Static analysis of nanobeams including surface effects by nonlocal finite element

In reality, there are two phenomena should be considered to describe behaviors of nanostructures adequately and accurately. The first one is the surface properties, especially for a relatively high ratio of the surface area to the volume of structural. The second phenomenon is the information about bulk material, which contains the forces between atoms and the internal length scale. Therefore, the objective of the current work is to study the coupled effects of surface properties and nonlocal elasticity on the static deflection of nanobeams. Surface elasticity is employed to describe the behavior of the surface layer and the Euler-Bernoulli beam hypothesis is used to state the bulk deformation kinematics. Both, the surface layer and bulk volume of the beam are assumed elastically isotropic. Information about the forces between atoms, and the internal length scale are proposed by the nonlocal Eringen model. Galerkin finite element technique is employed for the discretization of the nonlocal mathematical model with surface properties. The present results are compared favorably with those published results. The effects of nonlocal parameter and surface elastic constants are figured out and presented.