Exact Stiffness Matrices for Lateral–Torsional Buckling of Doubly Symmetric Tapered Beams with Axially Varying Material Properties

Abstract

In this paper, a finite element model is developed for lateral–torsional stability analysis of axially functionally graded beams with tapered bi-symmetric I-section subjected to various boundary conditions. Considering the coupling between the lateral displacement and the twist angle, the equilibrium equations are derived via energy method in association with Vlasov’s thin-walled beam theory. The system of equilibrium equations is then transformed to a unique differential equation in terms of the angle of twist. Finally, new 4 * 4 elastic and buckling stiffness matrices are exactly determined by constructing the weak form of the governing equation and using cubic Hermite interpolation functions. Contemplating three comprehensive numerical examples, the influences of different parameters such as axial variation of material properties, tapering ratios, moment gradient, transverse load height and end conditions on lateral stability resistance of considered members are discussed in detail. It is believed that the numerical outcomes of this paper can be useful for future studies of web and/or flanges tapered I-beams with axially varying materials subjected to different boundary conditions.