Unsymmetrical rigid stamp on a nonlocal elastic half-plane

The problem of an unsymmetrical rigid stamp on a nonlocal elastic half plane is solved. Since the problem has not been solved even for the classical case in its full generality and because the latter is needed for comparison, the solution of a moving unsymmetrical stamp for the classical case is given in the Appendix which, of course, gives the case of the motionless stamp in the special case of the zero velocity. The solution of the problem of the unsymmetrical stamp on the nonlocal half-plane does not give any infinite stresses; hence it does not have the defect of the classical solution and its importance is mainly due to this property. In fact, the classical solution gives infinite stresses at the sharp edges of the stamp embedded in the half plane, but in the case of a nonlocal medium the maximum stresses are finite and what is more astounding, they are not at the tips of the edges. The results are given by several diagrams which, whenever necessary, include also the classical values.