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Mathematical Approach for Mechanical Behaviour Analysis of FGM Plates on Elastic Foundation

Fatima Zohra Zaoui, Djamel Ouinas, Belkacem Achour (), Mabrouk Touahmia, Mustapha Boukendakdji, Enamur R. Latifee, Ahmed A. Alawi Al-Naghi and Jaime Aurelio Viña Olay
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Fatima Zohra Zaoui: Laboratory of Science and Technology Environment and Valorization, Faculty of Sciences and Technology, Ibn Badis University, Mostaganem 27000, Algeria
Djamel Ouinas: Laboratory of Science and Technology Environment and Valorization, Faculty of Sciences and Technology, Ibn Badis University, Mostaganem 27000, Algeria
Belkacem Achour: Civil Engineering Department, University of Ha’il, Ha’il 55476, Saudi Arabia
Mabrouk Touahmia: Civil Engineering Department, University of Ha’il, Ha’il 55476, Saudi Arabia
Mustapha Boukendakdji: Civil Engineering Department, University of Ha’il, Ha’il 55476, Saudi Arabia
Enamur R. Latifee: Civil Engineering Department, University of Ha’il, Ha’il 55476, Saudi Arabia
Ahmed A. Alawi Al-Naghi: Civil Engineering Department, University of Ha’il, Ha’il 55476, Saudi Arabia
Jaime Aurelio Viña Olay: Department of Materials Science and Metallurgical Engineering, University of Oviedo, Viesques Campus, 33203 Gijón, Spain

Mathematics, 2022, vol. 10, issue 24, 1-29

Abstract: This paper presents the flexural analysis of functionally graded plates resting on elastic foundations using new two-dimensional (2D) and quasi-three-dimensional (quasi-3D) higher order shear deformation theories. The main interesting feature of this theory is that it proposes a new displacement field with undetermined integral variables which involves only five unknown functions, unlike other shear and normal deformation theories, hence making it easier to use. A parabolic transverse shear deformation shape function satisfying the zero shear stress conditions on the plate outer surfaces is considered. The elastic foundation follows the Pasternak mathematical model. The material properties change continuously across the thickness of the FG plate using different distributions: power law, exponential, and Mori–Tanaka models. The governing equations of FG plates subjected to sinusoidal and uniformly distributed loads are established through the principle of virtual works and then solved via Navier’s procedure. In this work, a detailed discussion on the influence of material composition, geometric parameters, stretching effect, and foundation parameters on the deflection, axial displacements, and stresses is given, and the obtained results are compared with those published in previous works to demonstrate the accuracy and the simplicity of the present formulations. The different obtained results were found to be in good agreement with the available solutions of other higher-order theories. The proposed model is able to represent the cross section warping in the deformed shape and to demonstrate the validity and efficiency of the approach, the findings reported herein prove that this theory is capable of predicting displacements and stresses more accurately than other theories, as its results are closer when compared to numerical methods reported in other literatures.

Keywords: bending; stress; functionally graded plate; shear deformation theory; stretching effect; Winkler–Pasternak parameters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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