Bending analysis of functionally graded nanobeams based on stress-driven nonlocal model incorporating surface energy effects

The bending response of Bernoulli-Euler nanobeams made of a functionally graded (FG) material with different cross-sectional shapes is investigated in this manuscript by a stress-driven model incorporating surface energy effects. In particular, the FG nanobeam is composed of a bulk vol ume and a surface layer regarded as a membrane of zero thickness perfectly adhered to the bulk continuum. The bulk material is made of a mixture of metal and ceramic, whose distributions spatially vary from the bottom to the top surface of the FG nanobeams. The nonlocal governing equations of the elastostatic bending problem are derived by using the virtual work principle. The main results of a parametric investigation are also presented and discussed varying the nonlocal parameter, the material gradient index and the boundary conditions at the ends of the nano beams. They show how the proposed model is able to study the bending behavior of inflected FG nanobeams including surface effects.