GREENS-FUNCTION SOLUTIONS FOR SEMI-INFINITE TRANSVERSELY ISOTROPIC MATERIALS

The Green's function problem of a semi-infinite transversely isotropic medium with the plane boundary parallel to the plane of isotropy is solved by using the potential function method. The Green's function solutions are expressed in terms of harmonic and bi-harmonic functions which are obtained by the separation of variables method. Closed form solutions for point forces applied in the interior of the medium are obtained. The present solution reduces to Sveklo's results when the point force is normal to the plane of isotropy and √(C11C33)-C13-2C44 ≠ 0. The Green's function solutions of Michell, Lekhnitzki and Hu, which deal with point forces applied at the free surface of a half-plane and √(C11C33)-C13-2C44≠ 0, can also be reproduced from the present approach. Furthermore, the present solution can be reduced to the results of Mindlin for semi-infinite isotropic materials by suitable substitutions of elastic constants. © 1979.