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 generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells

Othmane Allam,Kada Draiche,Abdelmoumen Anis Bousahla,Fouad Bourada,Abdeldjebbar Tounsi,Kouider Halim Benrahou,S.R. Mahmoud,E.A. Adda Bedia,Abdelouahed Tounsi 사단법인 한국계산역학회 2020 Computers and Concrete, An International Journal Vol.26 No.2

This research is devoted to investigate the bending and free vibration behaviour of laminated composite/sandwich plates and shells, by applying an analytical model based on a generalized and simple refined higher-order shear deformation theory (RHSDT) with four independent unknown variables. The kinematics of the proposed theoretical model is defined by an undetermined integral component and uses the hyperbolic shape function to include the effects of the transverse shear stresses through the plate/shell thickness; hence a shear correction factor is not required. The governing differential equations and associated boundary conditions are derived by employing the principle of virtual work and solved via Navier-type analytical procedure. To verify the validity and applicability of the present refined theory, some numerical results related to displacements, stresses and fundamental frequencies of simply supported laminated composite/sandwich plates and shells are presented and compared with those obtained by other shear deformation models considered in this paper. From the analysis, it can be concluded that the kinematics based on the undetermined integral component is very efficient, and its use leads to reach higher accuracy than conventional models in the study of laminated plates and shells.

On transverse matrix cracking in composite laminates loaded in flexure under transient hygrothermal conditions

M. Khodjet-Kesba,A. Benkhedda,E. A. Adda Bedia,B. Boukert 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.67 No.2

A simple predicted model using a modified Shear-lag method was used to represent the moisture absorption effect on the stiffness degradation for [0/90]2s composite laminates with transverse cracks and under flexural loading. Good agreement is obtained by comparing the prediction model and experimental data published by Smith and Ogin (2000). The material properties of the composite are affected by the variation of temperature and moisture absorption. The transient and non-uniform moisture concentration distribution give rise to the transient elastic moduli of cracked composite laminates. The hygrothermal effect is taken into account to assess the changes in the normalised axial and flexural modulus due to transverse crack. The obtained results represent well the dependence of the stiffness properties degradation on the cracks density, moisture absorption and operational temperature. The composite laminate with transverse crack loaded in axial tension is more affected by the hygrothermal condition than the one under flexural loading. Through this theoretical study, we hope to contribute to the understanding of the moisture absorption on the composite materials with matrix cracking.

A higher order shear deformation theory for static and free vibration of FGM beam

L. Hadji,T.H. Daouadji,A. Tounsi,E.A. Bedia 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.16 No.5

In this paper, a higher order shear deformation beam theory is developed for static and free vibration analysis of functionally graded beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present higher-order shear deformation beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Different higher order shear deformation theories and classical beam theories were used in the analysis. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

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 n-order refined theory for bending and free vibration of functionally graded beams

Lazreg Hadji,T. Hassaine Daouadji,A. Tounsi,E.A. Bedia 국제구조공학회 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.54 No.5

In this paper, a simple n-order refined theory based on neutral surface position is developed for bending and frees vibration analyses of functionally graded beams. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, 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 governing equations are derived by employing the Hamilton’s principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.

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.

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.

On transverse matrix cracking in composite laminates loaded in flexure under transient hygrothermal conditions

Khodjet-Kesba, M.,Benkhedda, A.,Adda Bedia, E.A.,Boukert, B. Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.67 No.2

A simple predicted model using a modified Shear-lag method was used to represent the moisture absorption effect on the stiffness degradation for $[0/90]_{2s}$ composite laminates with transverse cracks and under flexural loading. Good agreement is obtained by comparing the prediction model and experimental data published by Smith and Ogin (2000). The material properties of the composite are affected by the variation of temperature and moisture absorption. The transient and non-uniform moisture concentration distribution give rise to the transient elastic moduli of cracked composite laminates. The hygrothermal effect is taken into account to assess the changes in the normalised axial and flexural modulus due to transverse crack. The obtained results represent well the dependence of the stiffness properties degradation on the cracks density, moisture absorption and operational temperature. The composite laminate with transverse crack loaded in axial tension is more affected by the hygrothermal condition than the one under flexural loading. Through this theoretical study, we hope to contribute to the understanding of the moisture absorption on the composite materials with matrix cracking.