Exact nonlocal solution for postbuckling of single-walled carbon nanotubes

The purpose of this paper is to present exact and efficient analytical expressions for the postbuckling configurations of single-walled carbon nanotubes with different boundary conditions. The nonlinear governing partial-integral differential equations are derived based on Eringen's nonlocal elasticity model and the Euler-Bernoulli beam theory. The geometric nonlinearity is taken into account, which arises from the mid-plane stretching. The exact nonlocal model results can be conveniently used to assess the sensitivity of the small-scale parameter on the nanotubes postbuckling load-deflection relationship. The accuracy of the solution is demonstrated by comparing the critical buckling load results with those available in literature. The influences of small-scale parameter, various end conditions as well as nonlinearity on the postbuckling deformation are examined. (C) 2011 Elsevier B.V. All rights reserved.