摘要
無網格方法採用基於點的近似，可以徹底或部分地消除網格，不需要網格的初始劃分和重構，不僅可以保證計算的精度，而且可以大大減小計算的難度。無網格法是1種前景廣闊的方法，能夠解決許多其他傳統方法（如有限元方法、有限差分法等）所不能解決的問題。由於無單元網格法不需要複雜的`網格劃分，不存在網格畸變問題，因此在大變形分析領域有著廣闊的應用前景。本文利用無網格伽遼金（element free Galerkin menthod 簡稱 EFGM）方法，對2維結構大變形問題進行了分析。文中詳細討論了無網格伽遼金方法的基函式、權函式的選取及影響域的設定，並給出了各引數的具體取值。用計算例項說明了無網格伽遼金方法在解決結構大變形問題上的優勢。
關鍵詞:無網格伽遼金方法；大變形；無單元網格法；移動最小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.