Lateral-Torsional Stability Analysis of a Simply Supported Axially Functionally Graded Beam with a Tapered I-Section

A lateral buckling analysis of simply supported web- and/or flange-tapered I-beams made of axially functionally graded materials and subjected to a uniformly distributed load is performed. The properties of beam material vary continuously along the beam axis, depending on the volume fraction of constituent materials, according to an exponential or power law. Considering the coupling between the lateral displacement and twist angle, equilibrium equations are derived via the energy method in association with the Vlasov thin-walled beam theory. For simply supported beams with free warping, the system of equilibrium equations is transformed into a differential equation in the twist angle. The differential quadrature method is then used to numerically solve the resulting fourth-order differential equation with variable coefficients and to determine the lateral buckling loads. A numerical example is finally considered to study the influence of different parameters — the axial variation of material properties, tapering ratios, and load eccentricities — on the lateral stability of the beams considered. The numerical results of this paper can be used as benchmarks for future studies on axially functionally graded nonprismatic I-beams with pinned-pinned end conditions.