中文摘要：

采用位错分析法，研究弹性纵向剪切情况下圆域中分叉裂纹问题．在给出无限大域中点位错复势的基础上，引入补充项以满足圆边界自由的条件，得到圆域中分叉裂纹问题的基本解．通过裂纹面上的应力边界条件，建立一组以位错密度为未知函数的Cauchy型奇异积分方程．由位移单值条件可以得到另一个约束方程．利用半开型数值积分公式把奇异积分方程化为代数方程求解，由位错密度直接得到裂纹尖端处的应力强度因子值．这是一种解析数值相结合求解应力强度因子的方法，充分利用解析方法精度高和数值方法适用性广的特点，同时又克服保角变换等解析解的局限，各裂纹位置可以是任意的．算例中所得的图表可以应用于工程实际．

英文摘要：

The bifurcated cracks problem in circular region in the case of elastic longitudinal shearing was investigated by using dislocation analysis method. Based on a given complex potential of a point dislocation in an infinite region, a complementary term was introduced to satisfy the traction-free condition along the circular boundary, and then the elementary solution for the bifurcated crack problem in circular region was obtained. By matching the traction along the cracks, Cauchy singular integral equations with dislocation density as unknown function in them were established for the bifurcated cracks in circular region. A con- straint equation could be formulated for displacement single value condition. By using a semi-open quadrature rule, the singular integral equations were transformed into algebraic equations. Finally, the stress intensity factors at the crack tips could be obtained directly from the dislocation density. This semi-analytical method was a combined method of both analytic and numerical ones to find the stress intensity factors, where the use of high accuracy with the former and the wide applicability with the latter were fully made. In addition, the limitation of analytical solution such as conformal mapping was overcome. The position of cracks could be arbitrary. The results given by an evaluation examples could be applied to actual engineering practice.