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Axisymmetric and non-axisymmetric post-buckling of a very thin spherical shell under uniform external pressure

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From:
Hutchinson, J.W. and Thompson, J.M.T., 2017, “Nonlinear buckling behaviour of spherical shells: barriers and symmetry breaking dimples.” Phil. Trans. R. Soc. A, pp. 20160154. (doi.org/10.1098/rsta.2016.0154)

ABSTRACT: The nonlinear axisymmetric post-buckling behavior of perfect thin spherical shells subject to external pressure and their asymmetric bifurcations are characterized providing results for a structure/loading combination with an exceptionally nonlinear buckling response. Immediately after the onset of buckling, the buckling mode localizes into a dimple at the poles. The relations among the pressure, the dimple amplitude and the change in volume of the shell are determined for large deflections. These results allow accurate evaluation of criteria such as the Maxwell condition for which the energy in the unbuckled and buckled states are the same and evaluation of the influences of pressure versus volume controlled loadings. Non-axisymmetric bifurcation from the axisymmetric state which occurs deep into the post-buckling regime in the form of multi-lobed dimples is also established and discussed.

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