Flexural-torsional analysis of functionally graded sandwich I-beams considering shear effects

This paper presents a flexural-torsional analysis of shear flexible thin-walled sandwich I-beams with functionally graded materials (FGMs). The transverse shear and warping shear deformations are considered in this study. Based on the power law distribution of volume fraction of ceramic or metal, the mechanical properties of beam such as Young's and shear moduli are assumed to continuously vary in the thickness direction. The locations of center of gravity and shear center for FG beams are derived. Governing equations are also derived from the principle of minimum total potential energy. To solve the static problems of FG beams, the isoparametric beam element using the reduced Gauss numerical integration scheme is employed with the scope to discretize the governing equations. In order to demonstrate the validity of this study, the numerical solutions for the flexural-torsional problem of beams with bisymmetric and mono-symmetric I-sections are presented and compared with the previously published results. The effects of shear deformation, gradient index, thickness ratio of ceramic, material ratio, boundary condition and span-to-height ratio on the flexural-torsional response of FG I-beams are parametrically investigated.