SH波入射时半空间界面裂纹与圆形衬砌的相互作用

Scattering of SH-wave by the circular lining with an interface crack in a bi-material half-space

利用复变函数和Green函数法研究了双相介质半空间界面裂纹及界面附近圆形衬砌对SH波的散射与动应力集中问题。首先,采用"映像"思想构造满足自由边界条件的散射波表达式,进而求解所需的Green函数;其次,采用裂纹"切割"技术构造裂纹,并根据连续性条件建立了求解该问题的无穷代数方程组;最后,给出了不同入射波数时界面裂纹与衬砌的相互作用。结果表明,裂纹的存在显著放大了衬砌界面的动应力集中。

Based on the complex variable function method and the Green＇s function method, the scattering of SH-wave by a bi-material interface crack and a circular lining near a bimaterial interface in half-space was explored and the corresponding dynamic stress concentration at the circular lining interface was investigated. Firstly, the expression of the scattering wave was proposed which satisfied the free boundary conditions, and then the Green＇s function was constructed. Secondly, the crack was made out by the crack-division technique, and a series of algebraic equations for determining the un- known forces were developed from the continuity conditions. Finally, some examples for the dynamic stress concentration factors of the circular elastic lining were given, and the effects of the interface crack, the incident wave and the free boundary on the dynamic stress .concentration factors at the edge of the circular elastic inclusion were analyzed. The calculated results show that the existence of the interface crack has great effects on the dynamic stress concentration factors at the circular lining interface.