpolants are strictly linear between adjacent nodes on the boundary of the convex hull, which facilitates imposition of essential boundary conditions with ease as it is in the conventional finite element method. By introducing the conception of load vertex in the basic load domain, the numerical difficulties caused by the variable of time parameter in lower bound shakedown analysis are overcome. Based on the reducedbasis technique, the lower bound shakedown analysis problem is reduced to a series of non-linear programming sub-problems with relatively few optimization variables. In each sub-problem of non-linear programming, the self-equilibrium stress field is simulated by linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors are generated by performing an equilibrium iteration procedure during elasto-plastic incremental analysis. Several numerical examples are presented to verify the availability of the developed method.

关 键 词：局部Petrov-Galerkin法 VORONOI图 安定分析 非线性规划 复合形法 

分 类 号：TB125[理学—工程力学]