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 Eringenʹs 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.