Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions

Riccardo De Pascalis, Michel Destrade, Alain Goriely

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

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 languageEnglish (US)
Pages (from-to)191-200
Number of pages10
JournalJournal of Elasticity
Volume102
Issue number2
DOIs
StatePublished - Jul 22 2010
Externally publishedYes

Fingerprint Dive into the research topics of 'Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions'. Together they form a unique fingerprint.

Cite this