A new quasi-3D sinusoidal shear deformation theory for functionally graded plates

Mamia Benchohra, Hafida Driz, Ahmed Bakora, Abdelouahed Tounsi, E.A. Adda Bedia and S.R. Mahmoud

Abstract

In this paper, a new quasi-3D sinusoidal shear deformation theory for functionally graded (FG) plates is proposed. The theory considers both shear deformation and thickness-stretching influences by a trigonometric distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower faces of the plate without employing any shear correction coefficient. The advantage of the proposed model is that it posses a smaller number of variables and governing equations than the existing quasi-3D models, but its results compare well with those of 3D and quasi-3D theories. This benefit is due to the use of undetermined integral unknowns in the displacement field of the present theory. By employing the Hamilton principle, equations of motion are obtained in the present formulation. Closed-form solutions for bending and free vibration problems are determined for simply supported plates. Numerical examples are proposed to check the accuracy of the developed theory.

Key Words

quasi 3D theory; bending; vibration; functionally graded plate

Address

Mamia Benchohra, Hafida Driz and Ahmed Bakor: Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Algeria Abdelouahed Tounsi: 1)Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Algeria 2) Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia 3) Laboratory of Modeling and Multi-scale Simulation, Department of Physics, Faculty of Exact Sciences, University of Sidi Bel Abbes, Algeria E.A. Adda Bedia: Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Algeria S.R. Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

← Back to Volume 65, No. 1