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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 191-200 |
| Number of pages | 10 |
| Journal | Journal of Elasticity |
| Volume | 102 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jul 22 2010 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.