无网格法及其应用

摘要

关键词:无网格伽辽金方法；大变形；无单元网格法；移动最小2乘近似。

Abstract

Meshless method is base on approximation of points, it can remove the mesh completely or partly and don’t require the mesh initiate divided and reconstruction. It can not only ensure the precision of calculation, but also can decrease the difficulty of the calculation. Meshless method is a kind of method with good prospection, it can deal with many problems which can not be resolved by traditional method (finite element method, finite difference method). Meshless method has an obviously advantage in large deformation area, because there is no mesh needed, and no mesh distortion happens. Large deformation for plane problems are analyzed in this paper with mesh free Galerkin method (EFGM). In order to improve the speed and the stability of computation, the three basic problems for moving least square method (MLS) in EFGM, which are the base function, the weight function and the influence area, are discussed in details, respectively. The values of each parameter used in this analysis are also listed. The examples show that the EFGM can solve some special problems that are difficult for the finite element method.

Keywords : mesh free Galerkin method; large deformation; meshless method; moving least square approximation.