Pascalis, R. De and Destrade, M. and Goriely, A.
Nonlinear Correction to the Euler Buckling Formula for
Compressible Cylinders. Nonlinear Correction to the Euler Buckling Formula for Compressible Cylinders . (Submitted)
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
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.
|Subjects:||D - G > General|
|Research Groups:||Oxford Centre for Collaborative Applied Mathematics|
|Deposited By:||Ruby Hawkins|
|Deposited On:||02 Sep 2010 09:39|
|Last Modified:||29 May 2015 18:39|
Repository Staff Only: item control page