buckling of nanotubes under compression considering surface effects

in this paper, the modified euler-bernoulli beam model is presented to examine the influence of surface elasticity and residual surface tension on the critical force of axial buckling of nanotubes in the presence of rotary inertia. an explicit solution is derived for the buckling loads of microscaled euler beams considering surface effects. the size-dependent buckling behavior of the nanotube due to surface effects is well elucidated in the obtained solutions. the critical forces are evaluated for axial buckling of cantilever beams. the results are compared with those corresponding to the classical beam model. the influences of the surface effects on the critical forces are discussed in detail.