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

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