General procedure for solution of contact problems under dynamic normal and tangential loading based on the known solution of normal contact problem

In this article, we show that the normal contact problem between two elastic bodies in the half-space approximation can always be transformed to an equivalent problem of the indentation of a profile into an elastic Winkler foundation. Once determined, the equivalent profile can also be used for tangential contact problems and arbitrary superimposed normal and tangential loading histories as well as for treating of contact problems with linearly viscoelastic bodies. In the case of axis-symmetric shapes, the equivalent profile is given by the method of dimensionality reduction integral transformation. For all other shapes, the profile is deduced from the solution of the elastic contact normal problem, which can be obtained numerically or experimentally.