On Establishing Buckling Knockdowns for Imperfection-Sensitive Shell Structures

Abstract

This paper investigates issues that have arisen in recent efforts to revise long-standing knockdown factors for elastic shell buckling, which are widely regarded as being overly conservative for well-constructed shells. In particular, this paper focuses on cylindrical shells under axial compression with emphasis on the role of local geometric dimple imperfections and the use of lateral force probes as surrogate imperfections. Local and global buckling loads are identified and related for the two kinds of imperfections. Buckling loads are computed for four sets of relevant boundary conditions revealing a strong dependence of the global buckling load on overall end-rotation constraint when local buckling precedes global buckling. A reasonably complete picture emerges, which should be useful for informing decisions on establishing knockdown factors. Experiments are performed using a lateral probe to study the stability landscape for a cylindrical shell with overall end rotation constrained in the first set of tests and then unconstrained in the second set of tests. The nonlinear buckling behavior of spherical shells under external pressure is also examined for both types of imperfections. The buckling behavior of spherical shells is different in a number of important respects from that of the cylindrical shells, particularly regarding the interplay between local and global buckling and the post-buckling load-carrying capacity. These behavioral differences have bearing on efforts to revise buckling design rules. The present study raises questions about the perspicacity of using probe force imperfections as surrogates for geometric dimple imperfections.

Harnessing energy landscape exploration to control the buckling of cylindrical shells

“…Computationally, the only transition which has been followed previously is the simplest unbuckled-singly dimpled pathway, where the dimple is centrally located on the cylinder 32,33 . Meanwhile, local probing of cylindrical shells has been suggested as an experimental technique which may allow the true dimpling transition state to be accessed 26,[34][35][36] . In Fig.…”

“…An explicit link has therefore been made between the ease of single dimple formation and the sensitivity of loaded cylinders to lateral loading 32 . As important for structural applications, it has been suggested that these theoretical minimum-energy barriers can be accessed experimentally via a local probing technique for cylindrical 26,[34][35][36] and spherical shells 37,38 .…”

On the role of localizations in buckling of axially compressed cylinders

“…Furthermore, while the SP-8007 guideline converges to P / P cl ≈ 0.2 for large R / t , the present shock-sensitivity threshold of figure 10 b converges to P / P cl ≈ 0.35 for large L 2 / Rt . It is interesting to note that in a recent publication [53] on imperfect cylinders, the knockdown factor approaches a similar value of P / P cl ≈ 0.35 with increasing dimple imperfection amplitude (normalized by cylinder thickness). Furthermore, this trend persists for different R / t and L / R ratios (assuming the cylinder is not very short), providing further credence to the newly developed knockdown factor.…”

Transition to stress focusing for locally curved sheets

“…Here, we show that the induced compression strain has the same effect than an external compression load applied to a shell with the same curvature: The geometric stability criterion c ∼ t/W with 1/W the typical curvature of the transversely curved sheet is the equivalent of the classical buckling of perfect cylindrical shells where the linear stability analysis predicts c = 1/ 3(1 − ν 2 )t/R [42] with ν denoting the Poisson coefficient of the shell and 1/R its curvature. Notably, the above-mentioned formula infamously overestimates the buckling load of cylindrical shells [44] because those systems are extremely imperfection sensitive [45,46]. This affects the reliability of thin shell structures, even for precisely manufactured shells, such as soda cans [47] and space rockets [44].…”