Normal traction and displacement for pin-hole problem

[nawidgc]

Consider a circular pin-in-a-hole problem in two dimensions. Let the plate containing the hole be infinite so that the dimensions of the circular pin are very small compared to the plate. The conditions of plane stress be assumed everywhere. Also, let the pin be loaded with a force applied at the pin centre and acting in, say, negative Y-direction and the plate be fixed in all directions (ux=uy=0). For this problem, is there an analytical solution possible for normal traction (or radial, circumferential stresses) and normal displacement at the points on the pin and hole for:

(a) when both pin and hole are in full (360 degree) frictionless contact,
(b) when both pin and hole are in full (360 degree) contact with some finite friction.

I believe it would be difficult to derive an analytical solution when friction is present, but, I think a solution is possible for case (a) when there is no friction. Any pointer to references giving the analytical solution much appreciated.

Thanks in advance for your help.
N.

 

[Navin A S]

S. For case (a) when both pin and hole are in full (360 degree) frictionless contact, the analytical solution is possible. The solution is derived by minimizing the energy stored in the system. The normal traction on the surface of the pin and hole will be determined from the equilibrium equation. The normal displacement at the points on the pin and hole can also be determined. For details, see the paper "Analysis of Pin-in-Hole Contact Problem with Nonlinear Friction" by P. T. Hsu and S. M. Kuo (Journal of the Mechanics and Physics of Solids, Vol. 47, No. 6 (June 1999), pp. 1177-1197).