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A new quasi-3D HSDT for buckling and vibration of FG plate
Mohamed Sekkal,Bouazza Fahsi,Abdelouahed Tounsi,S. R. Mahmoud 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.64 No.6
A new quasi-3D higher shear deformation theory (quasi-3D HSDT) for functionally graded plates is proposed in this article. The theory considers both shear deformation and thickness-stretching influences by a hyperbolic distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower surfaces of the plate without using any shear correction factor. The highlight of the proposed theory is that it uses undetermined integral terms in displacement field and involves a smaller number of variables and governing equations than the conventional quasi-3D theories, but its solutions compare well with 3D and quasi-3D solutions. Equations of motion are obtained from the Hamilton principle. Analytical solutions for buckling and dynamic problems are deduced for simply supported plates. Numerical results are presented to prove the accuracy of the proposed theory.
A new hybrid HSDT for bending, free vibration, and buckling analysis of FGM plates (2D & quasi-3D)
D. Ouinas,Y. Belkhodja,H. Fekirini,J.A. Viña Olay,B. Achour,M. Touahmia,M. Boukendakdji 국제구조공학회 2022 Smart Structures and Systems, An International Jou Vol.29 No.3
A new hybrid quasi-3D and 2D high-order shear deformation theory is studied in this mathematical formulation, for an investigation of the bending, free vibrations and buckling influences on a functionally graded material plate. The theoretical formulation has been begun by a displacement field of five unknowns, governing the transverse displacement across the thickness of the plate by bending, shearing and stretching. The transverse shear deformation effect has been taken into consideration, satisfying the stress-free boundary conditions, especially on plate free surfaces as parabolic variation through its thickness. Thus, the mechanical properties of the functionally graded plate vary across the plate thickness, following three distributions forms: the power law, exponential form and the Mori-Tanaka scheme. The mechanical properties are used to develop the equations of motion, obtained from the Hamilton principle, and solved by applying the Navier-type solution for simply supported boundary conditions. The results obtained are compared with other solutions of 2D, 3D and quasi-3D plate theories have been found in the literature.
Khadidja Bouafia,Mahmoud M. Selim,Fouad Bourada,Abdelmoumen Anis Bousahla,Mohamed Bourada,Abdeldjebbar Tounsi,E.A. Adda Bedia,Abdelouahed Tounsi 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.41 No.4
In this investigation, a novel analytical model based on combined (cubic, sinusoidal and exponential) higher order quasi-3D formulation is developed to examine flexural and free vibrational response on the various FG-plate resting on elastic foundation. The presented model is simple and contains a variable number less than others quasi-three dimensional theories. The effective properties of the structure are computed using linear, cubic, quadratic and inverse quadratic formulations which represent the volume fraction of the ceramic. The elastic foundation is structured by the constant parameter of Winkler which represents the reaction of the elastic springs and Pasternak one's in the form of a shear layer of subgrade. The analytical solution of the problem is obtained on the basis of the both Hamilton’s principle and Navier’s technique. The exactness of the current combined quasi-3D HSDT which takes into account the thickness stretching effect are checked and compared with others existing analytical models. Parametric studies are performed to shows the effects of the material distribution, inhomogeneity index, elastic foundation parameters, geometry and dimension ratios on displacements, stresses and naturel frequencies of the simply supported FG-plates.
A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation
Zoulikha Boukhlif,Mohammed Bouremana,Fouad Bourada,Abdelmoumen Anis Bousahla,Mohamed Bourada,Abdelouahed Tounsi,Mohammed A. Al-Osta 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.31 No.5
This work presents a dynamic investigation of functionally graded (FG) plates resting on elastic foundation using a simple quasi-3D higher shear deformation theory (quasi-3D HSDT) in which the stretching effect is considered. The culmination of this theory is that in addition to taking into account the effect of thickness extension (εz ≠ 0), the kinematic is defined with only 4 unknowns, which is even lower than the first order shear deformation theory (FSDT). The elastic foundation is included in the formulation using the Pasternak mathematical model. The governing equations are deduced through the Hamilton‟s principle. These equations are then solved via closed-type solutions of the Navier type. The fundamental frequencies are predicted by solving the eigenvalue problem. The degree of accuracy of present solutions can be shown by comparing it to the 3D solution and other closed-form solutions available in the literature.
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.
Novel quasi 3D theory for mechanical responses of FG-CNTs reinforced composite nanoplates
Alazwari, Mashhour A.,Daikh, Ahmed Amine,Eltaher, Mohamed A. Techno-Press 2022 Advances in nano research Vol.12 No.2
Effect of thickness stretching on free vibration, bending and buckling behavior of carbon nanotubes reinforced composite (CNTRC) laminated nanoplates rested on new variable elastic foundation is investigated in this paper using a developed four-unknown quasi-3D higher-order shear deformation theory (HSDT). The key feature of this theoretical formulation is that, in addition to considering the thickness stretching effect, the number of unknowns of the displacement field is reduced to four, and which is more than five in the other models. Two new forms of CNTs reinforcement distribution are proposed and analyzed based on cosine functions. By considering the higher-order nonlocal strain gradient theory, microstructure and length scale influences are included. Variational method is developed to derive the governing equation and Galerkin method is employed to derive an analytical solution of governing equilibrium equations. Two-dimensional variable Winkler elastic foundation is suggested in this study for the first time. A parametric study is executed to determine the impact of the reinforcement patterns, nonlocal parameter, length scale parameter, side-t-thickness ratio and aspect ratio, elastic foundation and various boundary conditions on bending, buckling and free vibration responses of the CNTRC plate.
Mohamed Rabhi,Kouider Halim Benrahou,Redha Yeghnem,Hicham Zakaria Guerroudj,Abdelhakim Kaci,Abdelouahed Tounsi,Muzamal Hussain 국제구조공학회 2022 Structural Engineering and Mechanics, An Int'l Jou Vol.83 No.6
This research investigates the free vibration of porous advanced composite plates resting on Winkler/Pasternak/ Kerr foundations by using a new hyperbolic quasi three dimensional (quasi-3D) shear deformation theory. The present theory, which does not require shear correction factor, accounts for shear deformation and thickness stretching effects by parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate. In this work, we consider imperfect FG plates with porosities embedded within elastic Winkler, Pasternak or Kerr foundations. Implementing an analytical approach, the obtained governing equations from Hamilton’s principle according to FG plates are derived. The closed form solutions are obtained by using Navier technique, and natural frequencies of FG plates are found, for simply supported plates, by solving the results of eigenvalue problems. A comprehensive parametric study is presented to evaluate effects of the geometry of material, mode numbers, porosity volume fraction, Power-law index and stiffness of foundations parameters on free vibration characteristics of FG plates.
Djaloul Zarga,Abdelouahed Tounsi,Abdelmoumen Anis Bousahla,Fouad Bourada,S. R. Mahmoud 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.32 No.3
In this article, a simple quasi-3D shear deformation theory is employed for thermo-mechanical bending analysis of functionally graded material (FGM) sandwich plates. The displacement field is defined using only 5 variables as the first order shear deformation theory (FSDT). Unlike the other high order shear deformation theories (HSDTs), the present formulation considers a new kinematic which includes undetermined integral variables. The governing equations are determined based on the principle of virtual work and then they are solved via Navier method. Analytical solutions are proposed to provide the deflections and stresses of simply supported FGM sandwich structures. Comparative examples are presented to demonstrate the accuracy of the present theory. The effects of gradient index, geometrical parameters and thermal load on thermo-mechanical bending response of the FG sandwich plates are examined.
Anfel Ameri,Abdelkader Fekrar,Fouad Bourada,Mahmoud M. Selim,Kouider Halim Benrahou,Abdelouahed Tounsi,Muzamal Hussain 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.41 No.1
The current investigation presents hygro-thermo-mechanical analysis of simply supported anti-symmetric composite plates by using an original computational four unknown’s quasi-3D inverse tangent hyperbolic theory. The developed formulations take into account the thickness stretching effect and contain indeterminate integral variables to reduce the number of unknowns. The present model ensures the transverse shear stresses nullity at the top and the bottom surfaces without using any shear correction factor. The governing equations are determined with the help of virtual work principle. The analytical solution of the hygro-thermo-mechanical analysis is derived via Navier’s procedure. The accuracy and efficiency of current model is checked by comparing the results with others models found in the literature. Several numerical results are presented in graphs form to show the effects of the aspect, geometry and modulus ratio on the stress and transverse displacement of the simply supported anti-symmetric composite plates.
Tran, Loc V.,Wahab, M. Abdel,Kim, Seung-Eock Elsevier 2017 COMPOSITE STRUCTURES -BARKING THEN OXFORD- Vol.179 No.-
<P><B>Abstract</B></P> <P>Temperature rise in a plate structure produces non-zero transverse normal strain. Thus, a six-variable quasi-3D model with one additional variable in transverse displacement of higher-order shear deformation theory (HSDT) is developed in this paper to take into account the effects of transverse shears and normal strain in a laminated composite plate. The governing equation is discretized by isogeometric analysis (IGA), which naturally fulfills the <I>C</I> <SUP>1</SUP>-continuity requirement of the plate model. Due to the presence of bending-extension coupling, two kinds of thermal plate issues are considered – thermal buckling and thermal bending phenomena. Several numerical examples are provided to show the accuracy of the present method compared to reference results. Furthermore, it has been confirmed that the transverse normal strain cannot be discarded, especially for thick plates under a temperature environment.</P>