Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory

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.

Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models

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.

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.

A quasi 3D solution for thermodynamic response of FG sandwich plates lying on variable elastic foundation with arbitrary boundary conditions

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.

Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models

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.

Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory

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.

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.

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.

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.

A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates

Hafid Khetir,Mohamed Bachir Bouiadjra,Mohammed Sid Ahmed Houari,Abdelouahed Tounsi,S. R. Mahmoud 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.64 No.4

In this paper, a new nonlocal trigonometric shear deformation theory is proposed for thermal buckling response of nanosize functionally graded (FG) nano-plates resting on two-parameter elastic foundation under various types of thermal environments. This theory uses for the first time, undetermined integral variables and it contains only four unknowns, that is even less than the first shear deformation theory (FSDT). It is considered that the FG nano-plate is exposed to uniform, linear and sinusoidal temperature rises. Mori-Tanaka model is utilized to define the gradually variation of material properties along the plate thickness. Nonlocal elasticity theory of Eringen is employed to capture the size influences. Through the stationary potential energy the governing equations are derived for a refined nonlocal four-variable shear deformation plate theory and then solved analytically. A variety of examples is proposed to demonstrate the importance of elastic foundation parameters, various temperature fields, nonlocality, material composition, aspect and side-to-thickness ratios on critical stability temperatures of FG nano-plate.