The Dynamic Stress Concentration of a Vertical Transverse Isotropic Cylindrical Cavity Subjected to Time-Harmonic Elastic Wave

The objective of this thesis is to study the scattering as well as dynamic stress concentration phenomenon of a vertically transversely isotropic circular cylindrical cavity subjected to the obliquely incidence of time harmonic plane elastic wave. The total displacement field of either the anti-plane or in-plane scattering problem can be decomposed into two parts, namely, the incidence field as well as the scattering field part. We propose that the unknown scattering field part can be expanded into a series of n-th order wave function. Each wave function is defined by a trigonometric angular spectrum along a complex contour integral path with a kernel function which is non-trivial plane wave solution of the corresponding wave equation. The phase velocity of the plane wave kernel function varies with the phase angle. The trigonometric angular spectrum of each n-th order wave function can be further converted to infinite horizontal slowness integral which can be evaluated efficiently in complex slowness domain by employing the steepest descend-stationary phase method. In order to satisfy the boundary condition at each collocation point which allocate along the cavity surface, Least Square method is employed to solve the unknown coefficients of the expansion series of the scattering field. Once the coefficients are determined, the complete displacement field and stress field can be obtained. Thus, the dynamic stress concentration phenomenon of a vertically transversely isotropic circular cylindrical cavity subjected to the obliquely incidence of time harmonic plane elastic wave is thoroughly studied. Specially, for the anti-plane scattering problem of a circular cylindrical cavity embedded in a vertically transversely isotropic medium, In order to demonstrate the above proposed procedure is valid theoretically, through a coordinate transformation technique and recombination of the original expansion series, it can be shown that the original expansion series is identical to elliptic cylindrical wave function expansion for an isotropic medium, However, the original circular cylindrical cavity is transformed into an elliptic cylindrical cavity whose scattering problem can be solved analytically. From which the dynamic stress concentration phenomenon is thoroughly studied.