讨论了数值流形方法使用高阶覆盖位移函数时权函数、位移函数的选择和位移边界条件的处理。对该方法得到的高精度位移解，利用滑动最小二乘法在全域上构造位移近似函数，得到了与位移解一样连续的应力解。算例结果表明，理论和方法是正确、有效的。

The design. and management of the objects about the numerical manifold method are studied by abstracting the finite cover system of numerical manifold method as independent data classes and the theoretical basis for the researching and expanding of numerical manifold method is also put forward. The Hammer integration of triangular area coordinates is used in the integration of the element. The calculation result shows that the program is accuracy and effective.

基于自然邻结点近似位移函数提出了一种用于求解弹性力学平面问题的无网格局部Petrov-Galerkin 方法。这种方法在结构的求解域Ω内任意布置离散的结点，并且利用需求解点的自然邻结点和Voronoi 结构来构造整体求解的近似位移函数。对于构造好的近似位移函数，在局部的Delaunay 三角形子域上采用局部Petrov-Galerkin 方法建立整体求解的平衡控制方程，这样平衡方程的积分可在背景三角形积分网格的形心上解析计算得到，而采用标准Galerkin 方法的自然单元法需要三个数值积分点。该方法能够准确地施加边界条件，得到的系统矩阵是带状稀疏矩阵，对软件用户来说，它还是一种完全的、真正的无网格方法。所得计算结果表明，本文方法的计算精度与有限元法四边形单元相当，但计算和形成系统平衡方程的时间比有限元法四边形单元提高了将近一倍，是一种理想的数值求解方法。

用覆盖所有材料区域但独立于材料实际几何边界的任意形状数学网格和实际的物理网格来建立流形方法的覆盖系统，直接从数学覆盖和物理覆盖的定义出发，探讨了流形方法覆盖系统的全自动生成技术，并用Visio C++及其标准类库实现了流形单元和2套覆盖的自动形成和编号。

A method for direct imposition of essential boundary condition and treatment of material discontinuity in element free galerkin (EFG) method is presented. By using the actual displacements at the nodes on the essential boundary and the material interface in each material domain, the stiffness matrix and load vector at an integral point have been rewritten and transformed. As a result, the proposed method yields a positive, symmetrical and banded global stiffness matrix like it is in finite element methods and has the advantages of stabilization and easy implementation as compared to the penalty method, the Lagrange method, and other methods. Numerical results indicate that the present method is effective and retains high rates of convergence for both displacements and energy.