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Fahsi, Asmaa,Tounsi, Abdelouahed,Hebali, Habib,Chikh, Abdelbaki,Adda Bedia, E.A.,Mahmoud, S.R. Techno-Press 2017 Geomechanics & engineering Vol.13 No.3
This work presents a simple and refined nth-order shear deformation theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on elastic foundation. The proposed refined nth-order shear deformation theory has a new displacement field which includes undetermined integral terms and contains only four unknowns. Governing equations are obtained from the principle of minimum total potential energy. A Navier type analytical solution methodology is also presented for simply supported FG plates resting on elastic foundation which predicts accurate solution. The accuracy of the present model is checked by comparing the computed results with those obtained by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed theory can achieve the same accuracy of the existing HSDTs which have more number of variables.
Bouazza Fahsi,Abdelhakim Kaci,Abdelouahed Tounsi,El Abbas Adda Bedia 대한기계학회 2012 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.26 No.12
In this paper we present a new application for a four variable refined plate theory to analyse the nonlinear cylindrical bending behavior of functionally graded plates subjected to thermomechanical loadings. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and,likewise, the shear components do not contribute toward bending moments. 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 material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The non-linear strain–displacement relations in the von Karman sense are used to study the effect of geometric non-linearity. The solutions are achieved by minimizing the total potential energy and the results are compared to the classical and the first-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the nonlinear cylindrical bending behavior of functionally graded plates.
Abdlillah Benahmed,Bouazza Fahsi,Abdelnour Benzair,Mohamed Zidour,Fouad Bourada,Abdelouahed Tounsi 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.69 No.4
This paper presents an efficient higher-order nonlocal beam theory for the Critical buckling, of functionally graded (FG) nanobeams with porosities that may possibly occur inside the functionally graded materials (FG) during their fabrication, the nonlocal elastic behavior is described by the differential constitutive model of Eringen. The material properties of (FG) nanobeams with porosities are assumed to vary through the thickness according to a power law. The governing equations of the functionally graded nanobeams with porosities are derived by employing Hamilton’s principle. Analytical solutions are presented for a simply supported FG nanobeam with porosities. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, Illustrative examples are given also to show the effects of porosity volume fraction, and thickness to length ratios on the critical buckling of the FG beams.
Yahiaoui, Mohammed,Tounsi, Abdelouahed,Fahsi, Bouazza,Bouiadjra, Rabbab Bachir,Benyoucef, Samir Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.68 No.1
This paper presents an analysis of the bending, buckling and free vibration of functionally graded sandwich beams resting on elastic foundation by using a refined quasi-3D theory in which both shear deformation and thickness stretching effects are included. The displacement field contains only three unknowns, which is less than the number of parameters of many other shear deformation theories. In order to homogenize the micromechanical properties of the FGM sandwich beam, the material properties are derived on the basis of several micromechanical models such as Tamura, Voigt, Reuss and many others. The principle of virtual works is used to obtain the equilibrium equations. The elastic foundation is modeled using the Pasternak mathematical model. The governing equations are obtained through the Hamilton's principle and then are solved via Navier solution for the simply supported beam. The accuracy of the proposed theory can be noticed by comparing it with other 3D solution available in the literature. A detailed parametric study is presented to show the influence of the micromechanical models on the general behavior of FG sandwich beams on elastic foundation.
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.
Mohammed Yahiaoui,Abdelouahed Tounsi,Bouazza Fahsi,Rabbab Bachir Bouiadjra,Samir Benyoucef 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.68 No.1
This paper presents an analysis of the bending, buckling and free vibration of functionally graded sandwich beams resting on elastic foundation by using a refined quasi-3D theory in which both shear deformation and thickness stretching effects are included. The displacement field contains only three unknowns, which is less than the number of parameters of many other shear deformation theories. In order to homogenize the micromechanical properties of the FGM sandwich beam, the material properties are derived on the basis of several micromechanical models such as Tamura, Voigt, Reuss and many others. The principle of virtual works is used to obtain the equilibrium equations. The elastic foundation is modeled using the Pasternak mathematical model. The governing equations are obtained through the Hamilton’s principle and then are solved via Navier solution for the simply supported beam. The accuracy of the proposed theory can be noticed by comparing it with other 3D solution available in the literature. A detailed parametric study is presented to show the influence of the micromechanical models on the general behavior of FG sandwich beams on elastic foundation.
Tahar Hacen Lamine Bekkaye,Bouazza Fahsi,Abdelmoumen Anis Bousahla,Fouad Bourada,Abdeldjebbar Tounsi,Kouider Halim Benrahou,Abdelouahed Tounsi,Mesfer Mohammad Al-Zahrani 사단법인 한국계산역학회 2020 Computers and Concrete, An International Journal Vol.26 No.5
In this research, bending and buckling analyses of porous functionally graded (FG) plate under mechanical load are presented. The properties of the FG plate vary gradually across the thickness according to power-law and exponential functions. The material imperfection is considered to vary depending to a logarithmic function. The plate is modeled by a refined trigonometric shear deformation theory where the use of the shear correction factor is unnecessary. The governing equations of the FG plate are derived via virtual work principle and resolved via Navier solutions. The accuracy of the present model is checked by comparing the obtained results with those found in the literature. The various effects influencing the stresses, displacements and critical buckling loads of the plate are also examined and discussed in detail.
An investigation of the thermodynamic effect on the response of FG beam on elastic foundation
Rabbab Bachir Bouiadjra,Attia Bachiri,Samir Benyoucef,Bouazza Fahsi,Fabrice Bernard 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.76 No.1
This study presents an analytical approach to investigate the thermodynamic behavior of functionally graded beam resting on elastic foundations. The formulation is based on a refined deformation theory taking into consideration the stretching effect and the type of elastic foundation. The displacement field used in the present refined theory contains undetermined integral forms and involves only three unknowns to derive. The mechanical characteristics of the beam are assumed to be varied across the thickness according to a simple exponential law distribution. The beam is supposed simply supported and therefore the Navier solution is used to derive analytical solution. Verification examples demonstrate that the developed theory is very accurate in describing the response of FG beams subjected to thermodynamic loading. Numerical results are carried out to show the effects of the thermodynamic loading on the response of FG beams resting on elastic foundation.