Abstract

Department of Applied Mathematics & Theoretical Physics, University of Cambridge

This talk describes the static-dynamic analogy and its role in understanding the localized post-buckling of shell-like structures. We show, for example, the true significance of the Maxwell energy criterion load in predicting the sudden onset of “shock sensitivity” to lateral disturbances. For technically ‘non-integrable’ systems, such as thin compressed shells, we show how the emergence of spatial chaos generates a multiplicity of localized paths (and escape routes) with complex snaking and laddering phenomena. These are illustrated in the response and energy barriers of an axially compressed cylindrical shell.

​After surveying NASA ’s current shell-testing programme, we propose a new non-destructive technique to estimate the “shock sensitivity” of a laboratory specimen that is in a compressed metastable state before buckling. This uses a probe 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. A symmetry-breaking bifurcation can be encountered on this path, and we show how this can be suppressed by a controlled secondary probe tuned to deliver zero force on the shell.