Non-local Finite Element Formulation for Stability Analysis of Thin-Walled Nanobeams with Varying I-section

Abstract

In this paper, the flexural–torsional stability analysis of tapered thin-walled nanobeams with doubly symmetric I-section subjected to transverse loading and axial force is studied through a finite element approach. At first, the non-local equilibrium governing equations are derived on the basis of Vlasov's thin-walled beam theory and the principle of minimum potential energy. The influence of nanoscale is considered via the theory of non-local elasticity of Eringen. The variational form of the resulting system of differential equations is then constructed. The exact 12 × 12 static and buckling stiffness matrices are finally established by applying cubic Hermitian polynomials as the shape functions into the variational statement. After verification, the effects of tapering ratio, non-local parameter, end conditions and loading height parameter on the lateral torsional stability capacity of web-tapered nanobeam are numerically investigated. The numerical results of this study can serve as a reference for future studies on the lateral stability analysis of nanoscale thin-walled beams.