Abstract
This paper addresses the flexural–torsional stability of functionally graded (FG) nonlocal thin-walled beam-columns with a tapered I-section. The material composition is assumed to vary continuously in the longitudinal direction based on a power-law distribution. Possible small-scale effects are included within the formulation according to the Eringen nonlocal elasticity assumptions. The stability equations of the problem and the associated boundary conditions are derived based on the Vlasov thin-walled beam theory and energy method, accounting for the coupled interaction between axial and bending forces. The coupled equilibrium equations are solved numerically by means of the differential quadrature method (DQM) to determine the flexural–torsional buckling loads associated to the selected structural system. A parametric study is performed to check for the influence of some meaningful input parameters, such as the power-law index, the nonlocal parameter, the axial load eccentricity, the mode number and the tapering ratio, on the flexural–torsional buckling load of tapered thin-walled FG nanobeam-columns, whose results could be used as valid benchmarks for further computational validations of similar nanosystems.
Highlights
A modified couple stress theory was differently combined with the first-order shear deformable beam model of Ke et al [42] to describe the size effect on the dynamic stability of microbeams made of functionally graded materials (FGMs)
Paper, we we explore explore the theflexural–torsional flexural–torsionalbuckling bucklingofofAFG
Material properties vary in the axial direction of structural elements according ory
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. A modified couple stress theory was differently combined with the first-order shear deformable beam model of Ke et al [42] to describe the size effect on the dynamic stability of microbeams made of FGMs. A novel finite element solution was proposed by Borbon [43] to study the coupled vibrational responses of beams with non-symmetric thin-walled cross-sections, accounting for the possible influence of loading eccentricities, shear deformation and rotatory inertia, and a further approximate methodology was successfully introduced by Serna et al [44] to study the elastic flexural buckling of non-uniform columns subjected to arbitrary axial forces.
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