Advances in Shell Buckling: Theory and Experiments

摘要

In a recent feature article in this journal, co-authored by Gert van derHeijden, I described the static-dynamic analogy and its role in understandingthe localized post-buckling of shell-like structures, looking exclusively atintegrable systems. We showed the true significance of the Maxwell energycriterion load in predicting the sudden onset of 'shock sensitivity' to lateraldisturbances. The present paper extends the survey to cover non-integrablesystems, such as thin compressed shells. These exhibit spatial chaos,generating a multiplicity of localized paths (and escape routes) with complexsnaking and laddering phenomena. The final theoretical contribution shows howthese concepts relate to the response and energy barriers of an axiallycompressed cylindrical shell. After surveying NASA's current shell-testing programme, a new non-destructivetechnique is proposed to estimate the 'shock sensitivity' of a laboratoryspecimen that is in a compressed meta-stable state before buckling. A probe isused to measure the nonlinear load-deflection characteristic under a rigidlyapplied lateral displacement. Sensing the passive resisting force, it can beplotted in real time against the displacement, displaying an equilibrium pathalong which the force rises to a maximum and then decreases to zero: havingreached the free state of the shell that forms a mountain-pass in the potentialenergy. The area under this graph gives the energy barrier against lateralshocks. The test is repeated at different levels of the overall compression. Ifa symmetry-breaking bifurcation is encountered on the path, computersimulations show how this can be supressed by a controlled secondary probetuned to deliver zero force on the shell.