On the mechanics of FG nanobeams: A review with numerical analysis

Abstract

Since the classical continuum theories are insufficient to account the small size effects of nanobeams, the nonlocal continuum theories such as Eringen's nonlocal elasticity theory, couple stress theory, strain gradient theory and surface elasticity theory have been proposed by researchers to predict the accurate structural response of isotropic and functionally graded composite nanobeams. This review focuses on research work concerned with analysis of size dependent nanoscale isotropic and functionally graded beams using classical and refined beam theories based on Eringen's nonlocal elasticity theory. The present review article also highlight the possible scope for the future research on nanobeams. In the present study, the authors have developed a new hyperbolic shear deformation theory for the analysis of isotropic and functionally graded nanobeams. The theory satisfy the traction free boundary conditions at the top and the bottom surfaces of the nanobeams. Analytical solutions for the bending, buckling and free vibration analysis of simply-supported nanobeams are obtained using the Navier method. To ensure that the present theory is accurate and valid, the results are compared to previous research.

Keywords

• Nonlocal continuum theories
• Eringen's nonlocal elasticity theory
• A new hyperbolic nonlocal beam theory
• Functionally graded nanobeams