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Published January 2011 | Published
Journal Article Open

A Zero-Stiffness Elastic Shell Structure


A remarkable shell structure is described that, due to a particular combination of geometry and initial stress, has zero stiffness for any finite deformation along a twisting path; the shell is in a neutrally stable state of equilibrium. Initially the shell is straight in a longitudinal direction, but has a constant, nonzero curvature in the transverse direction. If residual stresses are induced in the shell by, for example, plastic deformation, to leave a particular resultant bending moment, then an analytical inextensional model of the shell shows it to have no change in energy along a path of twisted configurations. Real shells become closer to the inextensional idealization as their thickness is decreased; experimental thin-shell models have confirmed the neutrally stable configurations predicted by the inextensional theory. A simple model is described that shows that the resultant bending moment that leads to zero stiffness gives the shell a hidden symmetry, which explains this remarkable property.

Additional Information

© 2011 Mathematical Sciences Publishers. Received: 17 May 2010. Revised: 4 August 2010. Accepted: 4 August 2010. Published: 28 June 2011. This research was sponsored by the EPSRC (research grant GR/M72852/01) and supported by Rolatube Technology Ltd. Guest acknowledges support from the Leverhulme Trust.

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