无网格法及其在岩石力学与工程中的应用  

Meshless Method and Its Application in Rock Mechanics and Engineering

作　　者：楼芬[1] 邓建[1] 

机构地区：[1]中南大学资源与安全工程学院,长沙410083

出　　处：《地下空间与工程学报》2007年第6期1014-1017,共4页Chinese Journal of Underground Space and Engineering

基　　金：国家自然科学基金(50574098)资助

摘　　要：无网格法是一种新的数值分析方法,它只需要节点信息和计算域的几何边界,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,从而不仅可以保证计算精度和收敛性,而且可以减少计算难度。文章首先介绍了无网格法的基本思想及其计算步骤。重点介绍了无网格伽辽金法(EFGM)的基本原理和方程。EFGM是无网格方法的一种,它采用移动最小二乘法构造位移函数,脱离了单元的概念,因此特别适合用来模拟岩石裂纹的扩展。最后探讨了无网格法在岩石力学与工程中的应用前景。Meshless method is a new numerical method similar to the finite element method.The method requires only a set of nodes and a boundary description of the calculation domain,no element connectivity is needed totally or partly,and no elements remeshing is needed.So it ensures not only high precision and quick convergence,but also reduces the calculaion difficulty. This paper introduces the basic concept and calculation procedure of the element-free method,and then introduces the basic principle and the fundamental equation of the element-free Galerkin method（EFGM）.The approximate function is constructed with moving least squares method in EFGM,which is one of the meshless methods.EFGM is especially suitable for analysis of rock crack propagation because of no element connectivity is needed.At last,the prospect of its application in rock mechanics and engineering are presented in this paper.

关 键 词：无网格法 移动最小二乘法 裂纹扩展 断裂准则 岩石力学与工程 

分 类 号：TU928[建筑科学—建筑设计及理论]