Issue 51

A. Chikh, Frattura ed Integrità Strutturale, 51 (2020) 115-126; DOI: 10.3221/IGF-ESIS.51.09 115 Investigations in static response and free vibration of a functionally graded beam resting on elastic foundations Abdelbaki Chikh Department of Civil Engineering, Faculty of Applied Sciences, Ibn Khaldoun University, Tiaret, Algeria cheikhabdelbakki@yahoo.fr A BSTRACT . In this article, an analytical study was done to predict the behavior of the beam vis-à-vis bending, buckling, and dynamic responses of isotropic homogeneous beams based on an elastic foundation. The material properties of the FG-beams vary across the thickness using the power law. In this work, the sinusoidal shear deformation beams theory is used to investigate the static and dynamic behavior of FG beams. The present theory fulfills the condition of nullity of edge stresses and does not require the use of a shear correction factor. Hamilton's principle is used to deduce equations of motion, and analytical solutions for simply supported beams were obtained using the Navier resolution method. Nondimensional displacements, eigenfrequencies and critical-buckling loads of isotropic homogeneous beams were obtained for various values of the foundation parameters. The numerical results obtained by the present technique have been compared with the results of literature and are in excellent agreement with them. It can be concluded that the current HSDBT is simple and accurate in solving the bending, eigenfrequency and critical-buckling load problems for FGM beams. K EYWORDS . Undetermined integral terms; Free vibration; isotropic- homogeneous beams; Navier’s solution; Elasticity. Citation: A. Chikh, Investigations in static response and free vibration of a functionally graded beam resting on elastic foundations, Frattura ed Integrità Strutturale, 51 (2020) 115-126. Received: 08.10.2019 Accepted: 04.11.2019 Published: 01.01.2020 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. I NTRODUCTION he functionally graded materials (FGM) may be defined as materials having a progressive variation of material properties. This material is produced by mixing two or more materials in a certain percentage of volume (ceramic and metal). The mixing ratio of the constituents varies regularly and the material properties change without any interruption throughout the thickness. There are a large number of works have been done on the dynamics, flexion and buckling behavior of FGM structures. The Conventional composite structures suffer from a discontinuity in the properties of materials at the interface of layers and constituents. Therefore, constraint fields in intersection areas create interface problems and thermal stress concentrations in high-temperature environments. Many authors have studied the dynamic behavior of FGM beams, mostly, T