# Normal traction and displacement for pin-hole problem

1. Jun 9, 2014

### 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.

N.