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Steel and Composite Structures   Volume 25, Number 6, December30 2017, pages 717-726
A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations
Houari Hachemi, Abdelhakim Kaci, Mohammed Sid Ahmed Houari, Mohamed Bourada, Abdelouahed Tounsi and S.R. Mahmoud

Abstract     [Full Text]
    In this paper, a new simple shear deformation theory for bending analysis of functionally graded plates is developed. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not required. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. Equations of motion are obtained by utilizing the principle of virtual displacements and solved via Navier\'s procedure. The elastic foundation is modeled as two parameter elastic foundation. The results are verified with the known results in the literature. The influences played by transversal shear deformation, plate aspect ratio, sideto-thickness ratio, elastic foundation, and volume fraction distributions are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the bending behaviour of functionally graded plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.
Key Words
    a simple 3-unknown theory; bending; functionally graded plates, elastic foundation
Houari Hachemi, Abdelhakim Kaci, Mohamed Bourada, Abdelouahed Tounsi : Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Houari Hachemi, Abdelhakim Kaci : Department of Civil Engineering and Hydraulics, University Dr. Taher Moulay of Saida, Algeria
Mohammed Sid Ahmed Houari : Department of Civil Engineering, Universite Mustapha Stambouli de Mascara, Mascara, Algeria
Mohammed Sid Ahmed Houari, Mohamed Bourada, Abdelouahed Tounsi : Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Faculte de Technologie
Abdelouahed Tounsi : Laboratoire de Modelisation et Simulation Multi-echelle, Faculte des Sciences, Departement de Physique, Universite de Sidi Bel Abbes, Algeria
S.R. Mahmoud : Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

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