出平面线源荷载作用下半空间内浅埋圆孔对半圆形凸起的圆柱形弹性夹杂的动力影响

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振动与冲击 ›› 2013, Vol. 32 ›› Issue (17) : 109-112.

论文

出平面线源荷载作用下半空间内浅埋圆孔对半圆形凸起的圆柱形弹性夹杂的动力影响

齐辉1 ，赵春香1，2，黄敏1

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Dynamic Effect of Out-Plane Line Source Load by A Cylindrical Elastic Inclusion with A Semi-Cylindrical Hill Above Subsurface Cavity in Half Space

QI Hui 1, ZHAO Chun-xiang1,2,HUANG Min1

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摘要

采用复变函数和多极坐标方法研究了在水平界面承受出平面线源荷载时弹性半空间内浅埋圆孔对半圆形凸起的圆柱形弹性夹杂的动力作用。该问题采用先“分区”再“契合”的思想求解，首先，将整个求解区域分割成两部分，其一为含半圆形凹陷和圆孔的弹性半空间，其二为圆柱形弹性夹杂；其次，构造满足含半圆形凹陷半空间水平界面应力自由和圆孔边界应力自由的散射波，构造满足圆形夹杂上半表面应力自由下半表面应力连续条件的驻波和散射波；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，同时满足圆孔边界应力自由的边界条件，建立起求解该问题的无穷代数方程组，并就具体算例讨论了圆柱形弹性夹杂周边动应力集中系数的数值结果。结果表明：圆孔的存在对“软”、“硬”夹杂周边动应力集中系数有不同的影响。

Abstract

The dynamic effect of a cylindrical elastic inclusion with a semi-cylindrical hill above subsurface circular cavity in half space while bearing out-of-plane harmonic line source load on horizontal interface have been considered using the methods of complex function and multi-polar coordinate. The solution of dynamic effect was given by the idea of “partitioning” and “conjunction”. Firstly, divide the solution domain into two. The one was an elastic half space with the semi-circular canyon and circular cavity, and the second one was a cylindrical elastic inclusion. Secondly, the scattering wave field, which satisfies the free stress boundary conditions of the half space on the horizontal interface and circular cavity boundary could be constructed, moreover, a standing wave in the inclusion and a scattering wave outside it were formulated separately. Finally, we conjoin the two domains to satisfy the continuous condition of displacement and stress around the common boundary and the stress free boundary condition of circular cavity boundary, and a series of infinite algebraic equations could be obtained to settle this problem. In the examples, numerical results for dynamic stress concentration factor of around cylindrical elastic inclusion edge are presented and discussed. Numerical results show that the existence of circular cavity will have different effects on dynamic stress concentration factor of around the ‘soft ’and ‘hard’ cylindrical inclusion edge.

导出引用

齐辉;赵春香;黄敏. 出平面线源荷载作用下半空间内浅埋圆孔对半圆形凸起的圆柱形弹性夹杂的动力影响[J]. 振动与冲击, 2013, 32(17): 109-112

QI Hui;ZHAO Chun-xiang;HUANG Min. Dynamic Effect of Out-Plane Line Source Load by A Cylindrical Elastic Inclusion with A Semi-Cylindrical Hill Above Subsurface Cavity in Half Space [J]. Journal of Vibration and Shock, 2013, 32(17): 109-112