Scattering of SH waves by cavity with arbitrary shapes and crack at arbitrary positions in anisotropic elastic half-space media

Abstract

In this paper, the complex function method, Green's function method and coordinate transformation method are used to solve the scattering problem of cavity with arbitrary shape and crack at arbitrary position in the orthotropic elastic half-space under the incidence of SH waves. Firstly, the displacement field and stress field caused by cavity scattering in the orthotropic elastic half-space under the action of incident SH wave are obtained. Secondly, the solution of Green's function is derived when the plane line source load acts on the orthotropic elastic half-space with cavity. Then, the crack is constructed based on the method of crack ‘cutting.’ The total displacement field and stress field can be further obtained. Then, the analytical solutions of the dynamic stress concentration factor (DSCF) around the cavity, the surface displacement amplitude |W| and the dynamic stress intensity factor (DSIF) at the crack tip are obtained. Finally, taking the existence of elliptical cavity and crack in the orthotropic elastic half-space as an example, a large number of numerical calculations were carried out. Numerous numerical examples show that different parameters have a great influence on the DSCF around the cavity, the surface displacement amplitude |W| and the DSIF at the crack tip.