Lateral buckling analysis of axially functionally graded thin-walled beam with varying cross-section under different boundary conditions

Abstract

In this article, lateral-torsional stability of axially functionally graded (AFG) non-prismatic beam with doubly symmetric thin-walled cross-section under transverse loading is investigated. Material properties of FG beam with variable cross-section are supposed to vary through longitudinal direction of the constituents according to simple power-law distribution (P-FGM). Based on Vlasov’s model and using small displacements theory, the governing equilibrium equations are derived through the energy principle for AFG web and/or flanges tapered I-beams. The differential quadrature method is then selected to numerically solve the resulting system of governing fourth-order differential equations with variable coefficients. In this approach, a non-uniform mesh point distribution (Chebyshev-Gauss-Lobatto) is used for provide accuracy of solutions and convergence rate. Finally, the lateral-torsional buckling loads are calculated by solving an eigenvalue problem of the obtained algebraic system. In the case of homogenous members with variable cross-section, the outcomes of this work are compared with the available benchmarks and there is an excellent agreement. Finally, the impacts of involved parameters such as boundary conditions, load height parameter, power law index and web and flanges tapering ratios on the non-dimensional lateral buckling load are discussed. The results of this research reveal that the impacts of non-uniformity in the cross-section and gradient index play significant roles on lateral-torsional stability behavior of tapered I-beams. Furthermore, the highest buckling capacity is acquired when the transverse load is applied to the bottom flange.