中文摘要：

严格从三维横观各向同性材料弹性空间问题的Green函数出发。采用Hadamard有限部积分概念。导出了三维状态下单位位移间断（位错）集度的基本解。在此基础上。将三维任意形状的片状裂纹问题归结为求解一组以未知位移间断表示的超奇异积分方程；并给出了边界元离散形式。对方程中出现的超奇异积分．采用了Had-amard定义的有限部积分来处理。论文最后给出了若干典型片状裂纹问题的教值算例，数值结果表明了本文方法是非常有效的。

英文摘要：

In this paper, isotropic materials, the Hadamard＇ s finite-part with arbitrary shape in started rigorously from Green functions for elastic space problems of transversely fundamental solutions for a displacement-jump （dislocation） were derived by integral concepts. Subsequently,the problem of a three-dimensional planar crack an infinite transversely isotropic solid was reduced to the solution of a set of hyper-singular integral equations with unknown displacement jumps. Discretization of the boundary element method on the crack surfaces was discussed. The hyper-singular integrals in the equations were numerically treated by the use of Hadamard＇s finite-part integral concepts. Finally,some numerical examples of typical-shaped planar crack problems were given and the effectiveness of the analysis was validated.