Scattering of Qut-of-plane Line Source Load by Shallow-embedded Circular Lining Structure and Crack in Half Space

摘要

In this paper, we study the problems of scattering of out-of-plane line source load by half-space shallow-embedded circular lining structure and a crack in the field of linearly elastic dynamic mechanics. This is an essential solution to the displacement field for the elastic space possessing shallow-embedded circular lining structure and a crack while bearing out-of-plane harmonic line source load at arbitrary point. The wave function of scattering of shallow-embedded circular lining structure impacted by incident steady SH-wave is constructed based on the symmetry of SH-wave scattering and the method of multi-polar coordinates system. Then a crack is made out using the method of "crack-division". Thus expressions of displacement and stress are established when shallow-embedded circular lining structure and a crack are both in existent. Finally, with two different dimensionless parameters, numerical results of scattering of out-of-plane line source load by half-space shallow-embedded circular lining structure and a crack are obtained and numerical examples are provided to show the influence of wave number ratio, shear modulus ratio, thickness ratio and the ratio of distance between the center of the different cavity and ground surface and the radius of the circular lining structure upon the dynamic stress concentration factor(DSCF) and dynamic stress intensity factor(DSIF) at crack tip.