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

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. (C) 2013 American Society of Civil Engineers.