【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。更多还原

【Abstract】 The dynamic effect of a subsurface circular cavity in half space bearing out-of-plane harmonic line source load along horizontal interface on a cylindrical elastic inclusion with a semi-cylindrical hill was studied using the methods of complex function and multi-polar coordinate.The dynamic effect was solved with an idea of partitioning and conjunction.Firstly,the solving domain was divided into two.The one was an elastic half space with a semi-circular canyon and a circular cavity,and the second one was a cylindrical elastic inclusion.Secondly,the scattering wave field satisfying stress free boundary conditions of the half space along horizontal interface and circular cavity boundary was constructed,moreover,a standing wave in the inclusion and a scattering wave outside the inclusion were constructed separately.Finally,the two sub-domains satisfying the continuous conditions of displacement and stress around the common boundary and the stress free boundary condition of the circular cavity boundary were conjoined,and a group of infinite algebraic equations were built to solve this problem.In examples,numerical results for dynamic stress concentration factor around the cylindrical elastic inclusion edge were presented and discussed.Numerical results showed that the existence of the circular cavity has different effects on the dynamic stress concentration factors around soft and hard edges of the cylindrical inclusion.更多还原