新型边界积分方程的无单元解及其应用

›› 2007, Vol. 28 ›› Issue (12): 2549-2552.

新型边界积分方程的无单元解及其应用

李树忱¹，周锦添²，李术才¹

1 山东大学土建与水利学院地下系，济南 250061；2香港理工大学土木与结构工程系香港

收稿日期:2005-12-06 出版日期:2007-12-10 发布日期:2013-10-18
作者简介:李树忱，男，1973年生，博士，副教授，主要从事隧道及地下工程、岩石工程等方面的教学和科研
基金资助:
国家自然科学基金重点项目(No. 50539080)；山东省自然科学基金面上项目(No. Y2006F13)。

An element-free solution of the new boundary integral equation and its application

LI Shu-chen¹, Zhou Jintian², LI Shu-cai¹

1. Department of City Underground Space, School of Civil and Hydraulic Engineering，Shandong University，Jinan 250061，China； 2. Department of Civil and Structural Engineering, Hong Kong Polytechnic University, Hong Kong, China

Received:2005-12-06 Online:2007-12-10 Published:2013-10-18

摘要/Abstract

摘要： 目前隧道及大型地下工程往往在裂隙岩体中开挖，而裂隙与地下空间的距离及裂隙的扩展条件，制约着隧道及地下工程的稳定性。应用能考虑孔洞和裂纹问题的新型边界积分方程与无网格加辽金法结合，建立一种新型的边界无单元法。在该方法中基本的未知量是由边界上的面力和边界上位移密度函数构成的复变量边界函数。文中应用的边界积分公式和Muskhelishvili的积分公式直接相关。将无网格构造方法引入新型的边界积分方程，建立了新型的边界无单元法。应用该方法详细分析了含隧道和裂纹间相互关系等问题，其数值结果与解析结果吻合很好，说明该方法的正确性和可行性。

关键词: 移动最小二乘逼近法, 新型边界积分方程, 边界无单元法, 裂隙岩体, 应力强度因子

Abstract: At present, the tunnels and big underground space were excavated in the fractured rock; their stability are controlled by crack growth condition and distance from crack and tunnel and underground space. By applying the new boundary integral equation (BIE) for two-dimensional elastic bodies containing cracks and holes to couple the element-free Galerkin method, a new boundary element-free solution for calculating the interaction between cracks and holes is presented. The basic unknown in the new boundary integral equation is a complex boundary function , which is a linear combination of the boundary traction and boundary displacement density. The present BIE formulation can be related directly to Muskhelishvili’s formalism. The constructed methods of the element-free try functions are introduced into the new boundary integral equation to develop the new boundary element-free solution. At last, the validity and accuracy of the presented method are illustrated by the elastic mechanics problem containing cracks and tunnel from that the method results agree well with those obtained from the analytical solution.

Key words: moving least-square approximation method, new boundary integral equation, boundary element-free method, fractured rockmass, stress intensity factor.

中图分类号:

TU 443

李树忱，周锦添，李术才. 新型边界积分方程的无单元解及其应用[J]. , 2007, 28(12): 2549-2552.

LI Shu-chen, Zhou Jintian, LI Shu-cai. An element-free solution of the new boundary integral equation and its application[J]. , 2007, 28(12): 2549-2552.

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