通过数学物理方法中的Green函数法研究了界面上含有上半圆形脱胶圆形衬砌及其边缘界面直线型裂纹的均匀双相介质全空间对出平面动力的响应。首先,给出了在含有半圆形凸起的圆形衬砌的下半空间和含半圆形凹陷的上半空间在水平分界面上任意一点加载出平面线源波动时在各自区域产生的位移场;再者,给出出平面波任意角度入射时的入射波、反射波、折射波和散射波函数;其次,采用裂纹"切割"方法构造直线型裂纹,并应用边界条件对上下半空间在界面处实施“契合”,建立起问题的定解方程组;最后做为算例讨论分析了裂纹尖端动应力强度因子的数值结果。
Abstract
The dynamic response of anti-plane force by a circular lining with a semicircular degumming and interface cracks emanating from the edge in whole space of homogeneous Bi-medium is reserched by Green's function. First, the displacement functions,that are Green's functions ,were given in the upper half space with a semicircular hollow and the lower half space which contains a cylindrical elastic lining with a semicircular hill, when an out of-plane line source wave is applied on the horizontal interface. Secondly, the functions of incidenting wave,reflecting wave, refracting wave,scattering wave were given,while anti-plane wave incident at any angle.Third,linear cracks were construcked using method of “cutting”, the upper and lower parts were joined where satisfy the continuous conditions at the conjunction area,and the problem equations of definite solution were established. Finally, as a example,the numerical results of dynamic stress intensify factor(DSIF) of the linear cracks were dicussed.
关键词
动应力强度因子(DSIF) /
半圆形脱胶 /
直线型裂纹 /
Green函数;出平面动力响应
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Key words
dynamic stress intensify factor(DSIF);semicircular disconnected curve;linear cracks;Green's function /
the dynamic response of anti-plane force
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