Some observations on the potential functions for transverse isotropy in the presence of body forces

Abstract

In this paper the potential function formulation for a transversely isotropic material is examined in the presence of body force terms. The equations of equilibrium are reduced to Poisson type equations with the body force terms on the right hand side. The potentials are evaluated for a concentrated body force in an infinite material. For a force perpendicular to the isotropic plane, it is shown that some degree of ambiguity exists in the choice of the potential which explains the different forms used by previous researchers. For a point force parallel to the z = 0 isotropic plane, the present results for the potentials agree with previous analysis when z > 0 but differ for z < 0. The ramifications of this on a recent ring loading analysis conducted by the author are discussed and certain confusing features of this recent solution are resolved.