Prof J. Michael T. Thompson

University of Cambridge

Nonlinear dynamics of shell buckling: energy probes and step loading

Fluids and Materials Seminar

14th March 2019, 2:00 pm – 3:00 pm
Main Maths Building, SM3

Classic problems of shell buckling are the sphere under uniform external pressure and the axially compressed cylinder. Historically, these two well-defined archetypal examples have been widely studied to understand their notorious imperfection sensitivity. I use them here to illustrate two new advances, discussing always a shell with a geometrical imperfection.

First is the non-destructive laboratory probing of a progressively loaded shell to assess its decreasing energy barrier against the random dynamic disturbances of a real-world environment. Spheres and cylinders have been studied, and for the former theoretical and experimental results of this ‘shock sensitivity’ are in excellent agreement. Generically encountered bifurcations that might interfere with the probing process are carefully examined.

Second is the response of a spherical shell to a dynamical step in its pressure loading, modelling perhaps a nearby explosive blast. Accurate nonlinear dynamical simulations show how the initial overall breathing oscillations slowly transfer their energy to a localized buckling mode. This makes damping the key factor, rather than the amount of energy initially transmitted. A detailed examination is made of the phase-space features encountered as buckling trajectories pass the centre manifold of the unstable energy-barrier solution.

Organisers: John Russo, Aurore Loisy

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