Displacements of the surface elastic half-space points caused by an instantaneous axisymmetric loading (Q2719360)

The paper deals with a general approach to the solution of axisymmetric instantaneous loading problems for the elastic half-space which is based on the Laplace transform with respect to the time coordinate and the Hankel transform with respect to the spatial coordinate. For any normally distributed instantaneous loading of the half-space boundary the normal displacements are shown to take their static values right after passing through the observation point of the Raleigh wave generated at the farthest point of the load application. The singularities are studied appearing in the displacements field on the Raleigh waves fronts moving from the loading area boundaries. The obtained results enable the conclusions useful in nonstationary contact problems.