Approximate rate formulation of non-elastic bifurcation problem for thin-walled structures

Simplified set of equations is derived for solution of a non-elastic bifurcation problem in thin-walled structures. The rate formulation is preferable, and based on the classical Hill's approach. It is shown that for a particular case of small strain the problem can be reduced to a more simple eigenvalue problem. As an example, the approach proposed has been applied to a circular stationary disk subjected to thermal expansion. The material of the disk is assumed to be elastic-perfectly plastic obeying the von Mises yield criterion with its associated flow rule. The influence of the width ratio on the bifurcation behavior has been discussed.