Stability Landscape of Shell Buckling

Abstract

We measure the response of cylindrical shells to poking and identify a stability landscape, which fully characterizes the stability of perfect shells and imperfect ones in the case where a single defect dominates. We show that the landscape of stability is independent of the loading protocol and the poker geometry. Our results suggest that the complex stability of shells reduces to a low dimensional description. Tracking ridges and valleys of this landscape defines a natural phase-space coordinates for describing the stability of shells.

Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force

“…For these numerical results [13], the shape of the imperfection was approximated and modeled as a Gaussian dimple (see Eq. (3) As proposed recently [10][11][12], our results demonstrate that measuring the variation of the energy barrier with the normalized internal pressure can be interpreted as a nondestructive technique to probe the stability of a shell that is uniformly compressed close, but just prior, to its working load. The initial amplitude of the imperfection can therefore be extracted by sequentially increasing the depressurization on the shell and: (i) probing the loaddisplacement curve (with a minimum threshold slightly larger than zero for the force signal to avoid the catastrophic collapse of the structure); (ii) computing the corresponding energy barrier; and (iii) increasing the depressurization on the shell.…”

“…Nonetheless, a detailed a priori knowledge of the geometrical imperfections of the shell is still needed in order to predict the stability of such a structure. In an attempt toward circumnavigating this requirement, a novel nondestructive framework has recently been proposed to probe the stability of uniformly compressed cylindrical shells [10][11][12] and spherical shells [13]. The basis of this approach is to measure the relationship between the nonlinear deflections of an elastic shell that was initially compressed close to its working load, by subjecting it to a point indentation force, which hereon we shall refer to as probing force.…”

“…Following the work of Thompson and Hutchinson [13], and supported by our own experiments and FEM simulations, we demonstrate that the combination of pneumatic loading, together with the compressive indentation loading, is a successful local strategy to nondestructively probe the mechanical behavior of the shell. We highlight a parallel effort by Emmanuel Virot, Shmuel M. Rubinstein (Harvard University), Tobias Kreilos and Tobias Schneider on the stability of cylindrical shells set to various levels of axial compression, and probed by a point load to obtain force-displacement curves [12,16]. By contrast, throughout our current study, we shall focus exclusively on hemispherical shells.…”

Probing Shells Against Buckling: A Nondestructive Technique for Laboratory Testing

“…Recently, Virot et al [2017] have made a pioneering series of probing (poking) tests on axially compressed Coke cans. The axial compression is usually rigid (displacement controlled) but they do make a few dead (force controlled) tests to confirm that this makes no essential difference to the measured buckling load.…”

“…Tests on a single specimen were used to generate the smoothest landscape, illustrated in figure 10. Fig 10. The smoothest experimental force landscape created using a single specimen by Virot et al [2017]. On the left is a photograph of their experimental testing of an axially compressed Coke can.…”