The nonlocal effect on FG nanobeams: an uncoupled theory and a superposition approach

The nonlocal effect is studied for a functionally graded (FG) nanobeam, which is widely used in the Nanoelectromechanical system. First, the higher-order deformation mode is introduced in terms of the generalized displacements defined for the cross section. Generalized stresses and strains are accordingly defined and uncoupled constitutive relations are derived by combining the nonlocal elasticity theory. Next, according to the principle of virtual work, an uncoupled beam theory is established for a FG nanobeam, including governing equations and boundary conditions. The current work shows that, due to the decoupling of bending, tension and higher-order bending, the nonlocal effect can be attributed to the superimposition of equivalent initial generalized stresses. Typical FG nanobeam problems are analytically solved. It is found that the nonlocal effect on the deflection of FG nanobeam is case dependent for different boundary constraints.