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Bouiadjra, Rabbab Bachir,Mahmoudi, Abdelkader,Benyoucef, Samir,Tounsi, Abdelouahed,Bernard, Fabrice Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.66 No.3
In this paper, a new refined quasi-three-dimensional (3D) shear deformation theory for the bending analysis of functionally graded plate is presented. The number of unknown functions involved in this theory is only four against five or more in the case of the other shear and normal deformation theories. Due to its quasi-3D nature, the stretching effect is taken into account in the formulation of governing equations. In addition, the effect of different micromechanical models on the bending response of these plates is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG plates whose properties vary continuously across the thickness according to a simple power law. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of displacements across the thickness, and the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The problem is solved for a plate simply supported on its edges and the Navier solution is used. The results of the present method are compared with others from the literature where a good agreement has been found. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG plates.
Bouiadjra, Rabbab Bachir,Bedia, E.A. Adda,Tounsi, Abdelouahed Techno-Press 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.48 No.4
Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The non-linear strain-displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.
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.
Rabbab Bachir Bouiadjra,Abdelkader Mahmoudi,Samir Benyoucef,Abdelouahed Tounsi,Fabrice Bernard 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.66 No.3
In this paper, a new refined quasi-three-dimensional (3D) shear deformation theory for the bending analysis of functionally graded plate is presented. The number of unknown functions involved in this theory is only four against five or more in the case of the other shear and normal deformation theories. Due to its quasi-3D nature, the stretching effect is taken into account in the formulation of governing equations. In addition, the effect of different micromechanical models on the bending response of these plates is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG plates whose properties vary continuously across the thickness according to a simple power law. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of displacements across the thickness, and the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The problem is solved for a plate simply supported on its edges and the Navier solution is used. The results of the present method are compared with others from the literature where a good agreement has been found. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG plates.
Rabbab Bachir Bouiadjra,E.A. Adda Bedia,Abdelouahed Tounsi 국제구조공학회 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.48 No.4
Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The non-linear strain–displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.
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.
Elastic-plastic analysis of the J integral for repaired cracks in plates
Salem, Mokadem,Bouiadjra, Belabbes Bachir,Mechab, Belaid,Kaddouri, Khacem Techno-Press 2015 Advances in materials research Vol.4 No.2
In this paper, three-dimensional finite element method is used to analyze the J integral for repaired cracks in plates with bonded composite patch and stiffeners. For elastic the effect of cracks, the thickness of the patch ($e_r$) and properties of the patch are presented for calculating the J integral. For elastic-plastic a several calculations have been realized to extract the plasticized elements around the crack tip of repaired and un-repaired crack. The obtained results show that the presence of the composite patch and stiffener reduces considerably the size of the plastic zone ahead of the crack. The effects of crack size and the inter-distance of repaired cracks were analysed.
Hygro-thermo-mechanical bending analysis of FGM plates using a new HSDT
Boukhelf, Fouad,Bouiadjra, Mohamed Bachir,Bouremana, Mohammed,Tounsi, Abdelouahed Techno-Press 2018 Smart Structures and Systems, An International Jou Vol.21 No.1
In this paper, a novel higher-order shear deformation theory (HSDT) is proposed for the analysis of the hygro-thermo-mechanical behavior of functionally graded (FG) plates resting on elastic foundations. The developed model uses a novel kinematic by considering undetermined integral terms and only four variables are used in this model. The governing equations are deduced based on the principle of virtual work and the number of unknown functions involved is reduced to only four, which is less than the first shear deformation theory (FSDT) and others HSDTs. The Navier-type exact solutions for static analysis of simply supported FG plates subjected to hygro-thermo-mechanical loads are presented. The accuracy and efficiency of the present model is validated by comparing it with various available solutions in the literature. The influences of material properties, temperature, moisture, plate aspect ratio, side-to-thickness ratios and elastic coefficients parameters on deflections and stresses of FG plates are also investigated.
Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation
Bakhadda, Boumediene,Bouiadjra, Mohamed Bachir,Bourada, Fouad,Bousahla, Abdelmoumen Anis,Tounsi, Abdelouahed,Mahmoud, S.R. Techno-Press 2018 Wind and Structures, An International Journal (WAS Vol.27 No.5
This work examines vibration and bending response of carbon nanotube-reinforced composite plates resting on the Pasternak elastic foundation. Four types of distributions of uni-axially aligned single-walled carbon nanotubes are considered to reinforce the plates. Analytical solutions determined from mathematical formulation based on hyperbolic shear deformation plate theory are presented in this study. An accuracy of the proposed theory is validated numerically by comparing the obtained results with some available ones in the literature. Various considerable parameters of carbon nanotube volume fraction, spring constant factors, plate thickness and aspect ratios, etc. are considered in the present investigation. According to the numerical examples, it is revealed that the vertical displacement of the plates is found to diminish as the increase of foundation parameters; while, the natural frequency increase as the increment of the parameters for every type of plate.
Numerical modeless of the damage, around inclusion in the orthopedic cement PMMA
Cherfi Mohamed,Benbarek Smail,Bachir Bouiadjra,B. Serier 국제구조공학회 2016 Structural Engineering and Mechanics, An Int'l Jou Vol.57 No.4
In orthopedic surgery and more especially in total arthroplastie of hip, the fixing of the implants generally takes place essentially by means of constituted surgical polymer cement. The damage of this materiel led to the fatal rupture and thus loosening of the prosthesis in total hip, the effect of over loading as the case of tripping of the patient during walking is one of the parameters that led to the damage of this binder. From this phenomenon we supposed that a remain of bone is included in the cement implantation. The object of this work is to study the effect of this bony inclusion in the zones where the outside conditions (loads and geometric shapes) can provoke the fracture of the cement and therefore the aseptic lousing of the prosthesis. In this study it was assumed the presence of two bones –type inclusions in this material, one after we analyzed the effect of interaction between these two inclusions damage of damage to this material. One have modeled the damage in the cement around this bone inclusion and estimate the crack length from the damaged cement zone in the acetabulum using the finite element method, for every position of the implant under the extreme effort undergone by the prosthesis. We noted that the most intense stress position is around the sharp corner of the bone fragment and the higher level of damage leads directly the fracture of the total prosthesis of the hip.