Assessment of New Quasi-3D Finite Element Model for Free Vibration and Stability Behaviors of Thick Functionally Graded Beams

A new quasi-3D finite element model is formulated and implemented in this research to evaluate the free vibration and stability behaviors of thick functionally graded (FG) beams. The current model is founded on an accurate shear and normal deformation beam theory. The traction-free boundary conditions are guaranteed with no shear correction factors by employing the hyperbolic warping function for both transverse shear deformation and stress through the thickness coordinate. The provided two-node beam element has four degrees of freedom per node, and the discrete model maintains inter-element continuity using both C1 and C0 continuities for the kinematics variables. As a result, the isoparametric coordinate system is used to produce the elementary stiffness, geometric, and mass matrices in order to improve the current formulation. The governing equations are derived from the variational principle’s weak version. In accordance with the power-law form, the material characteristics of functionally graded beams utilized change continuously over the beam thickness. The excellent performance of the developed beam element is shown by comparing recent findings to those predicted earlier by other existing theories. Furthermore, detailed numerical research is conducted to investigate the impacts of boundary conditions, power-law index, and span-to-height ratio on the free vibration and buckling responses of FG beams. Numerical findings indicate that evaluating the mechanical behavior of FG beams is difficult due to the issues mentioned earlier.