A new quasi-3D HSDT for buckling and vibration of FG plate

Mohamed Sekkal, Bouazza Fahsi, Abdelouahed Tounsi and S.R. Mahmoud

Abstract

A new quasi-3D higher shear deformation theory (quasi-3D HSDT) for functionally graded plates is proposed in this article. The theory considers both shear deformation and thickness-stretching influences by a hyperbolic distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower surfaces of the plate without using any shear correction factor. The highlight of the proposed theory is that it uses undetermined integral terms in displacement field and involves a smaller number of variables and governing equations than the conventional quasi-3D theories, but its solutions compare well with 3D and quasi-3D solutions. Equations of motion are obtained from the Hamilton principle. Analytical solutions for buckling and dynamic problems are deduced for simply supported plates. Numerical results are presented to prove the accuracy of the proposed theory.

Key Words

buckling; vibration; sandwich plate; functionally graded materials; quasi-3D HSDT

Address

Mohamed Sekkal : Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria Bouazza Fahsi : Faculty of Technology, Civil Engineering Department, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria Abdelouahed Tounsi : Faculty of Technology, Civil Engineering Department, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria; Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria; Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de Génie Civil, Algeria S.R. Mahmoud : Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia

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