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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.
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.
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.
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.
Rabbab Bachir Bouiadjra,Abdelkader Mahmoudi,Mohamed Sekkal,Samir Benyoucef,Mahmoud M. Selim,Abdelouahed Tounsi,Muzamal Hussain 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.41 No.6
In this paper, an analytical solution for thermodynamic response of functionally graded (FG) sandwich plates resting on variable elastic foundation is performed by using a quasi 3D shear deformation plate theory. The displacement field used in the present study contains undetermined integral terms and involves only four unknown functions with including stretching effect. The FG sandwich plate is considered to be subject to a time harmonic sinusoidal temperature field across its thickness with any combined boundary conditions. Equations of motion are derived from Hamilton’s principle. The numerical results are compared with the existing results of quasi-3D shear deformation theories and an excellent agreement is observed. Several numerical examples for fundamental frequency, deflection, stress and variable elastic foundation parameter’s analysis of FG sandwich plates are presented and discussed considering different material gradients, layer thickness ratios, thickness-to-length ratios and boundary conditions. The results of the present study reveal that the nature of the elastic foundation, the boundary conditions and the thermodynamic loading affect the response of the FG plate especially in the case of a thick plate.
Abdallah Zine,Abdelouahed Tounsi,Kada Draiche,Mohamed Sekkal,S. R. Mahmoud 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.26 No.2
In this work, the bending and free vibration analysis of multilayered plates and shells is presented by utilizing a new higher order shear deformation theory (HSDT). The proposed involves only four unknowns, which is even less than the first shear deformation theory (FSDT) and without requiring the shear correction coefficient. Unlike the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral variables. The equations of motion are derived by using the Hamilton's principle. These equations are then solved via Navier-type, closed form solutions. Bending and vibration results are found for cylindrical and spherical shells and plates for simply supported boundary conditions. Bending and vibration problems are treated as individual cases. Panels are subjected to sinusoidal, distributed and point loads. Results are presented for thick to thin as well as shallow and deep shells. The computed results are compared with the exact 3D elasticity theory and with several other conventional HSDTs. The proposed HSDT is found to be precise compared to other several existing ones for investigating the static and dynamic response of isotropic and multilayered composite shell and plate structures.
Lynda Amel Chaabane,Fouad Bourada,Mohamed Sekkal,Sara Zerouati,Fatima Zohra Zaoui,Abdeldjebbar Tounsi,Abdelhak Derras,Abdelmoumen Anis Bousahla,Abdelouahed Tounsi 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.71 No.2
In this investigation, study of the static and dynamic behaviors of functionally graded beams (FGB) is presented using ahyperbolic shear deformation theory (HySDT). The simply supported FG-beam is resting on the elastic foundation (Winkler-Pasternak types). The properties of the FG-beam vary according to exponential (E-FGB) and power-law (P-FGB) distributions. Thegoverning equations are determined via Hamilton’s principle and solved by using Navier’s method. To show the accuracy of thismodel (HySDT), the current results are compared with those available in the literature. Also, various numerical results are discussedto show the influence of the variation of the volume fraction of the materials, the power index, the slenderness ratio and the effect ofWinkler spring constant on the fundamental frequency, center deflection, normal and shear stress of FG-beam.
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.