Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory

Abstract

In this study, an efficient nonlocal finite element model is developed to investigate the bending and buckling behavior of functionally graded (FG) nanobeams. New two-node beam element with eight degrees of freedom is formulated based on the recently refined higher order shear deformation theory proposed by the authors. The present theory can provide an accurate parabolic distribution of transverse shear stress through the thickness direction satisfying the traction free boundary conditions needless of any shear correction factor. In order to capture the small size effect, Eringen’s nonlocal elasticity theory is incorporated. The material properties of the FG nanobeams are assumed to vary continuously through the thickness direction according to the power-law form. The performance and reliability of the proposed model is demonstrated by comparing the author’s results with those available in the literature. The numerical results show that the present element model is free of shear locking and has a high accuracy and fast rate of convergence. Moreover, a detailed numerical study is carried out to examine the effects of several parameters such as boundary conditions, power-law index, nonlocal parameter and length-to-height ratio on the deflection and critical buckling load of the FG nanobeams. Many new results are also reported in the current study, which will serve as a benchmark for future research.