On the mechanics of functionally graded nanobeams with the account of surface elasticity

In this paper, size-dependent bending, buckling and free vibration responses of functionally graded (FG) nanobeams are investigated using an integrated nonclassical continuum model. The integrated model accounts for the simultaneous effects of the microstructure local rotation and the surface energy in the framework of the nonlocal elasticity. The proposed nonlocal-couple stress-surface elasticity (NLCSSE) model is formulated by incorporating the Eringen nonlocal elasticity theory, modified couple stress theory and surface elasticity theory into the classical Euler-Bernoulli beam model. It is assumed that the material properties of the bulk and surface of the FG nanobeam change continuously through the thickness according to a power law. The size-dependent equations of motion and corresponding boundary conditions are derived utilizing the Hamilton's principle. The proposed model is validated by comparing the obtained results with available benchmark results. Numerical results are presented to reveal the effects of nonlocal parameter, material length scale parameter, surface energy, gradient index, Poisson ratio, thickness and length-to-thickness ratio on the deflection, critical buckling load and natural frequency of a FG simply supported nanobeam.