Advances in Shell Buckling: theory, experiments, localization and shock-sensitivity

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• Professor Mike Thompson - Dept of Applied Maths
• Friday 15 May 2015, 15:00-16:00
• Cambridge University Engineering Department, LR5.

If you have a question about this talk, please contact Lorna Everett.

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.

This talk is part of the Engineering Department Structures Research Seminars series.

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