摘要
研究了双相介质垂直半空间界面裂纹及界面附近圆孔对SH波的散射与动应力集中问题,该问题的解答采用镜像法,构造出含有圆孔的直角平面区域出平面问题的Green函数。在该问题的求解过程中,一般将问题的模型视为"契合"问题,并采用裂纹切割技术构造出界面裂纹及其附近圆形孔洞的散射模型。若在两个直角平面区域的水平表面上,分别加置待定的出平面荷载,并在欲出现裂纹位置加置出平面反力构造裂纹,然后利用Green函数写出界面上的位移连续条件,建立起确定待解外力系的第一类Fredholm积分方程组。给出了数值结果分析了圆孔的动应力集中情况,结果表明:与全空间中界面附近圆孔对SH波的散射相比,由于垂直半空间自由边界和界面裂纹的存在,孔边动应力集中系数明显增大。
The scattering of SH-wave by a bi-material interface crack and a neighbouring circular cavity in vertical half-space are studied based on the image method. Firstly, a suitable Green＇s function is constructed in right-angle plane. Secondly, the methods of ＇interface conjunction＇ and crack-division are used to construct the scattering model of SH-wave. The Bi-material media is divided into two right-angle planes along the horizontal interface, and horizontal surfaces are loaded with undetermined anti-plane forces in order to satisfy continuity conditions at the linking section, with some reverse forces to produce cracks by means of crack-division technique. Then the problem is converted into the solution of Fredholm integral equations of first kind by means of the Green＇s function. Finally, using the attenuation speciality of SH-wave, the integral equations can be dispersed to linear equations directly, so the numerical solution can be obtained. The dynamic stress concentration factors around the circular cavity are discussed. The calculating results show that the existence of free boundary of vertical half-space has great effects on the dynamic stress concentration factors. Moreover, the existence of interface crack has also great effects on the dynamic stress concentration factors around the circular cavity.
出处
《工程力学》
EI
CSCD
北大核心
2009年第5期245-250,256,共7页
Engineering Mechanics
关键词
双相介质垂直半空间
SH波散射
界面裂纹
圆形孔洞
GREEN函数
动应力集中系数
Bi-material vertical half-space
scattering of SH-wave
interface crack
circular cavity
Green＇s function
dynamic stress concentration factor
