An original four-variable quasi-3D shear deformation theory for the static and free vibration analysis of new type of sandwich plates with both FG face sheets and FGM hard core

Djilali Kouider , Abdelhakim Kaci , Mahmoud M. Selim , Abdelmoumen Anis Bousahla , Fouad Bourada , Abdeldjebbar Tounsi , Abdelouahed Tounsi , Muzamal Hussain

Abstract

This paper presents an original high-order shear and normal deformation theory for the static and free vibration of sandwich plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. New types of functionally graded materials (FGMs) sandwich plates are considered, namely, both FG face sheets which the properties vary according to power-law function and exponentially graded hard core. The equations of motion for the present problem are derived from Hamilton' principle. For simply-supported boundary conditions, Navier's approach is utilized to solve the motion equations. The accuracy of the present theory is verified by comparing the obtained results with three-dimensional elasticity solutions and other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending and free vibration responses of the FGM sandwich plates are studied. It can be concluded that present formulation which takes into account both the transverse shear and normal deformation, predicts the natural frequencies with the same degree of accuracy as that of 3D elasticity solutions and gives a good results of displacements and stress compared with others Quasi-3D theories. It can be also deduced that the central deflection is in direct correlation relation with inhomogeneity parameter and the natural frequency is in inverse relation with this parameter.

Key Words

bending and free vibration analysis; functionally graded plate; new quasi-3D theory; new type of sandwich plate; refined plate theory

Address

Djilali Kouider and Abdeldjebbar Tounsi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering, Algeria
Abdelhakim Kaci — Université Dr Tahar Moulay, Faculté de Technologie, Département de Génie Civil et Hydraulique, BP 138Cité En-Nasr 20000 Saida, Algérie
Mahmoud M. Selim — Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Aflaj 710-11912 Saudi Arabia
Abdelmoumen Anis Bousahla — Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria
Fouad Bourada — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering, Algeria; Département des Sciences et de la Technologie, université de Tissemsilt, BP 38004 Ben Hamouda, Algérie
Abdelouahed Tounsi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering, Algeria; 6YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia; Interdisciplinary Research Center for Construction and Building Materials, KFUPM, Dhahran, Saudi Arabia
Muzamal Hussain — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan

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