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A. Fekrar,A. Tounsi,N. El Meiche,A. Bessaim,E. A. Adda Bedia 국제구조공학회 2012 Steel and Composite Structures, An International J Vol.13 No.1
In this research, mechanical buckling of hybrid functionally graded plates is considered using a new four variable refined plate theory. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, 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 plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. The effectiveness of the theories is brought out through illustrative examples.
Abdelbari, Salima,Fekrar, Abdelkader,Heireche, Houari,Said, Hayat,Tounsi, Abdelouahed,Adda Bedia, E.A. Techno-Press 2016 Wind and Structures, An International Journal (WAS Vol.22 No.3
This work presents a simple hyperbolic shear deformation theory for analysis of functionally graded plates resting on elastic foundation. The proposed model contains fewer number of unknowns and equations of motion than the first-order shear deformation model, but the transverse shear stresses account for a hyperbolic variation and respect the tangential stress-free boundary conditions on the plate boundary surface without introducing shear correction factors. Equations of motion are obtained from Hamilton's principle. The Navier-type analytical solutions for simply-supported plates are compared with the existing solutions to demonstrate the accuracy of the proposed theory.
Salima Abdelbari,Abdelkader Fekrar,Houari Heireche,Hayat Saidi,Abdelouahed Tounsi,E.A Adda Bedia 한국풍공학회 2016 Wind and Structures, An International Journal (WAS Vol.22 No.3
This work presents a simple hyperbolic shear deformation theory for analysis of functionally graded plates resting on elastic foundation. The proposed model contains fewer number of unknowns and equations of motion than the first-order shear deformation model, but the transverse shear stresses account for a hyperbolic variation and respect the tangential stress-free boundary conditions on the plate boundary surface without introducing shear correction factors. Equations of motion are obtained from Hamilton`s principle. The Navier-type analytical solutions for simply-supported plates are compared with the existing solutions to demonstrate the accuracy of the proposed theory.
Issad, Mohammed Naim,Fekrar, Abdelkader,Bakora, Ahmed,Bessaim, Aicha,Tounsi, Abdelouahed Techno-Press 2018 Geomechanics & engineering Vol.15 No.1
The present work presents a free vibration and buckling analysis of orthotropic plates by proposing a novel two variable refined plate theory. Contrary to the conventional higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed theory utilizes a novel displacement field which incorporates undetermined integral terms and involves only two unknowns. The governing equations are obtained from the dynamic version of principle of virtual works. The analytical solution of a simply supported orthotropic plate has been determined by using the Navier method. Numerical investigations are performed by employing the proposed model and the obtained results are compared with the existing HSDTs.
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.
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 new quasi-3D theory for the study of the bending of thick FGM’s plates on elastic foundation
Abdelghani Belarouci,Abdelkader Fekrar 국제구조공학회 2021 Smart Structures and Systems, An International Jou Vol.27 No.5
In this work, a new theory quasi-3D shear deformation is presented to analyze the bending of thick FGM (functionally graded materials) plates resting on Pasternak elastic foundations, whose number of variables is limited to five. The mathematical model used presents a new range of displacement based on indeterminate integral variables where the stretching of thickness is taken into account according to the power laws P-FGM, E-FGM and S-FGM. The compositions and volume fractions of the constituents in the FGM are supposed to change through the thickness. The principle of virtual work, as well as the Naiver method, is used in this study to solve the governing equations of motion to study these types of plates. The equilibrium equations according to the FG plate resting on Pasternak foundations are presented. The results obtained are compared to those determined by the other authors. It was observed from the comparative studies that quasi-3D theories that take into account thickness stretching effects can predict bending behavior more accurately than other theories.