断裂力学中的两类奇异积分方程

Two Classes of Singular Integral Equations in Fracture Mechanics

本文利用边界积分方程方法,统一地导出了三维断裂力学现有文献中遇到的柯西主值型和强奇性型的两类奇异积分方程,经过退化处理,还得到了平面断裂力学的相应结果.此外,文中结合带裂纹柱体的扭转问题,介绍了作者将以上两类奇异积分方程用于裂纹切割解法研究而得到的新结果.

Using the method of boundary integral equations,two classes of singular integral equations,i.e.,the Cauchy principal-value type and the strongly singular type,are derived uniformly,which are encountered in present references of three-dimensional fracture mechanics.Through degeneration,the corresponding results of the plane fracture mechanics are also obtained.Also, several new results are introduced here,which are obtained by the author in his studies of the crack-cutting method for the torsion problems of the cracked cylinders by means of the above integral equtions.