THE ELASTIC FIELD RESULTING FROM ELLIPTIC HERTZIAN CONTACT OF TRANSVERSELY ISOTROPIC BODIES - CLOSED-FORM SOLUTIONS FOR NORMAL AND SHEAR LOADING

This analysis presents the elastic field in a half-space caused by an ellipsoidal variation of normal traction on the surface. Coulomb frict ion is assumed and thus the shear traction on the surface is taken as a friction coefficient multiplied by the normal pressure. Hence the sh ear traction is also of an ellipsoidal variation. The half-space is tr ansversely isotropic, where the planes of isotropy are parallel to the surface. A potential function method is used where the elastic field is written in three harmonic functions. The known point force potentia l functions are utilized to find the solution for ellipsoidal loading by quadrature. The integrals for the derivatives of the potential func tions resulting from ellipsoidal loading are evaluated in terms of ele mentary functions and incomplete elliptic integrals of the first and s econd kinds. The elastic field is given in closed-form expressions far both normal and shear loading.