The Mathematical Institute, University of Oxford, Eprints Archive

Nonlinear Correction to the Euler Buckling Formula for
Compressible Cylinders

Pascalis, R. De and Destrade, M. and Goriely, A. (2010) Nonlinear Correction to the Euler Buckling Formula for
Compressible Cylinders.
Nonlinear Correction to the Euler Buckling Formula for Compressible Cylinders . (Submitted)

[img]
Preview
PDF
152Kb

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/(π 3B2)=(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 nonlinear 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 non-linear elasticity for the homogeneous compression of a thick 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.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:964
Deposited By:Ruby Hawkins
Deposited On:02 Sep 2010 10:39
Last Modified:08 Oct 2012 12:44

Repository Staff Only: item control page