On the solvability of closest point projection procedures in contact analysis: Analysis and solution strategy for surfaces of arbitrary geometry

The uniqueness and existence of the closest point projection procedure widely used in contact mechanics are analyzed in the current article. First, a projection domain for C2C2-continuous surfaces is created based on the geometrical properties of surfaces. Then any point from the projection domain has a unique projection onto the given surface. It is shown that in order to construct a continuous projection domain for arbitrary globally C1C1, or C0C0-continuous surfaces, a projection routine should be generalized and also include a projection onto a curved edge and onto corner points. Criteria of uniqueness and existence of the corresponding projection routine are given and discussed from the geometrical point of view. Some examples showing the construction of the projection domain as well as the necessity of a generalized projection routine are given.