Probing the stability landscape of cylindrical shells for buckling knockdown factors

The buckling response of axially compressed cylindrical shells is well known for its imperfection sensitivity. Mapping out a stability landscape by localised probing has recently been proposed as a rational means for establishing shell buckling knockdown factors. Probing using a point force directed radially inwards and perpendicular to the cylinder wall is based on the insight that a localised single dimple exists as an edge state in the basin boundary of the stable prebuckling equilibrium. Here, we extend the idea of probing to bi-directional inwards and outwards forces to trigger both single-dimple and double-dimple edge states. We identify key features of the ensuing probing stability landscape and generalise these to derive three design curves of varying conservatism that are a function of the non-dimensional Batdorf parameter only. Interestingly, the most conservative of the three knockdown curves bounds a large data set of experimental buckling results from below, despite being derived from probing features of geometrically perfect cylinders. Overall, the three design curves permit a more nuanced design approach than legacy knockdown factors, as different levels of conservatism can be chosen based on expected manufacturing quality. For instance, the most and least conservative of the three design guidelines differ by a factor of 3 for the most slender cylinder geometries, and the associated reduction in safety factor has profound implications for efficient structural design.