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 Hillʹs 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.