dc.contributor.author De Pascalis, Riccardo dc.contributor.author Destrade, Michel dc.contributor.author Goriely, Alain dc.date.accessioned 2016-02-25T13:50:38Z dc.date.available 2016-02-25T13:50:38Z dc.date.issued 2010-07-22 dc.identifier.citation De Pascalis R, Destrade M, Goriely A (2010) Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions. Journal of Elasticity 102: 191–200. Available: http://dx.doi.org/10.1007/s10659-010-9265-6. dc.identifier.issn 0374-3535 dc.identifier.issn 1573-2681 dc.identifier.doi 10.1007/s10659-010-9265-6 dc.identifier.uri http://hdl.handle.net/10754/598986 dc.description.abstract Euler's celebrated buckling formula gives the critical load N for the buckling of a slender cylindrical column with radius B and length L as N/(π3B2)=(E/4)(B/L)2 where E is Young's modulus. Its derivation relies on the assumptions that linear elasticity applies to this problem, and that the slenderness (B/L) is an infinitesimal quantity. Here we ask the following question: What is the first non-linear correction in the right hand-side of this equation when terms up to (B/L)4 are kept? To answer this question, we specialize the exact solution of incremental non-linear elasticity for the homogeneous compression of a thick compressible cylinder with lubricated ends to the theory of third-order elasticity. In particular, we highlight the way second- and third-order constants-including Poisson's ratio-all appear in the coefficient of (B/L)4. © 2010 Springer Science+Business Media B.V. dc.description.sponsorship This work was supported by a Da Vinci Mobility Grant from the Franco-Italian University (R.D.P.); by a CNRS/USA Collaborative Grant from the French Centre National de la Recherche Scientifique (R.D.P., M.D.); by a Senior Marie Curie Fellowship from the European Commission (M.D.); and by a Visiting Professorship from the Universite Pierre et Marie Curie (A.G.). For A.G., this publication is based on work supported by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST), and based in part upon work supported by the National Science Foundation under grants DMS-0907773. dc.publisher Springer Nature dc.subject Column buckling dc.subject Euler formula dc.subject Guided end condition dc.subject Non-linear correction dc.title Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions dc.type Article dc.identifier.journal Journal of Elasticity dc.contributor.institution CNRS Centre National de la Recherche Scientifique, Paris, France dc.contributor.institution Universite Pierre et Marie Curie, Paris, France dc.contributor.institution Universita del Salento, Lecce, Italy dc.contributor.institution University College Dublin, Dublin, Ireland dc.contributor.institution University of Oxford, Oxford, United Kingdom kaust.grant.number KUK-C1-013-04 dc.date.published-online 2010-07-22 dc.date.published-print 2011-02
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