Bending behaviour of FGM plates via a simple quasi-3D and 2D shear deformation theories

Ali Youcef, Mohamed Bourada, Kada Draiche, Belhadj Boucham, Fouad Bourada and Farouk Yahia Addou

Abstract

This article investigates the static behaviour of functionally graded (FG) plates sometimes declared as advanced composite plates by using a simple and accurate quasi-3D and 2D hyperbolic higher-order shear deformation theories. The properties of functionally graded materials (FGMs) are assumed to vary continuously through the thickness direction according to exponential law distribution (E-FGM). The kinematics of the present theories is modeled with an undetermined integral component and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate; therefore, it does not require the shear correction factor. The fundamental governing differential equations and boundary conditions of exponentially graded plates are derived by employing the static version of principle of virtual work. Analytical solutions for bending of EG plates subjected to sinusoidal distributed load are obtained for simply supported boundary conditions using Navier\'is solution procedure developed in the double Fourier trigonometric series. The results for the displacements and stresses of geometrically different EG plates are presented and compared with 3D exact solution and with other quasi-3D and 2D higher-order shear deformation theories to verify the accuracy of the present theory.

Key Words

E-FGM; static behaviour; quasi-3D; shear deformation; bending

Address

Ali Youcef: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Laboratory of Mechanics of Structures and Solids (LMSS), Faculty of Technology, Department of Mechanical Engineering, University Sidi Bel Abbes University, Algeria Mohamed Bourada: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Kada Draiche: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Departement de Genie Civil, Universite Ibn Khaldoun Tiaret, BP 78 Zaaroura, 14000 Tiaret, Algerie Belhadj Boucham: Laboratory of Mechanics of Structures and Solids (LMSS), Faculty of Technology, Department of Mechanical Engineering, University Sidi Bel Abbes University, Algria Fouad Bourada: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Departement des Sciences et de la Technologie, Centre Universitaire de Tissemsilt, BP 38004 Ben Hamouda, Algerie Farouk Yahia Addou: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria

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