Techno Press
Techno Press

Steel and Composite Structures   Volume 22, Number 2, October10 2016, pages 257-276
A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates
Mohammed Sid Ahmed Houari, Abdelouahed Tounsi, Aicha Bessaim and S.R. Mahmoud

Abstract     [Full Text]
    In this paper, a new simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) plates is developed. The significant feature of this formulation is that, in addition to including a sinusoidal variation of transverse shear strains through the thickness of the plate, it deals with only three unknowns as the classical plate theory (CPT), instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The accuracy of the present solutions is verified by comparing the obtained results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and free vibration behaviours of FG 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; vibration; functionally graded plates
(1) Mohammed Sid Ahmed Houari, Aicha Bessaim:
Université Mustapha Stambouli de Mascara, Department of Civil Engineering, Mascara, Algeria;
(2) Mohammed Sid Ahmed Houari, Abdelouahed Tounsi, Aicha Bessaim:
Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria;
(3) Abdelouahed Tounsi:
Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria;
(4) S.R. Mahmoud:
Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia;
(5) S.R. Mahmoud:
Mathematics Department, Faculty of Science, University of Sohag, Egypt.

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