Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions
- 216 Downloads
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 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.
KeywordsColumn buckling Euler formula Non-linear correction Guided end condition
Mathematics Subject Classification (2000)74B15 74B10 74B20 74G05 74G15 74G60
Unable to display preview. Download preview PDF.
- 1.Timoshenko, S.P., Gere, J.M.: Theory of Elastic Stability. McGraw-Hill, New York (1961) Google Scholar
- 7.Ogden, R.W.: Non-Linear Elastic Deformations. Dover, New York (1984) Google Scholar
- 10.Landau, L.D., Lifshitz, E.M.: Theory of Elasticity, 3rd edn. Pergamon, New York (1986) Google Scholar
- 11.Murnaghan, F.D.: Finite Deformations of an Elastic Solid. Wiley, New York (1951) Google Scholar
- 15.Norris, A.N.: Finite amplitude waves in solids. In: Hamilton, M.F., Blackstock, D.T. (eds.) Nonlinear Acoustics, pp. 263–277. Academic Press, San Diego (1999) Google Scholar
- 19.Destrade, M., Ogden, R.W.: On the third- and fourth-order constants of incompressible isotropic elasticity (submitted) Google Scholar
© Springer Science+Business Media B.V. 2010