Advances in Shell Buckling: Theory and Experiments

TL;DR

This paper explores the complex buckling behavior of shells, extending theoretical understanding to non-integrable systems, and proposes a novel non-destructive testing method to estimate shock sensitivity in compressed shells.

Contribution

It extends shell buckling theory to non-integrable systems with chaos and introduces a new non-destructive technique for assessing shock sensitivity in shells.

Findings

Chaotic localized buckling paths observed in non-integrable shells

A new non-destructive test estimates energy barriers to buckling

Controlled secondary probing can suppress symmetry-breaking bifurcations

Abstract

In a recent feature article in this journal, co-authored by Gert van der Heijden, I described the static-dynamic analogy and its role in understanding the localized post-buckling of shell-like structures, looking exclusively at integrable systems. We showed the true significance of the Maxwell energy criterion load in predicting the sudden onset of 'shock sensitivity' to lateral disturbances. The present paper extends the survey to cover non-integrable systems, such as thin compressed shells. These exhibit spatial chaos, generating a multiplicity of localized paths (and escape routes) with complex snaking and laddering phenomena. The final theoretical contribution shows how these concepts relate to the response and energy barriers of an axially compressed cylindrical shell. After surveying NASA's current shell-testing programme, a new non-destructive technique is proposed to estimate the 'shock sensitivity' of a laboratory specimen that is in a compressed meta-stable state before buckling. A probe is used to measure the nonlinear load-deflection characteristic under a rigidly applied lateral displacement. Sensing the passive resisting force, it can be plotted in real time against the displacement, displaying an equilibrium path along which the force rises to a maximum and then decreases to zero: having reached the free state of the shell that forms a mountain-pass in the potential energy. The area under this graph gives the energy barrier against lateral shocks. The test is repeated at different levels of the overall compression. If a symmetry-breaking bifurcation is encountered on the path, computer simulations show how this can be supressed by a controlled secondary probe tuned to deliver zero force on the shell.