New Investigation of the Buckling Responses of Nano-Beams Based on Engesser and Haringx Theories by the New Model of Shear Deformation Theories

The objective of this work is to investigate the buckling responses of nano-beams while accounting for the impacts of surface stress. To accomplish this, a continuum elasticity model based on Gurtin-Murdoch elasticity theory was used to develop non-classical beam models that included the influence of surface stress on the buckling behaviours of nano-beams for two boundary conditions (hinge-hinge and clamped-clamped) based on Haringx and Engresser theories of buckling is employing a new model beam shear deformation is presented and discuted. The formulas were developed to determine critical buckling loads, transverse and angular displacements of nano-beams, and surface stress effects relevant to each type of beam theory.