## Nonlinear correction to the Euler buckling formula for compressed cylinders with guided-guided end conditions

Destrade, Michel

Destrade, Michel

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##### Repository DOI

##### Publication Date

2011-02

##### Type

Article

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##### Citation

Pascalis, R., Destrade, M., & Goriely, A. Nonlinear correction to the Euler buckling formula for compressed cylinders with guided-guided end conditions. Journal of Elasticity, 102(2), 191-200.

##### 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/([pi]^3 B^2 )=(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.

##### Funder

##### Publisher

Springer

##### Publisher DOI

http://dx.doi.org/10.1007/s10659-010-9265-6

##### Rights

Attribution-NonCommercial-NoDerivs 3.0 Ireland