Bending of functionally graded nanobeams incorporating surface effects based on Timoshenko beam model

- Analyzing the bending of functionally graded nanobeams based on Timoshenko beam theory.
- Considering surface stress effects of nanobeams by adopting the Gurtin-Murdoch theories.
- Deriving the governing equations by using the principle of minimum total potential energy.
- Investigating the influences of gradient index and surface stress on the bending responses.

The bending responses of functionally graded (FG) nanobeams with simply supported edges are investigated based on Timoshenko beam theory in this article. The Gurtin-Murdoch surface elasticity theory is adopted to analyze the influences of surface stress on bending response of FG nanobeam. The material properties are assumed to vary along the thickness of FG nanobeam in power law. The bending governing equations are derived by using the minimum total potential energy principle and explicit formulas are derived for rotation angle and deflection of nanobeams with surface effects. Illustrative examples are implemented to give the bending deformation of FG nanobeam. The influences of the aspect ratio, gradient index, and surface stress on dimensionless deflection are discussed in detail.