裂纹问题双边界元法中奇异积分保形变换计算方法  

Conformal Transformation Method for the Evaluation of Singular Integrals Arising in Dual BEM for Crack Problems

作　　者：汪文桥 胡泉光 吕加贺 陈炳瑞[2] WANG Wen-qiao;HU Quan-guang;LV Jia-he;CHEN Bing-rui(NO3 Engineering Co Ltd, China Gezhouba Group Corporation, Xi＇ an 710007, China;Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China)

机构地区：[1]中国葛洲坝集团第三工程有限公司,陕西西安710007 [2]中国科学院武汉岩土力学研究所,湖北武汉430071

出　　处：《土木工程与管理学报》2017年第6期51-56,共6页Journal of Civil Engineering and Management

基　　金：国家自然科学基金(51479192;41272347)

摘　　要：断裂是土木工程构件常见的一种破坏形式,也是计算力学中的难点。边界元法相比有限元法在处理裂纹问题上具有独特优势,目前采用的计算方法主要有子域法和双边界元法。为了避免病态矩阵出现,双边界元法在处理裂纹问题时,在上下裂纹面分别采用位移边界积分方程和面力边界积分方程,同时需要处理不同阶次的奇异积分。本文在传统奇异分解法的基础上,引入了保形变换,消除了积分单元几何形状对奇异积分计算精度的影响。计算结果表明,本文所提出方法可以有效地减少奇异积分所采用的高斯点数量,且对于不同网格划分形式并不敏感。Fracture is one of the common civil engineering components damage form, also be the difficulty in the computational mechanics. For crack problems, the boundary element method （BEM） inhibits individual advantage over the conventional finite element method （FEM）. The sub-region method and the dual boundary element method （DBEM） is widely used currently. In order to avoid the appearance of ill-conditioned matrix, the DBEM employs the displacement boundary integral equation on one crack surface and the traction boundary integral equation on the other crack surface, resulting in various orders of singular integrals. In this paper, on the basis of the original singularity subtraction method, the conformal transformation is introduced to eliminate the inaccuracy caused by the element shape during the evaluation of singular integrals. Numerical examples show that the proposed method can obviously reduce the total number of Gaussian points, and is feasible to coarse meshes.

关 键 词：断裂力学 双边界元法 奇异积分 保形变换 

分 类 号：TU312.3[建筑科学—结构工程]