Nonlocal elasticity theory for lateral stability analysis of tapered thin-walled nanobeams with axially varying materials

Abstract

The lateral-torsional buckling behavior of functionally graded (FG) non-local beams with a tapered I-section is here investigated using an innovative methodology. The material properties are supposed to vary continuously along the longitudinal direction according to a homogenization procedure, based on a power-law function, whereas the nanobeam is modeled within the framework of a Vlasov thin-walled beam theory. The flexural-torsional governing equations of the problem are derived based on the Eringen's nonlocal elasticity theory and the energy method. The system of lateral stability equations is, thus, reduced to a fourth-order differential equation in terms of the twist angle by uncoupling the equilibrium differential equations. The buckling loads are finally determined using the differential quadrature method (DQM), which is here applied as numerical tool to solve directly the differential equations of the problem in a strong form. A systematic investigation checks for the influence of some parameters such as the power-law index, tapering ratios, loading height parameter, boundary conditions and non-local parameter, on the lateral stability resistance of the tapered I-nanobeams. The numerical outcomes of this paper can be used as benchmarks for further studies on nanoscale tapered thin-walled beams.