Abstract
We perform a detailed analysis of first order Sobolev-regular infinitesimal isometries on developable surfaces without affine regions. We prove that given enough regularity of the surface, any first order infinitesimal isometry can be matched to an infinitesimal isometry of an arbitrarily high order. We discuss the implications of this result for the elasticity of thin developable shells.
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Acknowledgements
P. Hornung was supported by EPSRC grant EP/F048769/1. M. Lewicka was partially supported by the NSF grants DMS-0707275 and DMS-0846996, and by the Polish MN grant N N201 547438. M.R. Pakzad was partially supported by the University of Pittsburgh grant CRDF-9003034 and by the NSF grant DMS-0907844.
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Hornung, P., Lewicka, M. & Pakzad, M.R. Infinitesimal Isometries on Developable Surfaces and Asymptotic Theories for Thin Developable Shells. J Elast 111, 1–19 (2013). https://doi.org/10.1007/s10659-012-9391-4
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DOI: https://doi.org/10.1007/s10659-012-9391-4