Tracing the equilibrium path beyond compound critical points

Procedures to handle critical points with coincident or nearly coincident buckling loads in a geometrically non- linear continuation process are presented. The proposed branch switching algorithm is based on a Liapunov{ Schmidt{Koiter-type asymptotic reduction which is used for the prediction step into the post-buckling range. A critical review of the existing methodology for the numerical treatment of post-bifurcation branches at a multiple bifurcation point is also given. In the review the main emphasis is given to robustness, but also implementational issues and computational requirements are addressed. Some modi cations to the existing algorithms are proposed in order to improve their robustness or e ciency. Numerical examples of a at plate and a thin-walled structure are shown