无网格法及其应用

摘要

无网格方法采用基于点的近似，可以彻底或部分地消除网格，不需要网格的初始划分和重构，不仅可以保证计算的精度，而且可以大大减小计算的难度。无网格法是1种前景广阔的方法，能够解决许多其他传统方法（如有限元方法、有限差分法等）所不能解决的问题。由于无单元网格法不需要复杂的网格划分，不存在网格畸变问题，因此在大变形分析领域有着广阔的应用前景。本文利用无网格伽辽金（element free Galerkin menthod 简称 EFGM）方法，对2维结构大变形问题进行了分析。文中详细讨论了无网格伽辽金方法的基函数、权函数的选取及影响域的设定，并给出了各参数的具体取值。用计算实例说明了无网格伽辽金方法在解决结构大变形问题上的优势。

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.