Postbuckling strenth of an axially compressed elastic circular cylinder with all symmetry broken

Axially compressed circular cylinders repeat symmetry-breaking bifurcation in the postbucklingregion. There exist stable equilibria with all symmetry broken in the buckled configuration, and theminimum postbuckling strength is attained at the deep bottom of closely spaced equilibrium branches. Theload level corresponding to such postbuckling stable solutions is usually much lower than the initialbuckling load and may serve as a strength limit in shell stability design. The primary concern in thepresent paper is to compute these possible postbuckling stable solutions at the deep bottom of thepostbuckling region. Two computational approaches are used for this purpose. One is the application ofindividual procedures in computational bifurcation theory. Path-tracing, pinpointing bifurcation points and(local) branch-switching are all applied to follow carefully the postbuckling branches with the decreasingload in order to attain the target at the bottom of the postbuckling region. The buckled shell configurationloses its symmetry stepwise after each (local) branch-switching procedure. The other is to introduce theidea of path jumping (namely, generalized global branch-switching) with static imperfection. The staticresponse of the cylinder under two-parameter loading is computed to enable a direct access topostbuckling equilibria from the prebuckling state. In the numerical example of an elastic perfect circularcylinder, stable postbuckling solutions are computed in these two approaches. It is demonstrated that adirect path jump from the undeformed state to postbuckling stable equilibria is possible for an appropriatechoice of static perturbations.