Advances in Shell Buckling: Theory and Experiments

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.

31 pages, submitted version

References in corpus (3)

• The emergence of a coherent structure for coherent structures: localized states in nonlinear systems
• Systematic experimental exploration of bifurcations with non-invasive control
• Quantified 'shock sensitivity' above the Maxwell load

Cited by in corpus (11)

• Shock-Sensitivity in Shell-Like Structures: with Simulations of Spherical Shell Buckling
• Probing shells against buckling: a non-destructive technique for laboratory testing
• Snap buckling of bistable beams under combined mechanical and magnetic loading
• Nondestructive Prediction of the Buckling Load of Imperfect Shells
• Coupled electro-elastic deformation and instabilities of a toroidal membrane
• Cutting holes in bistable folds
• Snakes in square, honeycomb, and triangular lattices
• Buckling mediated by mobile localized elastic excitations
• Snakes on Lieb lattice
• Drying Pathways of an Evaporating Soft Matter Droplet
• A sequence of elastic patterns in a sheared bent sheet