摘要
建立了求解含有界面圆孔的二种不同弹性组合介质中ＳＨ波的散射和界面圆孔附近的动应力集中问题的Ｇｒｅｅｎ函数法给出了一个具有半圆形缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解取基本解作为Ｇｒｅｅｎ函数，建立起问题的定解积分方程最后给出了界面圆孔的动应力集中的算例和结果。
The present paper investigates the problem of SH-wave scattering and dynamic stress concentration by bi-material structure possessing cylindrical interface hole Green’s Function method is used here, which means a special essential solution suitable to the present problem must be constructed In terms of wave functions expansion method and Graf formula, we give the construction course for the special Green's function, and deduce it strictly from the essential solution for a perfect half space impacted by line source loading The special Green's function is an essential solution of displacement field for an elastic half space with a half cylindrical gap impacted by out-plane line source loading harmonically at horizontal surface Once the special Green's function is gotten,various scatering problems of SH-waves by a kind of interface blemish or complex flaw can be solved Here we only deal with the case of interface circular hole The model of the problem is composed of two half spaces with half cylindrical gaps Horizontal surfaces of the two half spaces are loaded with undetermined anti-plane forces in order to satisfy continuity conditions at interface section, and the added force at interface point of the circle is directly related to its dynamic stress concentration factor By combining two half spaces with unknown loading at surfaces into one infinite elastic body, the interface circular hole can be formed Therefore, a set of Fredholm integral equations of first kind to determine the unknown loading are established by use of the Green's function The integral equations can be transformed into algebraic equations and solved numerically Finally, examples of dynamic stress concentration are calculated, and the relations of dynamic stress concentration factors versus different parameters are illustrated The study indicates that wave number, incident wave angle and combination of different media parameters all play important roles for the problem of SH-wave scattering by interface circular hole Their influence often causes over-high stress appear at interface circle, and the circular hole may crack along interface section We can go on investigating scattering problem of SH-wave by cracks originating at hole edge in use of Green's function method shown above
出处
《力学学报》
EI
CSCD
北大核心
1998年第5期597-604,共8页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金
国家教委博士点基金
关键词
界面圆孔
SH波散射
动应力集中
弹性波
interface circle, Green function, SH-wave scattering, dynamic stress concentration, integral equation
