Point force and generalized point source on the surface of semi-infinite transversely isotropic material

摘要

For a three-dimensional semi-infinite transversely isotropic material, Green's functions (that give the full set of coupled fields due to the arbitrarily oriented point force and concentrated generalized point source, that represents either the diffusive chemical substance concentration or heat applied at the boundary of the half-space) are derived in elementary functions in a simple way, using methods of the potential theory. In the course of the analysis we derived the general solution of the field equations, represented in terms of four harmonic potential functions, which may also be relevant to other problems of chemical concentration or heat diffusion. These solutions constitute generalization of Boussinesq's and Cerruti's problems of elasticity for the chemically diffusive and/or thermoelastic materials.