Bending behavior and buckling of nanobeams including surface stress effects corresponding to different beam theories

A new frontier of research in the area of computational nanomechanics is to study the behavior of structures at very small length scales. As the dimensions of a structure approach the nanoscale, the classical continuum theories may fail to accurately predict the mechanical behavior of nanostructures. Among these nanostructures, nanobeams are attracting more and more attention due to their great potential engineering applications. One of the most important factors that influence the behavior of such submicron-sized structures is surface stress effect because of their high surface to volume ratio. In this paper, a non-classical solution is proposed to analyze bending and buckling responses of nanobeams including surface stress effects. Explicit formulas are proposed relevant to each type of beam theory to evaluate the surface stress effects on the displacement profile and critical buckling load of the nanobeams. Numerical results are presented to demonstrate the difference between the behaviors of the nanobeam predicted by the classical and non-classical solutions which depends on the magnitudes of the surface elastic constants.