Shakedown of a plate with a circular hole: An educational problem

The shakedown limit for an infinite plate containing a circular hole and subject to oscillatory arbitrary remote loading is found, first by using Melan’s lower bound theorem, and secondly by using a finite element model. It is shown that in some cases the limit found from the Melan theorem using the solution for the residual state of stress for an over-pressurized hole provides the exact solution, specifically when the limiting factor is the reversal of the state of stress at a particular point, while in other cases the shakedown limit is rather higher.