Modélisation du Flambement et de La Vibration des Poutres FGM par Les éléments Finis

Abstract

This dissertation describes a new quasi-3D finite element model for evaluating the free vibration and stability behaviors of thick functionally graded (FG) and functionally graded porous (FGP) beams. The FG beam model is based on an accurate shear and normal deformation beam theory, whereas the FGP beam model is based on a simple and efficient higher-order shear deformation theory. Without shear correction factors, traction-free boundary conditions are guaranteed for FG beams using the hyperbolic warping function for both transverse shear deformation and stress through the thickness coordinate, and inter- element continuity is maintained using both C1 and C0 continuities for kinematics variables. The FGP beam model, on the other hand, has three degrees of freedom per node and ensures inter-element continuity by using both C0 and C1 continuities for the displacement field and its first derivative form functions. The governing equations for FG beams are obtained from a weak version of the variational principle and the Hamilton principle for FGP beams. For both models, the isoparametric coordinate system is used to create the elementary stiffness, geometry, and mass matrices. According to the power-law form, the material properties of both FG and FGP beams vary constantly over the beam thickness. The effects of boundary conditions, power-law index, span-to-height ratio, and porosity distribution patterns on the free vibration and buckling responses of FG and FGP beams are studied in detail. The developed beam elements' performance is proved by comparing the results to those anticipated by alternative existing theories. The effects of these factors on natural frequencies and critical buckling loads are significant for the manufacturing process and mechanical modeling of such materials in aeronautical, nuclear, civil, and other structures.