BESSEL FUNCTIONS FOR AXISYMMETRIC ELASTICITY PROBLEMS OF THE ELASTIC HALF SPACE SOIL: A POTENTIAL FUNCTION METHOD
Elasticity problems are formulated using displacement methods or stress methods. In this paper a displacement formulation of axisymmetric elasticity problem is presented. The formulation uses the Boussinesqâ€“ Papkovich â€“ Neuber potential function. The problem is then solved by assuming Boussinesq â€“ Papkovich - Neuber potential functions in the form of Bessel functions of order zero and of the first kind. The potential functions are then made to satisfy the governing field equations and the associated boundary conditions for the particular problem of a point load at the origin of the semi-infinite linear elastic isotropic soil mass. The unknown parameters of the function are thus determined and used to find the stresses, strains and displacement fields in the loaded soil. The results obtained were identical with the results obtained by Boussinesq.