弹塑性结构安定下限分析的无网格局部

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． 

meshless local Petrov-Galerkin method for static shakedown analysis of elasto-plastic structures

Shakedown analysis is an important branch of plasticityand can provide a theoretical basis for engineering designs and safetyassessments. Based on the static theorem of shakedown analysis, a novelnumerical method is developed to perform lower bound shakedown analysis bymeans of meshless local Petrov-Galerkin method (MLPG) with the Voronoi cellsand the reduced-basis technique. The natural neighbour interpolation isemployed instead of the moving least squares approximation to constructtrial functions. The natural neighbour interpolants are strictly linearbetween adjacent nodes on the boundary of the convex hull, which facilitatesimposition of essential boundary conditions with ease as it is in theconventional finite element method. By introducing the conception of loadvertex in the basic load domain, the numerical difficulties caused by thevariable of time parameter in lower bound shakedown analysis are overcome.Based on the reduced-basis technique, the lower bound shakedown analysisproblem is reduced to a series of non-linear programming sub-problems withrelatively few optimization variables. In each sub-problem of non-linearprogramming, the self-equilibrium stress field is simulated by linearcombination of several self-equilibrium stress basis vectors with parametersto be determined. These self-equilibrium stress basis vectors are generatedby performing an equilibrium iteration procedure during elasto-plasticincremental analysis. Several numerical examples are presented to verify theavailability of the developed method.