EXISTENCE AND MULTIPLICITY OF SOLUTIONS OF p(x)-TRIHARMONIC PROBLEM

Adnane Belakhdar,Hassan Belaouidel,Mohammed Filali,Najib Tsouli 경남대학교 기초과학연구소 2022 Nonlinear Functional Analysis and Applications Vol.27 No.2

We prove the existence and nonexistence of eigenvalues for p(x)-triharmonic problem with Navier boundary value conditions on a bounded domain in ℝ^N. Our technique is based on variational approaches and the theory of variable exponent Lebesgue spaces

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.

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.

Thermal buckling resistance of simply supported FGM plates with parabolic-concave thickness variation

Fouad Benlahcen,Khalil Belakhdar,Mohammed Sellami,Abdelouahed Tounsi 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.29 No.5

This research presents an investigation on the thermal buckling resistance of FGM plates having parabolic-concave thickness variation exposed to uniform and gradient temperature change. An analytical formulation is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. A specific function of thickness variation is introduced where it controls the parabolic variation intensity of the thickness without changing the original material volume. The results indicated that the loss ratio in buckling resistance is the same for any gradient temperature profile. Influencing geometrical and material parameters on the loss ratio in the thermal resistance buckling are investigated which may help in design guidelines of such complex structures.

Thermal buckling of FGM beams having parabolic thickness variation and temperature dependent materials

Othman Arioui,Khalil Belakhdar,Abdelhakim Kaci,Abdelouahed Tounsi 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.27 No.6

An investigation on the thermal buckling resistance of simply supported FGM beams having parabolic-concave thickness variation and temperature dependent material properties is presented in this paper. An analytical formulation based on the first order beam theory is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. a function of thickness variation is introduced which controls the parabolic variation intensity of the beam thickness without changing its original material volume. The results showed the high importance of taking into account the temperature-dependent material properties in the thermal buckling analysis of such critical beam sections. Different Influencing parametric on the thermal stability are studied which may help in design guidelines of such complex structures.

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.

Nonlinear finite element analysis of high strength concrete slabs

M. M. Smadi,K. A. Belakhdar 한국계산역학회 2007 Computers and Concrete, An International Journal Vol.4 No.3

A rational three-dimensional nonlinear finite element model is described and implemented for evaluating the behavior of high strength concrete slabs under transverse load. The concrete was idealized by using twenty-nodded isoparametric brick elements with embedded reinforcements. The concrete material modeling allows for normal (NSC) and high strength concrete (HSC), which was calibrated based on experimental data. The behavior of concrete in compression is simulated by an elastoplastic work-hardening model, and in tension a suitable post-cracking model based on tension stiffening and shear retention models are employed. The nonlinear equations have been solved using the incremental iterative technique based on the modified Newton-Raphson method. The FE formulation and material modeling is implemented into a finite element code in order to carry out the numerical study and to predict the behavior up to ultimate conditions of various slabs under transverse loads. The validity of the theoretical formulations and the program used was verified through comparison with available experimental data, and the agreement has proven to be very good. A parametric study has been also carried out to investigate the influence of different material and geometric properties on the behavior of HSC slabs. Influencing factors, such as concrete strength, steel ratio, aspect ratio, and support conditions on the load-deflection characteristics, concrete and steel stresses and strains were investigated.

Nonlinear thermoelastic analysis of FGM thick plates

Bouhlali, Malika,Chikh, Abdelbaki,Bouremana, Mohammed,Kaci, Abdelhakim,Bourada, Fouad,Belakhdar, Khalil,Tounsi, Abdelouahed Techno-Press 2019 Coupled systems mechanics Vol.8 No.5

In this paper, a new application of a four variable refined plate theory to analyze the nonlinear bending of functionally graded plates exposed to thermo-mechanical loadings, is presented. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces, and similarly, the shear components do not contribute toward bending moments. The derived transverse shear strains has a quadratic variation across the thickness that satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The solutions are achieved by minimizing the total potential energy. The non-linear strain-displacement relations in the von Karman sense are used to derive the effect of geometric non-linearity. It is concluded that the proposed theory is accurate and simple in solving the nonlinear bending behavior of functionally graded plates.

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.

A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation

Benahmed, Abdelkarim,Houari, Mohammed Sid Ahmed,Benyoucef, Samir,Belakhdar, Khalil,Tounsi, Abdelouahed Techno-Press 2017 Geomechanics & engineering Vol.12 No.1

In this work, an efficient and simple quasi-3D hyperbolic shear deformation theory is developed for bending and vibration analyses of functionally graded (FG) plates resting on two-parameter elastic foundation. The significant feature of this theory is that, in addition to including the thickness stretching effect, it deals with only 5 unknowns as the first order shear deformation theory (FSDT). The foundation is described by the Pasternak (two-parameter) model. The material 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. Equations of motion for thick FG plates are obtained within the Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The numerical results are given in detail and compared with the existing works such as 3-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates resting on elastic foundation.