Buckling and Bending Analyses of Cantilever Carbon Nanotubes Using the Euler-Bernoulli Beam Theory Based on Non-Local Continuum Model

Euler-Bernoulli beam model based non-local elasticity theory is developed for the staticand buckling analysis of cantilever carbon nanotubes (CNTs). The size effect is takeninto consideration using the Eringen’s non-local elasticity theory. The derivation ofgoverning equation of bending and buckling from the shear and moment resultants of thebeam and stress-strain relationship of the one-dimensional non-local elasticity model ispresented. Buckling and deflection values of CNTs are obtained and presented ingraphical form. Numerical results are presented to show the small-scale effect onbending of CNTs.