半空间内椭圆夹杂对出平面荷载的Green函数解
Green’s function solution for elliptical inclusion in half-space impacted by out-plane load

采用复变函数法、多极坐标方法解答了弹性半空间中出平面线源荷载对椭圆夹杂的Green函数解，并结合“保角映射”技术构造线源荷载作用下椭圆夹杂激发的散射场和椭圆夹杂内的驻波场. 基于边界条件，利用Fourier积分变换推导出一系列求解未知系数的复系数代数方程组，截断有限项以控制精度，求出未知系数，进而得到Green函数解. 最后给出了大量算例，对线源荷载作用下不同参数对夹杂周围的动应力集中系数、水平地表位移的分布规律进行讨论，验证了Green函数的精确性.
The methods of complex variable function and multi-polar coordinates are developed to study Green’s function solution of elastic half-space containing elliptical elastic inclusion impacted by an out-plane line source load. Combined with the "conformal mapping" technology，the scattering displacement field excited by the inclusion and the standing wave in the inclusion are first constructed while bearing an out-plane line source load. According to the boundary conditions，a series of complex algebraic equations to determine the unknown coefficients are derived by Fourier integral transform，which can be solved by limited terms truncation to control precision，and the Green’s function solution is then solved. Lastly，numerical examples are given to discuss influence of different parameters on dynamic stress concentration factor (DSCF) around the elliptical inclusion and the horizontal surface displacement under different ratio of matrix to verify accuracy of the Green’s function