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In this paper, a refined exponential shear deformation theory for free vibration analysis of functionally graded beam with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton’s principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

International Symposium on Light Alloys and Composite Materials
UHAKS

Latifa Ould Larbi Lazreg HADJI Nafissa Zouatnia Kada DRAICHE

This study deals with free vibrations analysis of nanocomposite beams with stretching effect reinforced by single-walled carbon nanotubes (SWCNTs) resting on an elastic foundation. The SWCNTs are assumed to be aligned and straight with a uniform layout. Four different carbon nanotubes (CNTs) distributions including uniform and three types of functionally graded distributions of CNTs through the thickness are considered. The rule of mixture is used to describe the effective material properties of the nanocomposite beams. The governing equations are derived through using Hamilton’s principle and then solved by using the Navier solution. Natural frequencies are obtained for nanocomposite beams. Effects of several parameters, such as nanotube volume fraction, foundation stiffness parameters, slenderness ratios and CNTs distribution on both natural frequency are investigated. The results indicate that the above-mentioned parameters play a very important role on the free vibrations characteristics of the beam.

International Symposium on Light Alloys and Composite Materials
UHAKS

Lazreg Hadji Nafissa Zouatnia Kada DRAICHE

This paper presents a static flexure of laminated composite plates by using a novel first shear deformation theory (FSDT). This theory contains only four unknowns, with is even less than the classical FSDT and has strong similarities with the classical plate theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. The governing equations are derived by employing the Hamilton's principles and solved via Navier's solution. Analytical solutions of simply supported antisymmetric cross-ply and angle-ply laminates are obtained and the results are compared with the exact 3D [1], classical FSDT [2] and the Higher- order shear deformation theory (HSDT) with cubic variations for in-plane displacements developed by Reddy [3] and other solutions available in the literature. Comparison studies show that this novel first-order shear deformation theory can achieve the same accuracy of the existing first-order shear deformation theory which has more number of unknowns.

International Symposium on Light Alloys and Composite Materials
UHAKS

Kada DRAICHE Lazreg Hadji Abdelouahed TOUNSI El Abbas ADDA BEDIA

This work presents a simple quasi-3D theory for the static flexure analysis of exponential functionally graded material (simply called E-FGM) plates, whose material properties are assumed to vary exponentially through the thickness. This theory explains both the deformation of the transverse shear and thickness stretching effects by a hyperbolic variation of all displacements across the thickness. By dividing the transverse displacement into three components, bending, shear and stretching parts, the number of unknowns and governing equations of the present theory is reduced and hence, makes it simple to use. The governing equations and the boundary conditions are derived from the principle of virtual displacements. Analytical solutions are obtained for simply supported plates. The accuracy of the present theory is verified by comparing the obtained results with exact three dimensional elasticity theory and quasi-3D solutions and with other higher-order shear deformation theories (HSDT).

International Symposium on Light Alloys and Composite Materials
UHAKS

Khaled BOUAKKAZ Kada DRAICHE Lazreg HADJI