中文摘要：

相对于有限元法,边界单元法在求解断裂问题上有着独特的优势,现有的边界单元法中主要有子区域法和双边界积分方程法.采用一种改进的双边界积分方程法求解二维、三维断裂问题的应力强度因子,对非裂纹边界采用传统的位移边界积分方程,只需对裂纹面中的一面采用面力边界积分方程,并以裂纹间断位移为未知量直接用于计算应力强度因子.采用一种高阶奇异积分的直接法计算面力边界积分方程中的超强奇异积分;对于裂纹尖端单元,提供了三种不同形式的间断位移插值函数,采用两点公式计算应力强度因子.给出了多个具体的算例,与现存的精确解或参考解对比,可得到高精度的计算结果.

英文摘要：

Compared with finite element method, boundary element method has special advantages in solving the problems of fracture mechanics. The existing methods mainly include the subdomain method and dual boundary integral equation method. This paper presents an improved dual boundary integral equation method to evaluate stress intensity factors for two and three-dimensional crack problems. The method uses a pair of boundary integral equations, in which the traditional displacement boundary integral equation is collocated on the external boundary and the traction boundary integral equation is collocated on one of the crack surfaces. The relative crack opening displacements（CODs） are introduced as unknowns on the crack surface, and the evaluating results of CODs are used to evaluate the stress intensity factors（SIFs） of crack directly. The method uses a direct method to evaluate the hypersingular integral appeared in traction boundary integral equation. For crack tip elements, three kinds of interpolation functions for CODs are provided,and two of these are constructed in the present study. Two-point formula is used to evaluate the SIFs. Some examples are given to verify the correctness of the presented method, compared with the existing exact solution or reference solution,to show that this method can get high precision of the calculation results.