The Static Bending Analysis of Functionally Graded Nanobeams using Trigonometric Shear Deformation Theory

This paper examines the static bending behavior of functionally graded (FG) nanobeams using a thorough analysis within the context of trigonometric shear deformation theory. A mathematical model of the FG nanobeam has been developed, in which the power-law distribution of the material characteristics varies continuously through the thickness direction. Size-dependency at the nanoscale has been explained by Eringen's nonlocal elasticity theory. Unlike traditional beam theories, no shear correction factor is required since the fundamental equation of the FG nanobeam is developed using the trigonometric function that reflects the non-parabolic shear stress distribution throughout the thickness. The governing differential equations of the static bending of the FG nanobeam have been solved using the Navier solution method under simply supported boundary conditions. The correctness and efficiency of the presented study are demonstrated by the comparison studies carried out. The obtained results reveal in detail the effects of the nonlocal parameter, power-law index, and length-to-thickness ratio on the static bending of the FG nanobeam.