无网格法强制边界条件处理的一种新方法

A new method to treat essential boundary conditions for the meshless method

针对无网格法位移边界条件处理困难和计算效率低的问题,提出了一种简洁实用的边界条件处理方法.在构造试探函数中,通过修改节点的权函数使试探函数穿过预施加位移边界条件的节点.采用有限元法中的位移边界条件处理方法使试探函数预先满足位移边界条件.该方法的计算量小,可解决大多数无网格法的位移边界条件问题和有限元耦合问题.以移动最小二乘法为例,通过算例证明了该方法的精确性与实用性.

Since the meshless method has defects in treating displacement boundary conditions and lacks computational efficiency, a simple and practical method is proposed for the treatment of boundary conditions. During the process of constructing trial functions, we modified the weight functions of nodes to make the trial functions pass through nodes with given boundary conditions. Displacement boundary condition treatment methods in Finite Element Method was used to satisfied the boundary condition previously. The method presented here reduces computational effort and can solve problems of displacement boundary conditions and finite element coupling that the meshless method can not deal with. The moving least square （MLS） method improves the accuracy and effectiveness of this method.