Effect of tapered-end shape of FRP sheets on stress concentration in strengthened beams under thermal load

Benaoumeur El Mahi,Kouider Halim Benrahou,Sofiane Amziane,Khalil Belakhdar,Abdelouahed Tounsi,El Abbes Adda Bedia 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.17 No.5

Repairing and strengthening structural members by bonding composite materials have received a considerable attention in recent years. The major problem when using bonded FRP or steel plates to strengthen existing structures is the high interfacial stresses that may be built up near the plate ends which lead to premature failure of the structure. As a result, many researchers have developed several analytical methods to predict the interface performance of bonded repairs under various types of loading. In this paper, a numerical solution using finite . difference method (FDM) is used to calculate the interfacial stress distribution in beams strengthened with FRP plate having a tapered ends under thermal loading. Different thinning profiles are investigated since the later can significantly reduce the stress concentration. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both beam and bonded plate. The shear correction factor for I-section beams is also included in the solution. Numerical results from the present analysis are presented to demonstrate the advantages of use the tapers in design of strengthened beams.

Analyse of the behavior of functionally graded beams based on neutral surface position

Lazreg Hadji,El Abbes Adda Bedia 국제구조공학회 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.55 No.4

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.

A New Higher Order Shear Deformation Model for Functionally Graded Beams

Lazreg Hadji,Zoubida Khelifa,Adda Bedia El Abbes 대한토목학회 2016 KSCE JOURNAL OF CIVIL ENGINEERING Vol.20 No.5

In this paper, a new higher order shear deformation model 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. 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.

Effect of tapered-end shape of FRP sheetson stress concentration in strengthened beams

Khalil Belakhdar,Abdelouahed Tounsi,El Abbes Adda Bedia,Yeghnem Redha 국제구조공학회 2011 Steel and Composite Structures, An International J Vol.11 No.6

Bonding composite materials to structural members for strengthening purpose has received a considerable attention in recent years. The major problem when using bonded FRP or steel plates to strengthen existing structures is the high interfacial stresses that may be built up near the plate ends which lead to premature failure of the structure. As a result, many researchers have developed several analytical methods to predict the interface performance of bonded repairs. In this paper, a numerical solution using finite - differencemethod is used to calculate the interfacial stress distribution in beams strengthened with FRP plate having a tapered ends with different thinning profiles. These latter, can significantly reduce the stress concentration. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both beam and bonded plate. Numerical results from the present analysis are presented to demonstrate the advantages of use the tapers in design of strengthened beams.

A New Trigonometric Shear Deformation Theory for Bending Analysis of Functionally Graded Plates Resting on Elastic Foundations

Mohammed Ameur,Abdelouahed Tounsi,Ismail Mechab,El Abbes Adda Bedia 대한토목학회 2011 KSCE JOURNAL OF CIVIL ENGINEERING Vol.15 No.8

A new trigonometric shear deformation plate theory involving only four unknown functions, as against five functions in case of other shear deformation theories, is developed for flexural analysis of Functionally Graded Material (FGM) plates resting on an elastic foundation. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects,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. In the analysis, the two-parameter Pasternak and Winkler foundations are considered. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Governing equations are derived from the principle of virtual displacements. The accuracy of the present theory is demonstrated by comparing the results with solutions derived from other higher-order models found in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded plates.

Nonlinear cylindrical bending analysis of E-FGM plateswith variable thickness

Abdelhakim Kaci,Khalil Belakhdar,Abdelouahed Tounsi,El Abbes Adda Bedia 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.16 No.4

This paper presents a study of the nonlinear cylindrical bending of an exponential functionally graded plate (simply called E-FG) with variable thickness. The plate is subjected to uniform pressure loading and his geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of functionally graded plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution; and the solution is obtained using Hamilton's principle for constant plate thickness. In order to analyze functionally graded plate with variable thickness, a numerical solution using finite difference method is used, where parabolic variation of the plate thickness is studied. The results for E-FG plates are given in dimensionless graphical forms; and the effects of material and geometric properties on displacements and normal stresses through the thickness are determined.

Mechanical and hygrothermal behaviour of functionally graded plates using a hyperbolic shear deformation theory

Imene Laoufi,Mohammed Ameur,Mohamed Zidi,El Abbes Adda Bedia,Abdelmoumen Anis Bousahla 국제구조공학회 2016 Steel and Composite Structures, An International J Vol.20 No.4

Using the hyperbolic shear deformation plate model and including plate-foundation interaction (Winkler and Pasternak model), an analytical method in order to determine the deflection and stress distributions in simply supported rectangular functionally graded plates (FGP) subjected to a sinusoidal load, a temperature and moisture fields. The present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. Materials properties of the plate (elastic, thermal and moisture expansion coefficients) are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Numerical examples are presented and discussed for verifying the accuracy of the present theory in predicting the bending response of FGM plates under sinusoidal load and a temperature field as well as moisture concentration. The effects of material properties, temperature, moisture, plate aspect ratio, side-to-thickness ratio, ratio of elastic coefficients (ceramic-metal) and three distributions for both temperature and moisture on deflections and stresses are investigated.

Numerical analysis of FGM plates with variable thickness subjected to thermal buckling

Otbi Bouguenina,Khalil Belakhdar,Abdelouahed Tounsi,El Abbes Adda Bedia 국제구조공학회 2015 Steel and Composite Structures, An International J Vol.19 No.3

A numerical solution using finite difference method to evaluate the thermal buckling of simply supported FGM plate with variable thickness is presented in this research. First, the governing differential equation of thermal stability under uniform temperature through the plate thickness is derived. Then, the governing equation has been solved using finite difference method. After validating the presented numerical method with the analytical solution, the finite difference formulation has been extended in order to include variable thickness. The accuracy of the finite difference method for variable thickness plate has been also compared with the literature where a good agreement has been found. Furthermore, a parametric study has been conducted to analyze the effect of material and geometric parameters on the thermal buckling resistance of the FGM plates. It was found that the thickness variation affects isotropic plates a bit more than FGM plates.

A new and simple HSDT for isotropic and functionally graded sandwich plates

Hafida Driz,Mamia Benchohr,Ahmed Bakora,Abdelkader Benachour,Abdelouahed Tounsi,El Abbes Adda Bedia 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.26 No.4

A novel higher shear deformation theory (HSDT) is proposed for the bending, buckling and free vibration investigations of isotropic and functionally graded (FG) sandwich plates. It contains only four variables, which is even less than the first shear deformation theory (FSDT) and the conventional HSDTs. The model accounts for a parabolic variation of transverse shear stress, respects the traction free boundary conditions and contrary to the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral terms. Equations of motion determined in this work are applied for three types of FG structures: FG plates, sandwich plates with FG core and sandwich plates with FG faces. Analytical solutions are given to predict the transverse displacements, stresses, critical buckling forces and natural frequencies of simply supported plates and a comparison study is carried out to demonstrate the accuracy of the proposed model.

A novel first-order shear deformation theory for laminated composite plates

Mohamed Sadoune,Abdelouahed Tounsi,Mohammed Sid Ahmed Houari,El Abbes Adda Bedia 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.17 No.3

In the present study, a new simple first-order shear deformation theory is presented for laminated composite plates. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher-order shear deformation theories. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions of simply supported antisymmetric cross-ply and angle-ply laminates are obtained and the results are compared with the exact three-dimensional (3D) solutions and those predicted by existing theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of laminated composite plates.