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)

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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 handside of this equation when terms up to (B/L)4 are kept? To answer this question, we specialize the exact solution of nonlinear elasticity for the homogeneous compression of a thick cylinder with lubricated ends to the theory of thirdorder elasticity. In particular, we highlight the way second and thirdorder 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 09:39 
Last Modified:  29 May 2015 18:39 
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