Analyse of the behavior of functionally graded beams based on neutral surface position

Lazreg Hadji,El Abbes Adda Bedia 국제구조공학회 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.55 No.4

In this paper, a simple n-order refined theory based on neutral surface position is developed for bending and frees vibration analyses of functionally graded beams. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the Hamilton’s principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.

Static and dynamic behavior of FGM plate using a new first shear deformation plate theory

Lazreg Hadji,M. Ait Amar Meziane,Z. Abdelhak,T. Hassaine Daouadji,E.A Adda Bedia 국제구조공학회 2016 Structural Engineering and Mechanics, An Int'l Jou Vol.57 No.1

In this paper, a new first shear deformation plate theory based on neutral surface position is developed for the static and the free vibration analysis of functionally graded plates (FGPs). Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher order shear deformation theories. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present shear deformation plate theory and the neutral surface concept, the governing equations are derived from the principle of Hamilton. There is no stretchingbending coupling effect in the neutral surface based formulation. Numerical illustrations concern flexural and dynamic behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

A refined exponential shear deformation theory for free vibration of FGM beam with porosities

Hadji, Lazreg,Daouadji, T. Hassaine,Bedia, E. Adda Techno-Press 2015 Geomechanics & engineering Vol.9 No.3

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.

Buckling analysis of sandwich plates with functionally graded porous layers using hyperbolic shear displacement model

Lazreg Hadji 한국풍공학회 2021 Wind and Structures, An International Journal (WAS Vol.32 No.1

This study presents buckling analysis of a simply supported sandwich plate with functionally graded porous layers. In the kinematic relation of the plate, a hyperbolic shear displacement model is used. The governing equations of the problem are derived by using the principle of virtual work. In the solution of the governing equations, the Navier procedure is implemented. In the porosity effect, four different porosity types are used for functionally graded sandwich layers. In the numerical examples, the effects of the porosity parameters, porosity types and geometry parameters on the critical buckling of the functionally graded sandwich plates are investigated.

Bending and buckling of porous multidirectional functionality graded sandwich plate

Lazreg Hadji,Fabrice Bernard,Royal Madan,Ali Alnujaie,Mofareh Hassan Ghazwani 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.85 No.2

Bending and buckling analysis of multi-directional porous functionally graded sandwich plate has been performed for two cases namely: FG skin with homogeneous core and FG core with homogeneous skin. The principle of virtual displacements was employed and the solution was obtained using Navier’s technique. This theory imposes traction-free boundary conditions on the surfaces and does not require shear correction factors. The validation of the present study has been performed with those available in the literature. The composition of metal-ceramic-based FGM changes in longitudinal and transverse directions according to the power law. Different porosity laws, such as uniform distribution, unevenly and logarithmically uneven distributions were used to mimic the imperfections in the functionally graded material that were introduced during the fabrication process. Several sandwich plates schemes were studied based on the plate's symmetry and the thickness of each layer. The effects of grading parameters and porosity laws on the bending and buckling of sandwich plates were examined.

A n-order refined theory for bending and free vibration of functionally graded beams

Lazreg Hadji,T. Hassaine Daouadji,A. Tounsi,E.A. Bedia 국제구조공학회 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.54 No.5

In this paper, a simple n-order refined theory based on neutral surface position is developed for bending and frees vibration analyses of functionally graded beams. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the Hamilton’s principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.

Analyze of the interfacial stress in reinforced concrete beams strengthened with externally bonded CFRP plate

Lazreg Hadji,T. Hassaine Daouadji,M. Ait Amar Meziane,E. A. Adda Bedia 국제구조공학회 2016 Steel and Composite Structures, An International J Vol.20 No.2

A theoretical method to predict the interfacial stresses in the adhesive layer of reinforced concrete beams strengthened with externally bonded carbon fiber-reinforced polymer (CFRP) plate is presented. The analysis provides efficient calculations for both shear and normal interfacial stresses in reinforced concrete beams strengthened with composite plates, and accounts for various effects of Poisson's ratio and Young's modulus of adhesive. Such interfacial stresses play a fundamental role in the mechanics of plated beams, because they can produce a sudden and premature failure. The analysis is based on equilibrium and deformations compatibility approach developed by Tounsi. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both the reinforced concrete beam and bonded plate. The paper is concluded with a summary and recommendations for the design of the strengthened beam.

Bending analysis of FGM plates using a sinusoidal shear deformation theory

Hadji, Lazreg,Zouatnia, Nafissa,Kassoul, Amar Techno-Press 2016 Wind and Structures, An International Journal (WAS Vol.23 No.6

The response of functionally graded ceramic-metal plates is investigated using theoretical formulation, Navier's solutions, and a new displacement based on the high-order shear deformation theory are presented for static analysis of functionally graded plates. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. Numerical results of the new refined plate theory are presented to show the effect of the material distribution on the deflections, stresses and fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the static and free vibration behavior of functionally graded plates.

Bending and free vibration analysis for FGM plates containing various distribution shape of porosity

Hadji, Lazreg,Bernard, Fabrice,Safa, Abdelkader,Tounsi, Abdelouahed Techno-Press 2021 Advances in materials research Vol.10 No.2

In this paper hyperbolic shear deformation plate theory is presented for bending and the free vibration of functionally graded plates with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. Four different porosity types are used for functionally graded plates. Equations of motion are derived from Hamilton's principle. In the solution of the governing equations, the Navier procedure is implemented. In the numerical examples, the effects of the porosity parameters, porosity types and geometry parameters on the bending and free vibration of the functionally graded plates are investigated. It was found that the distribution form of porosity significantly influence the mechanical behavior of FG plates, in terms of deflection, normal, shear stress and frequency.

A new quasi-3D higher shear deformation theory for vibration of functionally graded carbon nanotube-reinforced composite beams resting on elastic foundation

Hadji, Lazreg,Meziane, Mohamed Ait Amar,Safa, Abdelkader Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.66 No.6

This study deals with free vibrations analysis with stretching effect of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) resting on an elastic foundation. 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 significant feature of this model is that, in addition to including the shear deformation effect and stretching effect it deals with only 4 unknowns without including a shear correction factor. The governing equations are derived through using Hamilton's principle. Natural frequencies are obtained for nanocomposite beams. The mathematical models provided in this paper are numerically validated by comparison with some available results. New results of free vibration analyses of CNTRC beams based on the present theory with stretching effect is presented and discussed in details. The effects of different parameters of the beam on the vibration responses of CNTRC beam are discussed.