Nonlocal Finite Element Model with Eight Degrees of Freedom and Sinusoidal Shear Deformation Theory for Bending and Buckling Analysis of Functionally Graded Nanobeams

In the present study, an efficient nonlocal finite element model is used to investigate the buckling and bending behavior of functionally graded (FG) nanobeams. A two-node element with eight degrees of freedom is formulated according to the sinusoidal higher-order shear deformation theory. This theory assumes an accurate sinusoidal distribution of transverse shear stress in the thickness direction to provide stress-free boundary conditions without requiring shear correction factors on the top and bottom surfaces of the nanobeams. To apply size effects, the nonlocal Eringen elasticity theory is used. The material properties of FG nanobeams vary in the thickness direction as a continuous power function. Numerical results indicate the acceptable accuracy of the nonlocal finite element model. Additionally, the effects of various parameters, such as FG material power law index, length-to-thickness aspect ratio, and nonlocal parameter, on the critical buckling load and deflection of FG nanobeams are investigated.