中文摘要：

讨论含有内部斜裂纹的弹性半平面静力学问题,其中载荷作用在裂纹面上.研究基于断裂力学原理、复变函数方法以及Riemann-Hilbert（R-H）边值问题的一般理论.提出模型耦合方法,将原问题分拆成含有有限长度裂纹的全平面问题和无裂纹半平面问题的叠加.与其他文献的结果比较表明,该方法具有精度高,便于实现的优点.最后,给出所研究问题的半解析解及裂纹尖端的应力强度因子.

英文摘要：

A static, semi-infinite plane problem with an internal oblique crack, in which surfaces are subject to continuous distributed forces, was discussed. The research was based on the principle of fracture mechanics, complex variable function method and the generalized Riemann-Hilbcrt boundary value problem theory. By means of the model coupling method proposed, the original problem can be transformed into the superposition of an infinite plane problem with a single finite length crack and a semi-infinite plane problem without any crack. By comparison with the results in the literatm＇es, this method manifests some merits, such as high accuracy and easy realization, etc. Finally, the seml-analytlcal solution of the internal crack problem and the stress intensity factor at the crack tips are provided.