Elastic halfspace under impulsive, distributed, vertical loading at the surface: exact solution at the center for a punch-like distribution

The exact analytical solution for the vertical displacement at the center of the surface of an elastic half space under an impulsive loading having the same spatial distribution as the contact stresses arising underneath a smooth, rigid disk when subjected to a static, vertical load, is obtained using Eason's method. The solution can be used to study the dynamical interaction and contact problems between soil and structures and can also be used to assess numerical computations with a finite element or boundary element program.