南景富, 齐辉. 含半圆形衬砌凸起弹性半空间问题的Green函数解[J]. 工程力学, 2012, 29(5): 31-36.
引用本文: 南景富, 齐辉. 含半圆形衬砌凸起弹性半空间问题的Green函数解[J]. 工程力学, 2012, 29(5): 31-36.
NAN Jing-fu, QI Hui. GREEN’S FUNCTION SOLUTION OF ELASTIC HALF SPACE INCLUDING A SEMI-LINING HILL[J]. Engineering Mechanics, 2012, 29(5): 31-36.
Citation: NAN Jing-fu, QI Hui. GREEN’S FUNCTION SOLUTION OF ELASTIC HALF SPACE INCLUDING A SEMI-LINING HILL[J]. Engineering Mechanics, 2012, 29(5): 31-36.

含半圆形衬砌凸起弹性半空间问题的Green函数解

GREEN’S FUNCTION SOLUTION OF ELASTIC HALF SPACE INCLUDING A SEMI-LINING HILL

  • 摘要: 采用复变函数法研究了含半圆形衬砌凸起的弹性半空间中水平界面承受出平面线源荷载时的Green 函数解。该问题采用“契合”的思想求解,首先,将整个求解区域分割成两部分来处理,其一为含半圆形凹陷的弹性半空间,其二为圆形衬砌区域;其次,构造满足含半圆形凹陷半空间水平界面应力自由的散射波,构造满足圆形衬砌半圆形凸起应力自由的驻波;最后,在两个区域的“公共边界”上实施“契合”,满足公共边界处位移和应力的连续性条件,同时满足圆形衬砌内边界应力自由边界条件,建立起求解该问题的无穷代数方程组,并给出了水平表面位移幅值的具体算例和数值结果,并对其进行了讨论。

     

    Abstract: The Green’s function of an elastic half space including a semi-circular lining hill while a bearing out-of-plane harmonic line source load on a horizontal interface has been considered, using the method of complex functions. The solution of Green’s function is given by the idea of ‘conjunction’. Firstly, we divide the solution domain into two domains. The one is a cylindrical lining, and the second one is an elastic half space with the semi-circular canyon. Secondly, we construct the scattering wave of semi-circular canyon satisfying the stress free boundary condition on the horizontal interface and the standing wave of cylindrical lining satisfying the stress free boundary condition on the semi-circular hill. Finally, we conjoin the two domains to satisfy the continuous condition of displacement and stress around the common ‘conjunction’ boundary and the stress free boundary condition of a circular lining inside boundary, and a series of infinite algebraic equations can be obtained to settle this problem. In the end, the computing expressions of the ground motion in the horizontal surface near elastic lining are given and discussed.

     

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