Issue 52

N. Hebbar et alii, Frattura ed Integrità Strutturale, 52 (2020) 230-246; DOI: 10.3221/IGF-ESIS.52.18 230 Numerical modeling of bending, buckling, and vibration of functionally graded beams by using a higher-order shear deformation theory Nabil Hebbar Department of Civil Engineering and Architecture, University of Abdelhamid Ibn-Badis, Mostaganem, Algeria. nabil_al@hotmail.fr, https://orcid.org/0000-0001-7648-9875 Imène Hebbar Department of Mechanical Engineering, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria. imhebbar@gmail.com Djamel Ouinas Department of Mechanical Engineering, University of Abdelhamid Ibn-Badis, Mostaganem, Algeria. douinas@netcourrier.com Mohamed Bourada Department of Civil Engineering, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria. Med_bourada@yahoo.fr A BSTRACT . The objective of this work is to analyze the behavior beams functionally graded, simply supported, under different conditions such as bending, buckling, and vibration and this by use shear deformation theories a two-dimensional (2D) and quasi-three-dimensional (quasi-3D). The proposed theories take into account a new field of displacement which includes indeterminate whole terms and contains fewer unknowns, compared to other theories of the literature; by taking account of the effects of the transverse shears and the thickness stretching. In this theory, the distribution of the transverse shear stress is hyperbolic and satisfies the boundary conditions on the upper and lower surfaces of the beam without the need for a shear correction factor. In this type of beam the properties of the materials vary according to a distribution of the volume fraction, the Hamilton principle is used to calculate the equations of motion, and in order to check the accuracy of the theory used comparison is made with the studies existing in the literature. K EYWORDS . Functionally graded beams; Bending; Buckling; Vibration; Hyperbolic theory of shear deformation. Citation: Hebbar, N., Hebbar, I., Ouinas, D., Bourada, M., Numerical modeling of bending, buckling, and vibration of functionally graded beams by using a higher-order shear deformation theory, Frattura ed Integrità Strutturale, 52 (2020) 230-246. Received: 12.02.2020 Accepted: 16.02.2020 Published: 01.04.2020 Copyright: © 2020 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.