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利用复变函数法和波函数展开法给出了具有地表覆盖层的弹性半空间内圆形孔洞和圆柱形夹杂在稳态SH波作用下动应力集中问题的解。根据SH波散射的衰减特性,该问题采用大圆弧假定法求解,利用半径很大的圆来拟合地表覆盖层的直边界,将具有地表覆盖层的半空间直边界问题转化为曲面边界问题。借助Helmholtz定理预先写出问题波函数的一般形式解,再利用边界条件并借助复数Fourier-Hankel级数展开把问题化为求解波函数中未知系数的无穷线性代数方程组,截断该无穷代数方程组可求得该问题的近似解析解。最后,通过算例讨论了地表覆盖层及圆孔对浅埋圆柱形夹杂动应力集中的影响。结果表明,覆盖层刚度和厚度的变化及圆孔的存在可显著改变圆夹杂周边动应力集中的分布。
The solution of the dynamic stress concentration problem under the action of steady SH wave by circular holes and cylindrical inclusions in the elastic half-space with the surface cover is given by means of the complex function method and the wave function expansion method. According to the attenuation characteristic of SH-wave scattering, this problem is solved by the method of big circular arc assumption. The circle with large radius is used to fit the straight boundary of the surface cover, and the problem of the straight boundary in half space with surface cover is transformed into the boundary problem . Helmholtz theorem is used to write the general formal solution of the problem wave function in advance. Then, the boundary conditions are used to solve the problem of infinite linear algebraic equations with unknown coefficients in the wave function by means of the complex Fourier-Hankel series expansion. The infinite algebraic equations are truncated An approximate analytical solution to this problem can be obtained. Finally, an example is given to discuss the effect of surface cover and circular hole on the stress concentration of shallow buried cylindrical inclusions. The results show that the change of stiffness and thickness of cover layer and the presence of circular holes can significantly change the distribution of dynamic stress concentration around circular inclusions.