Thermal Buckling Behavior of Nanobeams Using an Efficient Higher-Order Nonlocal Beam Theory

Abstract

This paper presents an efficient higher-order nonlocal beam theory for the thermal buckling of nanobeams. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stress vanishes on the nanobeam surfaces. Therefore, there is no need to use a shear correction factor. The present model is capable of capturing both the small-scale effect and transverse shear deformation effects of nanobeams, and it has strong similarities with the nonlocal Euler–Bernoulli beam theory in aspects such as equations of motion, boundary conditions, and stress resultant expressions. Using the nonlinear strain–displacement relations, the equilibrium and stability equations of nanobeams are derived. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the instability analysis of a complex nanobeam system such as a complex carbon nanotube system.