SH波作用下各向异性弹性半空间中浅埋圆孔附近的动应力集中研究

Dynamic stress concentration around shallow cylindrical cavity by SH wave in anisotropically elastic half-space

研究了稳态水平剪切(SH)波作用下含有圆柱形孔洞的各向异性弹性半空间的动力响应问题,探讨介质的各向异性对孔附近动应力的影响规律。运用复变函数和多极坐标方法在变换空间中构造出各向异性弹性半空间中圆孔的散射波函数,所构造的散射波函数能够自动满足半空间水平表面上应力自由的边界条件和无穷远处的Sommerfeld辐射条件。根据圆孔表面应力自由的边界条件,采用最小二乘法求解所构造的散射波函数的系数。分析了SH波以不同角度自弹性半空间内入射时,不同介质特性、入射波数和埋深对圆孔附近动应力集中系数的影响。数值结果表明,各向异性弹性半空间中孔附近的动应力比各向同性情况有明显增高。

The problem of dynamic stress concentration around a shallow cylindrical cavity incident by steady-state shear horizontal SH wave in an anisotropically elastic half-space ware solved; and the rules that anisotropy of the medium influenced dynamic stress concentration around the cavity were investigated. By using the function of complex variable and multi-polar coordinate system, we constructed scattering wave function of the cylindrical cavity, which automatically satisfied the zero-stress boundary condition on the horizontal surface in elastic half-space and the Sommerfeld radiation condition at infinity. According to zero-stress boundary condition of the cylindrical cavity, we solved coefficients of the scattering wave function by least square method. Finally, the effects of different media characteristics, wave numbers, and embedded depth on dynamic stress concentration factors around the cylindrical cavity were analyzed, when SH wave incident with different angles. Numerical results show that： the dynamic stress concentration factor around cylindrical cavity increases obviously in anisotropically elastic half-space in contrast with isotropic one.