带凹陷的弹性半空间表面作用反平面简谐线源载荷时的Green函数

Green Function in Elastic Half Space Impacted by Out-Place Harmonic Line Source Loading at Horizontal Surface

采用复变函数法构造了含有任意形凹陷的弹性半空间 ,在其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的位移函数 ,即Green函数 .将问题的解视为完整的弹性半空间在其表面作用反平面简谐线源荷载时产生的扰动和半空间的凹陷对扰动产生的散射波之和 .给出了半椭圆形凹陷的弹性半空间Green函数的数值结果 ,并讨论了Green函数的性质 .

The displacement function, Green's function, is constructed based on the complex function, which is the solution of displacement field for elastic half space with canyon of arbitrary shape impacted by anti_plane harmonic line source loading at horizontal surface. The problem to be determined can be regarded as the sum of twos: the particle motions impacted by out_place harmonic line source loading at horizontal surface and the scattering of canyon in half_space. Finally, numerical results of Green's functions of semi_elliptical canyon in half_space are given, and the characters of which are discussed. It presents a reference for solving the DSCF around the arbitrary shaped canyon across the interface by using Green's function method.