出平面荷载对各向异性半空间内圆孔的Green函数解

Green's function solution for circular cavity in anisotropic half-space impacted by out-plane load

采用波函数展开法和复变函数法研究了出平面线源荷载对各向异性半空间内圆形孔洞的Green函数解。首先利用复变函数法构造圆形孔洞激发的含未知系数的散射场,得到介质内总的位移场和应力场。其次根据边界条件,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。最后通过大量算例讨论了不同参数对圆孔周边的动应力集中系数的影响规律,验证Green函数的精确性,为各向异性半空间内复杂缺陷的地震动和动力学研究提供理论基础。

The methods of wave functions expansion and complex variable function are used to employ Green's function solution for circular cavity in anisotropic elastic half-space containing elliptical elastic inclusion impacted by an out-plane line source load.Firstly,complex variable function method is developed to construct scattering wave field with unknown coefficient excited by circular cavity,and consequently,total displacement and stress field are obtained.Then,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,vast numerical examples are provided to discuss influence of different parameters on dynamic stress concentration factor (DSCF)around the cavity to verify accuracy of the Green's function,and the obtained results can be referenced by study on ground motion and dy- namic response of complex defects in anisotropic elastic half-space.