瞬态反平面动力学问题的Cauchy型奇异积分方程解法

Cauchy Singular Integral Equation Method for Transient Antiplane Dynamic Problems

本文使用边界积分方程和分离奇异主部等技巧，将瞬态反平面动力学问题归结为求解Ｌａｐｌａｃｅ变换域上的Ｃａｕｃｈｙ型奇异积分方程，并严格证明了该方程与Ｓｉｈ导出的对偶积分方程等价。本文还进一步研究了两条裂纹间动态影响，使用高精度的奇异积分方程算法及Ｌａｐｌａｃｅ数值反演法，文中计算了若干典型例子的动态应力强度因子，有关结果表明本文方法是成功和可靠的。

in this paper, by use of the boundary integral equation method and the technique of separating dominant singular part, the antiplane dynamic problem is reduced to solving Cauchy singular integral equation in Laplace transform space. The equation is strictly proved to be equivalent with the dual integral equations obtained by Sih. The dynamic influence between two parallel cracks is also investigated. By use of the numerical method with high precision for singular integral equation and Laplace numerical inversion, several typical examples are calculated and their dynamic stress intensity factors are obtained. The result shows that the method proposed in this paper is successful and reliable.