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A n-order four variable refined theory for bending and free vibration of functionally graded plates
I. Klouche Djedid,Abdelkader Benachour,Mohammed Sid Ahmed Houari,Mohammed Ameur,Abdelouahed Tounsi 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.17 No.1
This paper presents a simple n-order four variable refined theory for the bending and vibration analyses of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. 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.
A new and simple HSDT for isotropic and functionally graded sandwich plates
Hafida Driz,Mamia Benchohr,Ahmed Bakora,Abdelkader Benachour,Abdelouahed Tounsi,El Abbes Adda Bedia 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.26 No.4
A novel higher shear deformation theory (HSDT) is proposed for the bending, buckling and free vibration investigations of isotropic and functionally graded (FG) sandwich plates. It contains only four variables, which is even less than the first shear deformation theory (FSDT) and the conventional HSDTs. The model accounts for a parabolic variation of transverse shear stress, respects the traction free boundary conditions and contrary to the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral terms. Equations of motion determined in this work are applied for three types of FG structures: FG plates, sandwich plates with FG core and sandwich plates with FG faces. Analytical solutions are given to predict the transverse displacements, stresses, critical buckling forces and natural frequencies of simply supported plates and a comparison study is carried out to demonstrate the accuracy of the proposed model.
S.H. Tagrara,Abdelouahed Tounsi,Abdelkader Benachour,Mohamed Bachir Bouiadjra 국제구조공학회 2015 Steel and Composite Structures, An International J Vol.19 No.5
In this work, a trigonometric refined beam theory for the bending, buckling and free vibration analysis of carbon nanotube-reinforced composite (CNTRC) beams resting on elastic foundation is developed. The significant feature of this model is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the Timoshenko beam (TBM) without including a shear correction factor. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are assessed by employing the rule of mixture. To examine accuracy of the present theory, several comparison studies are investigated. Furthermore, the effects of different parameters of the beam on the bending, buckling and free vibration responses of CNTRC beam are discussed.
Effect of material composition on bending and dynamic properties of FG plates using quasi 3D HSDT
Bakhti Damani,Abdelkader Fekrar,Mahmoud M. Selim,Kouider Halim Benrahou,Abdelkader Benachour,Abdelouahed Tounsi,E.A. Adda Bedia,Muzamal Hussain 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.78 No.4
In this work, quasi three-dimensional (quasi-3D) shear deformation theory is presented for bending and dynamic analysis of functionally graded (FG) plates. The effect of varying material properties and volume fraction of the constituent on dynamic and bending behavior of the FG plate is discussed. The benefit of this model over other contributions is that a number of variables is diminished. The developed model considers nonlinear displacements through the thickness and ensures the free boundary conditions at top and bottom faces of the plate without using any shear correction factors. The basic equations that account for the effects of transverse and normal shear stresses are derived from Hamilton’s principle. The analytical solutions are determined via the Navier procedure. The accuracy of the proposed formulation is proved by comparisons with the different 2D, 3D and quasi-3D solutions found in the literature.
A simple analytical model for free vibration and buckling analysis of orthotropic rectangular plates
Souad Sellam,Kada Draiche,Youcef Tlidji,Farouk Yahia Addou,Abdelkader Benachour 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.75 No.2
In the present paper, a simple analytical model is developed based on a new refined parabolic shear deformation theory (RPSDT) for free vibration and buckling analysis of orthotropic rectangular plates with simply supported boundary conditions. The displacement field is simpler than those of other higher-order theories since it is modeled with only two unknowns and accounts for a parabolic distribution of the transverse shear stress through the plate thickness. The governing differential equations related to the present theory are obtained from the principle of virtual work, while the solution of the eigenvalue problem is achieved by assuming a Navier technique in the form of a double trigonometric series that satisfy the edge boundary conditions of the plate. Numerical results are presented and compared with previously published results for orthotropic rectangular plates in order to verify the precision of the proposed analytical model and to assess the impacts of several parameters such as the modulus ratio, the side-to-thickness ratio and the geometric ratio on natural frequencies and critical buckling loads. From these results, it can be concluded that the present computations are in excellent agreement with the other higher-order theories.
Farouk Yahia Addou1,Mustapha Meradjah,Abdelmoumen Anis Bousahla,Abdelkader Benachour,Fouad Bourada,Abdelouahed Tounsi,S.R. Mahmoud 사단법인 한국계산역학회 2019 Computers and Concrete, An International Journal Vol.24 No.4
This work investigates the effect of Winkler/Pasternak/Kerr foundation and porosity on dynamic behavior of FG plates using a simple quasi-3D hyperbolic theory. Four different patterns of porosity variations are considered in this study. The used quasi-3D hyperbolic theory is simple and easy to apply because it considers only four-unknown variables to determine the four coupled vibration responses (axial-shear-flexion-stretching). A detailed parametric study is established to evaluate the influences of gradient index, porosity parameter, stiffness of foundation parameters, mode numbers, and geometry on the natural frequencies of imperfect FG plates.
F. Chattibi,Abdelouahed Tounsi,Kouider Halim Benrahou,Abdelkader Benachour,K. Nedri 국제구조공학회 2015 Steel and Composite Structures, An International J Vol.19 No.1
The thermomechanical bending response of anti-symmetric cross-ply composite plates is investigated by the use of the simple four variable sinusoidal plate theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. The validity of the present theory is demonstrated by comparison with solutions available in the literature. Numerical results are presented to demonstrate the behavior of the system. The influences of aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and stacking sequence on the thermally induced response are studied. The present study is relevant to aerospace, chemical process and nuclear engineering structures which may be subjected to intense thermal loads.
Léa Elias Mendes Carneiro Zaidan,Joan Manuel Rodriguez-Díaz,Daniella Carla Napoleão,Maria da Conceição Branco da Silva de Mendonça Mon,Alberto da Nova Araújo,Mohand Benachour,Valdinete Lins da Silva 한국화학공학회 2017 Korean Journal of Chemical Engineering Vol.34 No.2
We examined the photocatalytic degradation of phenol from laboratory samples under UV radiation by using BiPO4/H2O2 and TiO2/H2O2 advanced oxidation systems. Both catalysts prepared were characterized by scanning electron microscopy, Fourier transform infrared and X-ray diffraction. Surface area tests showed about 3.46 and 31.33m2·g−1, respectively, for BiPO4 and TiO2. A central composite design was developed with the following variables-- catalyst concentration, time and concentration of hydrogen peroxide--to optimize the degradation process. Removal rates of 99.99% for phenol degradation using BiPO4 and TiO2 were obtained, respectively. For mineralization of organic carbon were obtained 95,56% when using BiPO4 and 63,40% for TiO2, respectively. The lumped kinetic model represented satisfactorily the degradation of phenol process, using BiPO4/H2O2/UV (R2=0.9977) and TiO2/H2O2/UV (R2=0.9701) treatments. The toxicity tests using different seed species showed the benefits of the proposed advanced oxidation process when applied to waste waters containing these pollutants.