Inclined Circular Punch Bonded to Transversely Isotropic Half‐Space

Abstract

A complete solution is given for the first time to the problem of an inclined circular punch bonded to a transversely isotropic elastic half‐space. Explicit expressions are derived for the field of stresses and displacements around such punch subjected to a shifting load and a tilting moment. The method of solution is based on the new results in potential theory obtained by the writer earlier. The complete solution is initially expressed in terms of three potential functions. The displacements are defined through first derivatives of the potential functions, while the stresses are given by second derivatives. The complete solution for an isotropic body is obtained as a limiting case of the general solution. Specific computations are performed in order to compare the elastic field in the vicinity of a bonded punch with similar parameters for a smooth punch. It is found that the influence of bonding on normal displacement is relatively small, while its influence on tangential displacements may be quite significant.