Vertical Displacement of a Rigid Disk Buried in Semi-Infinite Transversely Isotropic Media

This paper is concerned with the investigation of the interaction of a vertically-loaded disc embedded in a transversely isotropic half-space. By virtue of transform methods, the generalized mixed boundary-value problem is formulated as a set of dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to including existing solutions for zero and infinite embedment as degenerate eases, the present analysis reveals a severe boundary-layer phenomenon which is apt to be of significance to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half-space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degree of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response.