Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations

The novelty of this paper is the use of an efficient beam theory for bending, free vibration and buckling analysis of functionally graded material (FGM) beams on two-parameter elastic foundation. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the beam without requiring any shear correction factor. Due to porosities, possibly occurring inside FGMs during fabrication, it is therefore necessary to consider the vibration, bending and buckling behaviors of beams having porosities in this work. The equation of motion for FGM beams is obtained through Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. The validity of the present theory is investigated by comparing some of the present in literature. It can be concluded that the proposed theory is accurate and simple in solving the bending, free vibration and buckling behaviors of FGM sandwich beams.