Investigation of coupled instability for shear flexible FG sandwich I-beams subjected to variable axial force

The general thin-walled beam model is presented to study the flexural-torsional coupled buckling behavior of shear flexible sandwich I-beams made of functionally graded materials based on an orthogonal Cartesian coordinate system. The derived beam model includes the transverse shear, the restrained warping induced shear deformations, the structural coupling coming from the material anisotropy, and the variable axial force effect. Material properties of the beam such as Young's and shear moduli are assumed to be graded across the wall thickness. The strain energy and the potential energy due to the variable axial force are introduced. The seven coupled instability equations are derived from the energy principle. To solve the instability problem, three types of finite beam elements, namely, linear, quadratic, and cubic elements are employed with the scope to discretize the governing equations. In order to verify the accuracy and efficiency of the beam model presented by this study, numerical results are presented and compared with results from other researchers. By numerical examples, the bisymmetric and mono-symmetric I-beams with two types of material distributions are considered to investigate the effects of shear deformation, variable axial force, gradient index, thickness ratio of ceramic, boundary conditions, material ratio, and span-to-height ratio on the buckling behavior of FG sandwich I-beams. Particularly, the crossover phenomenon in buckling modes with changes in gradient index and thickness ratio of ceramic in flanges is investigated.