Looping post-buckling paths of an axially loaded elastic cylindrical shell

We present first-order and second-order iteration solutions to the Donnell cylinder equations for the post-buckling response of an axially loaded elastic cylindrical shell. Both solutions possess looping equilibrium paths with a remote bifurcation point, a feature inaccessible to standard linear perturbation analysis. The implication of this result for linear perturbation theory is discussed.