Localized post-buckling states of axially compressed cylinders and their energy barriers

The buckling of axially compressed cylinders remains an interesting problem in the engineering mechanics literature. Here we revisit the problem by considering fully localized buckling modes in the form of a single dimple. By applying a combination of nonlinear finite element methods and numerical continuation algorithms, we study the evolution of a single dimple into a ring of circumferential diamond-shaped waves and further into the Yoshimura post-buckling pattern. This post-buckling sequence is established by cellular buckling (homoclinic snaking) as the axial compression is increased; i.e. a sequence of de-and restabilizations causes the single dimple to multiply circumferentially. The initial single-dimple seed corresponds to a saddle in the energy landscape, and the energy barrier provided by the single-dimple saddle around the stable pre-buckled path is quantified. The low magnitude of this energy barrier suggests that the pre-buckling equilibrium is metastable once the single dimple exists as a post-buckling equilibrium. We parameterize the onset of metastability with respect to geometric parameters and assess the suitability of this onset as a lower-bound design load. As NASA’s well-known lower-bound curve is overly conservative for shells manufactured using modern, tightly-toleranced manufacturing techniques, the onset of metastability could provide a viable and less conservative lower-bound design load.