Vol. 6, No. 1-4, 2011

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A zero-stiffness elastic shell structure

Simon D. Guest, Elizbar Kebadze and Sergio Pellegrino

Vol. 6 (2011), No. 1-4, 203–212

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.

zero-stiffness, morphing structure, reconfigurable structure
Received: 17 May 2010
Revised: 4 August 2010
Accepted: 4 August 2010
Published: 28 June 2011
Simon D. Guest
Department of Engineering
University of Cambridge
Trumpington Street
Cambridge CB2 1PZ
United Kingdom
Elizbar Kebadze
Department of Engineering
University of Cambridge
Trumpington Street
Cambridge CB2 1PZ
United Kingdom
BP Exploration
Chertsey Road
Sunbury-upon-Thames, TW16 7LN
United Kingdom
Sergio Pellegrino
Graduate Aerospace Laboratories
California Institute of Technology
Pasadena, CA 91125
United States