Vol. 6, No. 1-4, 2011

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ISSN: 1559-3959
A zero-stiffness elastic shell structure

Simon D. Guest, Elizbar Kebadze and Sergio Pellegrino

Vol. 6 (2011), No. 1-4, 203–212
Abstract
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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.

Keywords
zero-stiffness, morphing structure, reconfigurable structure
Milestones
Received: 17 May 2010
Revised: 4 August 2010
Accepted: 4 August 2010
Published: 28 June 2011
Authors
Simon D. Guest
Department of Engineering
University of Cambridge
Trumpington Street
Cambridge CB2 1PZ
United Kingdom
http://www.eng.cam.ac.uk/~sdg
Elizbar Kebadze
Department of Engineering
University of Cambridge
Trumpington Street
Cambridge CB2 1PZ
United Kingdom
BP Exploration
Chertsey Road
Sunbury-upon-Thames, TW16 7LN
Middlesex
United Kingdom
Sergio Pellegrino
Graduate Aerospace Laboratories
California Institute of Technology
Pasadena, CA 91125
United States
http://www.pellegrino.caltech.edu