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.

本文采用规则的矩形作为流形方法的数学覆盖网格来模拟裂纹试件中张裂纹的扩展过程，并在裂纹尖端区域的物理覆盖上采用高阶覆盖位移函数计算得到裂纹尖端的应力强度因子，与仅在物理覆盖上采用常位移函数相比，在相同计算网格的情况下，本文方法得到的应力强度因子精度有了较大幅度的提高。数值算例及实验结果的比较表明了文中数值方法的有效性。

利用面向对象设计思想将岩土力学中数值流形方法的物理覆盖系统抽象为独立的数据类，在此基础上完成了物理覆盖系统的自动剖分算法。对裂缝切割的连续材料，在裂缝的扩展过程中能自动生成正确的流形单元。算例表明，本算法是可靠和有效的。

A local basis algorithm for searching natural neighbours in Natural Element Method (NEM) is presented for solving the elasticity problems in this paper. Comparison with the global sweep algorithm used in natural element method or Natural Neighbour Method (NNM) for searching natural neighbours, the proposed algorithm is more expedient and convenient in the constructions and computation of natural neighbour interpolations. In the proposed NEM based on local search, the Laplace (non-sibson) interpolations are constructed with respect to the natural neighbour nodes of the given point which have been locally defined. The shape functions from the Laplace approximations have the delta function property and the Laplace interpolants are strictly linear between adjacent nodes, which facilitate imposition of essential boundary conditions and treatment of material discontinuity with ease as it is in the conventional finite element method. The Laplace interpolants derived from the local algorithm and the global algorithm in NEM are identical because of the uniqueness of the Voronoi diagram. Numerical results and convergence studies also show that the present NEM based on local search algorithm possesses the same accuracy and rate of convergence as they are in previous NEM.