Influence of surface effect on post-buckling behavior of graded porous nanobeam subjected to follower force

As the fundamental structural element of the nano electro mechanical system (NEMS), the mechanical properties of nano-beams are often affected by surface effects. In this study, we investigate the buckling and the post-buckling of graded porous nano-beams subjected to follower force, considering surface stiffness and surface residual stress. Considering two kinds of porosity models with symmetrical and asymmetric distribution in gradient porous material, it was assumed that the material properties change continuously in thickness. In order to capture the surface effect, the Gurtin–Murdoch surface elasticity theory, combined with geometrically non-linear beam theory, was utilized to establish the post-buckling control differential equations. And then, by using the shooting method to solve the coupled ordinary differential equations with simply supported nano-beams, some quantitative results of the post-buckling equilibrium path and configuration under different parameters are obtained. The results show that the pore distribution pattern, pore coefficient, surface elastic parameters, and residual surface stress have essential effects on the yield strength of nano-porous materials.