Comprehensive beam models for buckling and bending behavior of simple nanobeam based on nonlocal strain gradient theory and surface effects

In this paper, bending and buckling behavior of nanobeam utilizing different beam theories including Timoshenko, Euler Bernoulli, and higher-order beam theories are developed to investigate. The governing equations are derived based on nonlocal strain gradient theory incorporating surface effects. In order to solve the governing equation by a numerical solution, the Navier's method is utilized, and the simply supported boundary condition is imposed. Critical buckling load and maximum deflection are on the main concerns of this study. Obtained results represent the effect of surface, nonlocal, and length scale parameters. Moreover, various beam theories are evaluated, and their discrepancies are discussed. Results disclose that the Timoshenko and higher-order beam theories with negligible diversions are the critical ones which predict the lowest critical buckling load and highest maximum deflection compared to Euler Bernoulli beam theory. As a primary result, residual surface stress and surface Young's modulus magnitude reveal a direct relation with material stiffness. Finally, as the small scale parameter increases the material stiffness decreases whereas increasing the length scale parameter stiffens the material structure.