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

AuthorsM. Soltani, F. Atoufi
JournalActa Mechanica
Paper TypeFull Paper
Published At2022
Journal GradeISI
Journal TypeTypographic
Journal CountryIran, Islamic Republic Of
Journal IndexISI

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.