A Consistent Set of Nonlocal Bresse–Timoshenko Equations for Nanobeams With Surface Effects

Abstract

In this study, we propose governing differential equations for beams, taking into account shear deformation, rotary inertia, locality, and surface stress effects. It is shown that the equation is both simpler and more consistent than the appropriate Bresse–Timoshenko equations extended to include locality and surface stress effects. The proposed equation contains 11 terms with respect to displacement versus 19 terms appearing in the equations that extend the Bresse–Timoshenko equations to include nonlocality and surface effects.