轴对称结构极限下限分析的自然单元法

作为一种基于自然邻近插值的新型无网格法，自然单元法克服了大多数无网格法难以施加本质边界条件的困难．将自然单元法与减缩基技术相结合，建立了一种轴对称结构极限下限分析的数值格式和求解算法．通过不断修正自平衡应力场，轴对称结构极限下限分析可转化为一系列的非线性数学规划子问题，并由复合形法求解．在每个非线性规划子问题中，自平衡应力场表示为一组带有待定系数的自平衡应力场基矢量的线性组合，并且这些自平衡应力场基矢量可由弹塑性增量分析的平衡迭代结果得到．算例结果表明，本文所提的轴对称结构极限下限分析方法行之有效．

Lower Bound Limit Analysis of Axisymmetric Structures by Natural Element Method

As a novel meshless method based on the natural neighbour interpolation, the natural element method (NEM) can overcome the difficulty of applying essential boundary conditions in most meshless methods. Based on the lower bound theorem of limit analysis, a novel numerical method is developed for lower bound limit analysis of axisymmetric structures by means of the NEM and the reduced-basis technique. Through modifying the self-equilibrium stress field continuously, the whole solution process of the problem can be transformed into a series of sub-problems of nonlinear mathematical programming, which are solved by the complex method. In each sub-problem of nonlinear mathematical programming, the self-equilibrium stress field can be simulated by linear combination of a set of self-equilibrium stress field basis vectors with undetermined coefficients, which are determined by an equilibrium iteration procedure in the elasto-plastic incremental analysis. Numerical examples demonstrate that the solution procedure for the lower bound limit analysis of axisymmetric structures is effective.