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。

结合三角形、四边形等实体单元的位移插值函数和一维轴力杆单元的刚度矩阵推导出了一种用于锚杆支护数值模拟的单元列式，可以在地下结构有限元计算中的任何开挖步自由地加设或拆除锚杆，而且不必在划分初始计算网格时事先考虑或预留锚杆的结点位置，较大地简化了有限元的前处理或网格划分过程。

使用1 阶或1 阶以上最小滑动二乘法（MLS）形函数的无网格伽辽金法（EFGM）和无单元流形方法（EFMM），它们的主要缺点是形函数构造复杂、计算费用十分昂贵。本文提出了一种改进的EFMM法，它通过采用Shepard形函数（0 阶MLS 形函数）对结点的覆盖位移函数加权求和来简化整体近似位移函数的构造，且能够避免EFGM和EFMM里求解结点形函数时矩阵的求逆及相乘运算。文中的数值算例表明，这种改进的EFMM 法收敛快、精度高，与标准的EFGM相比其计算时间得到了大幅度的减少。

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.

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.