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Axisymmetric post-buckling of complete spherical shell under uniform external pressure

This and the next 2 images are from:

J. Michael T. Thompson (1) and Jan Sieber (2)
(1) Dept. of Applied Maths and Theoretical Physics, Universtiy of Cambridge and Dept. of Engineering, Aberdeen University
(2) CEMPS, University of Exeter, Exeter, UK

“Shock-sensitivity in shell-like structures: with simulations of spherical shell buckling”, Int. J. Bifurcation and Chaos, Vol. 26, No. 2, February 2016

ABSTRACT: Under increasing compression, an unbuckled shell is in a metastable state which becomes increasingly precarious as the buckling load is approached. So to induce premature buckling a lateral disturbance will have to overcome a decreasing energy barrier which reaches zero at buckling. Two archetypal problems that exhibit a severe form of this behaviour are the axially-compressed cylindrical shell and the externally pressurized spherical shell. Focussing on the cylinder, a non-destructive technique was recently proposed to estimate the ‘shock sensitivity’ of a laboratory specimen using a lateral probe to measure the nonlinear load-deflection characteristic. If a symmetry-breaking bifurcation is encountered on the path, computer simulations showed how this can be supressed by a controlled secondary probe. Here, we extend our understanding by assessing in general terms how a single control can capture remote saddle solutions: in particular how a symmetric probe could locate an asymmetric solution. Then, more specifically, we analyse the spherical shell with point and ring probes, to test the procedure under challenging conditions to assess its range of applicability. Rather than a bifurcation, the spherical shell offers the challenge of a de-stabilizing fold (limit point) under the rigid control of the probe.

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