以圆周为界面两相材料多裂纹反平面问题

运用复变函数及积分方程方法，求解了以圆周为界面的两相材料中的多裂纹反平面问题．为解决该问题，建立了两种类型的基本解，分别对应于单裂纹在圆域内和圆域外的情形．利用叠加原理和所得的基本解把两相材料中的多裂纹问题化为单裂纹问题的叠加，得出了一组以基本解密度函数为未知函数的Ｆｒｅｄｈｏｌｍ积分方程组．通过对该积分方程组的数值求解，可以得出密度函数的离散值，进而得出裂纹尖端的应力强度因子．文中对于两条裂纹分别位于圆域内和圆域外以及两条裂纹均在圆域外的情形进行了数值计算．

Antiplane Multiple Cracks Problems of Bi Material with Circular Interface

By using of complex variable function and integral equation method, the antiplane multiple crack problem in bi material with circular interface is considered in this paper. In order to solve the proposed problem, two kinds of elementary solution corresponding to a single crack in circular region and the external region respectively, are presented. Utilizing the proposed elementary solutions and taking density functions of elementary solutions as undetermined functions, a group of Fredholm integral equations can be established. Through the numerical solution of the integral equations, the SIF values at the cracks tips can be calculated. Two numerical examples are given in the paper.