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

LI Shu-chen; Zhou Jintian; LI Shu-cai

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

更新时间：2026-06-25

- An element-free solution of the new boundary integral equation and its application
- Vol. 28, Issue 12, (2007)
- 作者机构：
  
  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
- 作者简介：
- 基金信息：
- DOI：
  CLC： TU443
- Online First：18 October 2013，
  
  Published：2007
- 稿件说明：
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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).
DOI：

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). DOI：

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。

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.

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