Localization and snaking in axially compressed and internally pressurized thin cylindrical shells

Abstract This paper uncovers new manifestations of the homoclinic snaking mechanism in post-buckling regime a pressurized thin cylindrical shell under axial load. These forms tend to propagate either wholly or partially direction that is orthogonal applied load and so, unlike earlier Woods & Champneys (1999, Heteroclinic tangles unfolding degenerate Hamiltonian Hopf bifurcation. Phys. D, 129, 147–170), are fundamentally 2D nature. The main effect internal pressurization on firstly transition circumferential multiplication buckles from one-tier pattern three-tier pattern. Secondly, can induce oblique snaking, whereby sequential occurs helical across cylinder domain. For low levels pressure, single dimple remains—as unpressurized case—the unstable edge state smallest energy barrier around stable pre-buckling equilibrium. greater changes surrounded by four smaller dimples. By tracing limit point denotes onset these states parameter space pressure load, we justify validate empirically derived design guideline for buckling cylinders proposed Fung Sechler (1957, Buckling thin-walled circular compression pressure. J. Aeronaut. Sci., 24, 351–356).