On the solvability of closest point projection procedures in contact analysis: analysis and solution strategy for arbitrary surface approximations Alexander Konyukhov a , Karl Schweizerhof a,* a University of Karlsruhe, Institute of Mechanics, Kaiserstrasse 12, D-76128, Karlsruhe, Germany Abstract 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 C 2 -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 C 1 , or C 0 –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. Key words: closest point projection, uniqueness and existence, contact, covariant description 1 Introduction The so-called closest point projection procedure is often introduced as a nu- merical scheme to compute coordinates of a point projected onto a surface. In * Corresponding author. Email addresses: Alexander.Konyukhov@ifm.uni-karlsruhe.de (Alexander Konyukhov), Karl.Schweizerhof@ifm.uni-karlsruhe.de (Karl Schweizerhof). URLs: http://www.ifm.uni-karlsruhe.de/seite 203.php (Alexander Konyukhov), http://www.ifm.uni-karlsruhe.de (Karl Schweizerhof). Preprint submitted to Computer Methods in Applied Mechanics and Engineering16 March 2007