Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions
Type
ArticleKAUST Grant Number
KUK-C1-013-04Date
2010-07-22Online Publication Date
2010-07-22Print Publication Date
2011-02Permanent link to this record
http://hdl.handle.net/10754/598986
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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.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.Sponsors
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.Publisher
Springer NatureJournal
Journal of Elasticityae974a485f413a2113503eed53cd6c53
10.1007/s10659-010-9265-6