The dynamical problem of a rectangular stamp moving on an elastic half plane

In this work, the stresses under a rectangular rigid stamp moving on an elastic half plane are calculated. The boundary value problem has been formulated in the form of a singular integral equation whose unknown function is the stress distribution under the stamp. The solutions of the equation have been compared for the cases of absence or presence of friction and for the cases of motion or rest. The work is an extension of Muskhelishvili's results and differs numerically from these ones only when the speed of the stamp is comparable with the shear wave speed.