Anti-plane Dynamic Stress Analysis Of Infinite Wedge With Circular Hole

The scattering of SH-waves are studied in the field of linear elastic dynamics in this paper. Base on the methods of complex functions and multi-polar coordinates, the anti-plane dynamic response of a scalene triangular hill above a subsurface elastic cylindrical inclusion are researched. Green's functions are employed to obtain the interaction between the semi-circular canyon and the crack for incident SH wave,and the anti-plane stress analysis of an infinite wedge with a cavity.An analytical solution for the dynamic anti-plane response of a scalene triangular hill above a subsurface elastic cylindrical inclusion is studied based on 'conjunction' in complex plane. A standing wave function which is a fractional-order Bessel function is constructed in the scalene triangular region, which satisfies the traction free at the edges. This fractional-order Bessel function can be widely used in materials science and earthquake engineering with non-consecutive boundaries to research those dynamic capabilities. According to multi-polar coordinates method in complex plane, a series of infinite linear algebraic equations are constructed to satisfy the condition of displacement and stress equilibrium on the interfaces. Finally, some conclusions are concluded by discussing the computational results.The method of Green's function is used to investigate the interaction between the semi-circular canyon and the crack for incident SH-wave. The details of thought for this problem can be concluded as follows: Firstly, a Green's function is constructed for the problem, which is a fundamental solution of displacement field for an elastic half space containing a semi-circular canyon subjected to anti-plane harmonic linear source force at arbitrary point of the elastic-space. In terms of the solution of SH-wave's scattering by an elastic half-space with a semi-circular canyon, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the location where the crack exists actually,this process is called "crack-division".The expressions of the displacement and stress are given when the semi-cylindrical canyon and the crack co-exist. Finally, the influence of the existent crack and semi-cylindrical canyon on the ground motion are discussed.The solution for anti-plane stress analysis of an infinite wedge with a cavity can't be obtain by constructing fractional-order Bessel function and Hankel function, because of the singularity of Hankel function at zero point. Take the consideration of the incisal effect of Green's function, the problem can be transformed into an elastic half space with a cavity incised by a semi-infinite crack. Combine the complex functions and multi-polar coordinates, we can obtain the solution of the dynamic stress concentration factor (DSCF) around the cavity.