A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates

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.

A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position

Merazi, M.,Hadji, L.,Daouadji, T.H.,Tounsi, Abdelouahed,Adda Bedia, E.A. Techno-Press 2015 Geomechanics & engineering Vol.8 No.3

In this paper, a new hyperbolic shear deformation plate theory based on neutral surface position is developed for the static analysis of functionally graded plates (FGPs). The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present new hyperbolic shear deformation plate theory and the neutral surface concept, the governing equations of equilibrium are derived from the principle of virtual displacements. Numerical illustrations concern flexural behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

Analyze of the interfacial stress in reinforced concrete beams strengthened with externally bonded CFRP plate

Lazreg Hadji,T. Hassaine Daouadji,M. Ait Amar Meziane,E. A. Adda Bedia 국제구조공학회 2016 Steel and Composite Structures, An International J Vol.20 No.2

A theoretical method to predict the interfacial stresses in the adhesive layer of reinforced concrete beams strengthened with externally bonded carbon fiber-reinforced polymer (CFRP) plate is presented. The analysis provides efficient calculations for both shear and normal interfacial stresses in reinforced concrete beams strengthened with composite plates, and accounts for various effects of Poisson's ratio and Young's modulus of adhesive. Such interfacial stresses play a fundamental role in the mechanics of plated beams, because they can produce a sudden and premature failure. The analysis is based on equilibrium and deformations compatibility approach developed by Tounsi. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both the reinforced concrete beam and bonded plate. The paper is concluded with a summary and recommendations for the design of the strengthened beam.

A new quasi-3D sinusoidal shear deformation theory for functionally graded plates

Mamia Benchohr,Hafida Driz,Ahmed Bakora,Abdelouahed Tounsi,E.A. Adda Bedia,S. R. Mahmoud 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.1

In this paper, a new quasi-3D sinusoidal shear deformation theory for functionally graded (FG) plates is proposed. The theory considers both shear deformation and thickness-stretching influences by a trigonometric distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower faces of the plate without employing any shear correction coefficient. The advantage of the proposed model is that it posses a smaller number of variables and governing equations than the existing quasi-3D models, but its results compare well with those of 3D and quasi-3D theories. This benefit is due to the use of undetermined integral unknowns in the displacement field of the present theory. By employing the Hamilton principle, equations of motion are obtained in the present formulation. Closed-form solutions for bending and free vibration problems are determined for simply supported plates. Numerical examples are proposed to check the accuracy of the developed theory.

Buckling analysis of functionally graded hybrid composite plates using a new four variable refined plate theory

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.

A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis

Miloud Kaddari,Abdelhakim Kaci,Abdelmoumen Anis Bousahla,Abdelouahed Tounsi,Fouad Bourada,AbdeldjebbarTounsi,E.A. Adda Bedia,Mohammed A. Al-Osta 사단법인 한국계산역학회 2020 Computers and Concrete, An International Journal Vol.25 No.1

This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.

A new quasi-3D sinusoidal shear deformation theory for functionally graded plates

Benchohra, Mamia,Driz, Hafida,Bakora, Ahmed,Tounsi, Abdelouahed,Adda Bedia, E.A.,Mahmoud, S.R. Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.1

In this paper, a new quasi-3D sinusoidal shear deformation theory for functionally graded (FG) plates is proposed. The theory considers both shear deformation and thickness-stretching influences by a trigonometric distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower faces of the plate without employing any shear correction coefficient. The advantage of the proposed model is that it posses a smaller number of variables and governing equations than the existing quasi-3D models, but its results compare well with those of 3D and quasi-3D theories. This benefit is due to the use of undetermined integral unknowns in the displacement field of the present theory. By employing the Hamilton principle, equations of motion are obtained in the present formulation. Closed-form solutions for bending and free vibration problems are determined for simply supported plates. Numerical examples are proposed to check the accuracy of the developed theory.

Dynamic behaviour of stiffened and damaged coupled shear walls

S. A. Meftah,A. Tounsi,E. A. Adda-Bedia 한국계산역학회 2006 Computers and Concrete, An International Journal Vol.3 No.5

The free vibration of stiffened and damaged coupled shear walls is investigated using the mixed finite element method. The anisotropic damage model is adopted to describe the damage extent of the reinforced concrete shear wall element. The internal energy of a locally damaged shear wall element is derived. Polynomial shape functions established by Kwan are used to present the component of displacements vector on each point within the wall element. The principle of virtual work is employed to deduce the stiffness matrix of a damaged shear wall element. The stiffened system is reinforced by an additional stiffening beam at some level of the structure. This induces additional axial forces, and thus reduces the bending moments in the walls and the lateral deflection, and increases the natural frequencies. The effects of the damage extent and the stiffening beam on the free vibration characteristics of the structure are studied. The optimal location of the stiffening beam for increasing as far as possible the first natural frequency of vibration is presented.

Large deformation analysis for functionally graded carbon nanotube-reinforced composite plates using an efficient and simple refined theory

K. Bakhti,A. Tounsi,A. Kaci,A.A. Bousahla,M.S.A. Houari,E. A. Adda Bedia 국제구조공학회 2013 Steel and Composite Structures, An International J Vol.14 No.4

In this paper, the nonlinear cylindrical bending behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) is studied using an efficient and simple refined theory. This theory is based on assumption that the in-plane and 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 material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The fundamental equations for functionally graded nanocomposite plates are obtained using the Von-Karman theory for large deflections and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtainedas comparators.

Improved analytical method for adhesive stresses in plated beam: Effect of shear deformation

Guenaneche, B.,Benyoucef, S.,Tounsi, A.,Adda Bedia, E.A. Techno-Press 2019 Advances in concrete construction Vol.7 No.3

This paper introduces a new efficient analytical method, based on shear deformations obtained with 2D elasticity theory approach, to perform an explicit closed-form solution for calculation the interfacial shear and normal stresses in plated RC beam. The materials of plate, necessary for the reinforcement of the beam, are in general made with fiber reinforced polymers (Carbon or Glass) or steel. The experimental tests showed that at the ends of the plate, high shear and normal stresses are developed, consequently a debonding phenomenon at this position produce a sudden failure of the soffit plate. The interfacial stresses play a significant role in understanding this premature debonding failure of such repaired structures. In order to efficiently model the calculation of the interfacial stresses we have integrated the effect of shear deformations using the equilibrium equations of the elasticity. The approach of this method includes stress-strain and strain-displacement relationships for the adhesive and adherends. The use of the stresses continuity conditions at interfaces between the adhesive and adherents, results pair of second-order and fourth-order coupled ordinary differential equations. The analytical solution for this coupled differential equations give new explicit closed-form solution including shear deformations effects. This new solution is indented for applications of all plated beam. Finally, numerical results obtained with this method are in agreement of the existing solutions and the experimental results.