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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.
Mohamed Sekkal,Bouazza Fahsi,Abdelouahed Tounsi,S.R. Mahmoud 국제구조공학회 2017 Steel and Composite Structures, An International J Vol.25 No.4
In this work, a new higher shear deformation theory (HSDT) is developed for the free vibration and buckling of functionally graded (FG) sandwich plates. The proposed theory presents a new displacement field by using undetermined integral terms. Only four unknowns are employed in this theory, which is less than the classical first shear deformation theory (FSDT) and others HSDTs. Equations of motion are obtained via Hamilton\'s principle. The analytical solutions of FG sandwich plates are determined by employing the Navier method. A good agreement between the computed results and the available solutions of existing HSDTs is found to prove the accuracy of the developed theory.
Abdeljalil Meksi,Mohamed Sekkal,Rabbab Bachir Bouiadjra,Samir Benyoucef,Abdelouahed Tounsi 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.85 No.6
The effect of temperature dependent material properties on the free vibration of FG porous beams is investigated in the present paper. A quasi-3D shear deformation solution is used involves only three unknown function. The mechanical properties which are considered to be temperature-dependent as well as the porosity distributions are assumed to gradually change along the thickness direction according to defined law. The beam is supposed to be simply supported and lying on variable elastic foundation. The differential equation system governing the free vibration behavior of porous beams is derived based on the Hamilton principle. Navier’s method for simply supported systems is then used to determine and compute the frequencies of FG porous beam. The results of the present formulation are validated by comparing with those available literatures. Finally, the effects of several parameters such as porosity distribution and the parameters of variable elastic foundation on the free vibration behavior of temperature-dependent FG beams are presented and discussed in detail.
A novel four-unknown quasi-3D shear deformation theory for functionally graded plates
Nabil Hebbar,Mohamed Bourada,Mohamed Sekkal,Abdelouahed Tounsi,S. R. Mahmoud 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.27 No.5
In this article a four unknown quasi-3D shear deformation theory for the bending analysis of functionally graded (FG) plates is developed. The advantage of this theory is that, in addition to introducing the thickness stretching impact (<i>ε<sub>z</sub></i> ≠ 0), the displacement field is modeled with only four variables, which is even less than the first order shear deformation theory (FSDT). The principle of virtual work is utilized to determine the governing equations. The obtained numerical results from the proposed theory are compared with the CPT, FSDT, and other quasi-3D HSDTs.
Karima Bakhti,Mohamed Sekkal,E.A. Adda Bedia,Abdelouahed Tounsi 국제구조공학회 2020 Smart Structures and Systems, An International Jou Vol.25 No.4
In this study, a simple two-dimensional shear deformation model is employed for buckling analysis of functionally graded (FG) plates. The proposed theory has a kinematic with integral terms which considers the influence of shear deformation without using "shear correction factors". The impact of varying material properties and volume fraction of the constituent on buckling response of the FG plate is examined and discussed. The benefit of this theory over other contributions is that a number of variables is reduced. The basic equations that consider the influence of transverse shear stresses are derived from the principle of virtual displacements. The analytical solutions are obtained utilizing the "Navier method". The accuracy of the proposed theory is proved by comparisons with the different solutions found in the literature.
Bending analysis of functionally graded thick plates with in-plane stiffness variation
Ali Mazari,Amina Attia,Mohamed Sekkal,Abdelhakim Kaci,Abdelouahed Tounsi,Abdelmoumen Anis Bousahla,S. R. Mahmoud 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.68 No.4
In the present paper, functionally graded (FG) materials are presented to investigate the bending analysis of simply supported plates. It is assumed that the material properties of the plate vary through their length according to the power-law form. The displacement field of the present model is selected based on quasi-3D hyperbolic shear deformation theory. By splitting the deflection into bending, shear and stretching parts, the number of unknowns and equations of motion of the present formulation is reduced and hence makes them simple to use. Governing equations are derived from the principle of virtual displacements. Numerical results for deflections and stresses of powerly graded plates under simply supported boundary conditions are presented. The accuracy of the present formulation is demonstrated by comparing the computed results with those available in the literature. As conclusion, this theory is as accurate as other shear deformation theories and so it becomes more attractive due to smaller number of unknowns. Some numerical results are provided to examine the effects of the material gradation, shear deformation on the static behavior of FG plates with variation of material stiffness through their length.
An original single variable shear deformation theory for buckling analysis of thick isotropic plates
Faiza Klouche,Lamia Darcherif,Mohamed Sekkal,Abdelouahed Tounsi,S.R. Mahmoud 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.63 No.4
This work proposes an original single variable shear deformation theory to study the buckling analysis of thick isotropic plates subjected to uniaxial and biaxial in-plane loads. This theory is built upon the classical plate theory (CPT) including the exponential function in terms of thickness coordinate to represent shear deformation effect and it involves only one governing differential equation. Efficacy of the present theory is confirmed through illustrative numerical examples. The obtained results are compared with those of other higher-order shear deformation plate theory results.
Abdeljalil Meksi,Samir Benyoucef,Mohamed Sekkal,Rabbab Bachir Bouiadjra,Mahmoud M. Selim,Abdelouahed Tounsi,Muzamal Hussain 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.39 No.2
This paper investigates the effect of micromechanical models on the bending behavior of bidirectional functionally graded (BDFG) beams subjected to different mechanical loading. The material properties of the beam are considered to be graded in both axial and thickness directions according to a power law. The beam’s behavior is modeled by the mean of quasi 3D displacement field that contain undetermined integral terms and involves a reduced unknown functions. Navier’s method is employed to determine and compute the displacements and stress for a simply supported beam. Different homogenization schemes such as Voigt, Reus, and Mori-Tanaka are employed to analyze the response of the BDFG beam subjected to linear, uniform, exponential and sinusoidal distributed loading. The results obtained by the present method are compared with available results in the literature and a good agreement was found. Several numerical results are presented in tabular form and in figures to examine the effects of the material gradation, micromechanical models and types of loading on the bending response of BDFG beams. It can be concluded that the present theory is not only accurate but also simple in predicting the bending response of BDFG beam subjected to different static loads.
An original single variable shear deformation theory for buckling analysis of thick isotropic plates
Klouche, Faiza,Darcherif, Lamia,Sekkal, Mohamed,Tounsi, Abdelouahed,Mahmoud, S.R. Techno-Press 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.63 No.4
This work proposes an original single variable shear deformation theory to study the buckling analysis of thick isotropic plates subjected to uniaxial and biaxial in-plane loads. This theory is built upon the classical plate theory (CPT) including the exponential function in terms of thickness coordinate to represent shear deformation effect and it involves only one governing differential equation. Efficacy of the present theory is confirmed through illustrative numerical examples. The obtained results are compared with those of other higher-order shear deformation plate theory results.
Bending analysis of functionally graded thick plates with in-plane stiffness variation
Mazari, Ali,Attia, Amina,Sekkal, Mohamed,Kaci, Abdelhakim,Tounsi, Abdelouahed,Bousahla, Abdelmoumen Anis,Mahmoud, S.R. 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.68 No.4
In the present paper, functionally graded (FG) materials are presented to investigate the bending analysis of simply supported plates. It is assumed that the material properties of the plate vary through their length according to the power-law form. The displacement field of the present model is selected based on quasi-3D hyperbolic shear deformation theory. By splitting the deflection into bending, shear and stretching parts, the number of unknowns and equations of motion of the present formulation is reduced and hence makes them simple to use. Governing equations are derived from the principle of virtual displacements. Numerical results for deflections and stresses of powerly graded plates under simply supported boundary conditions are presented. The accuracy of the present formulation is demonstrated by comparing the computed results with those available in the literature. As conclusion, this theory is as accurate as other shear deformation theories and so it becomes more attractive due to smaller number of unknowns. Some numerical results are provided to examine the effects of the material gradation, shear deformation on the static behavior of FG plates with variation of material stiffness through their length.