基于流形覆盖思想的无网格方法的研究

本语言基于流形思想，利用有限覆盖，单位分解等概念，引入建立在覆盖上的覆盖函数和具有紧支撑特性的单位分解函数，建立场逼近的近似表达，由弱形式的Galerkin变分得到数值分析模型，结合边界条件用于边值问题的求解，由此建立了一类新的无网格数值方法，论文采用这种方法分析了平面弹性问题，分析了体积闭锁现象，h、p型收敛性等，提出了一种选择覆盖大小的方案，且对狭长城采用了椭圆覆盖形式，取得了比较好的效果。

Study on meshless method based on manifold cover ideas

In the paper, by the use of concepts of finite cover and partition of unit in manifold ideas, cover function and partition of unit function are established on finite covers so that approximation of displacement field function is got. The discrete system of equation is obtained by weak form Galerkin variational principle, so the boundary value problem can be solved combined with the boundary conditions. This class of new method called meshless method is formed. Several numerical examples on plane elastic problem are given in the paper. The locking phenomenon can be overcome in this method. The h,p convergence are analyzed. A scheme to choose the size of cover is presented. Elliptic cover shape is used for slender field, the well numerical results are obtained.