A three-unknown refined shear beam element model for buckling analysis of functionally graded curved sandwich beams

This research work is focused on the buckling analysis of functionally graded (FG) curved sandwich beams using an effective and simple three-unknown refined shear theory. Unlike the first shear deformation theory and higher-order shear deformation theory, this theoretical formulation only has three unknowns. This feature makes the formulation computationally faster to solve. It also provides a clear advantage over the classical plate theory since it considers the shear deformation effect in spite of having three unknowns. The present theory accounts for a new parabolic distribution of transverse shear stress through thickness direction and satisfies the traction-free boundary conditions needless of any shear correction factor. In this present study, the FG modeling encompasses a single layer and two kinds of sandwich beams: one composed of a homogeneous core with FG face sheets, and another made up of homogeneous face sheets with FG core. On the basis of the proposed kinematic model, a new efficient Hermite-Lagrangian finite element formulation is successfully developed to determine accurately the critical buckling loads of FG curved sandwich beams. The governing equations are derived by employing the principle of virtual works and solved by means of the finite element method. The accuracy and effectiveness of the proposed model are demonstrated by comparing the present results with those available in the literature. The results indicate that the developed finite element model is promising in terms of accuracy and fast rate of convergence for both thin and thick FG sandwich beams. Moreover, a detailed numerical study is carried out to examine the effects of the boundary conditions, power-law index, radii of curvature, length-to-height ratio and face-core-face thickness ratio on the buckling response of FG sandwich beams. Such parametric analysis can serve as a basis for engineering solutions in the context of FG sandwich curved beams.