An accurate solution for the surface of elastic layer under normal concentrated load acting on a rigid horizontal base (Q1080699)

The solution for a half-space elastic body subjected to a concentrated load on the surface was described by Boussinesq in 1885, but it could no longer be applied in civil engineering when there is a rigid rock layer underneath the soil. The solution of this problem has not been obtained. \textit{Guo Wenfu} [Acta Mech. Sinica 1984, 282-289 (1984)] described a layer submatrix inverse method and arrived successfully at a theoretical answer for the infinite elastic body with different contact conditions between layers subjected to circular distributed load. This paper gives an accurate solution by using Hankel transformation, and numerical results of the contact stress and displacements components are given. By taking the solution as a kernel of some integrals and integrating over the whole loaded area, the solution of axi-symmetry problems can be easily popularized for the non-axial-symmetric problems.