Bifurcation instabilities in finite bending of circular cylindrical shells

This work re-visits the finite pure bending problem for circular cylindrical shells within the elastic range. The interest here is primarily directed towards the bifurcation instabilities of such configurations when the progressive flattening of the cylindrical cross-section is explicitly taken into account (the so-called Brazier effect). By coupling Reissner's axisymmetric solution to the buckling equations for a quasi-shallow toroidal shell we formulate a novel boundary-value problem able to capture such bifurcations. Numerical simulations of this problem confirm that buckling occurs before the usual limit-point instability is reached, while singular perturbation methods allow us to obtain simple asymptotic approximations for the critical curvature and bending moment associated with the bifurcations.