Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory

Bachir Bouderba 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.27 No.3

This article presents the bending analysis of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment. Theoretical formulations are based on a recently developed refined shear deformation theory. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the plate. The present theory satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modeled as non-uniform foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermo-mechanical behavior of functionally graded plates. Numerical results show that the present theory can archive accuracy comparable to the existing higher order shear deformation theories that contain more number of unknowns.

Thermal stability of functionally graded sandwich plates using a simple shear deformation theory

Bachir Bouderba,Mohammed Sid Ahmed Houari,Abdelouahed Tounsi,S.R. Mahmoud 국제구조공학회 2016 Structural Engineering and Mechanics, An Int'l Jou Vol.58 No.3

In the present work, a simple first-order shear deformation theory is developed and validated for a variety of numerical examples of the thermal buckling response of functionally graded sandwich plates with various boundary conditions. Contrary to the conventional first-order shear deformation theory, the present first-order shear deformation theory involves only four unknowns and has strong similarities with the classical plate theory in many aspects such as governing equations of motion, and stress resultant expressions. Material properties and thermal expansion coefficient of the sandwich plate faces 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. The core layer is still homogeneous and made of an isotropic material. The thermal loads are considered as uniform, linear and non-linear temperature rises within the thickness direction. The results reveal that the volume fraction index, loading type and functionally graded layers thickness have significant influence on the thermal buckling of functionally graded sandwich plates. Moreover, numerical results prove that the present simple first-order shear deformation theory can achieve the same accuracy of the existing conventional first-order shear deformation theory which has more number of unknowns.

Some Properties of (y) Class Operators

Bachir, Ahmed,Mecheri, Salah Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.2

In this paper we study some spectral properties of the class (y) operators and we will investigate on the relation between this class and other usual classes of operators.

Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations

Bachir Bouderba,Mohammed Sid Ahmed Houari,Abdelouahed Tounsi 국제구조공학회 2013 Steel and Composite Structures, An International J Vol.14 No.1

The present work deals with the thermomechanical bending response of functionally graded plates resting on Winkler-Pasternak elastic foundations. Theoretical formulations are based on a recently developed refined trigonometric shear deformation theory (RTSDT). The theory accounts for trigonometric distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined trigonometric shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modelled as twoparameter Pasternak foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermomechanical behavior of functionally graded plates. It can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical bending response of functionally graded plates.

An Asymmetric Fuglede-Putnam’s Theorem and Orthogonality

AHMED, BACHIR,SEGRES, ABDELKDER 대한수학회 2006 Kyungpook mathematical journal Vol.46 No.4

An asymmetric Fuglede-Putnam theorem for p-hyponormal operators and class (y) is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.

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.

Initiation and propagation of a crack in the orthopedic cement of a THR using XFEM

Gasmi, Bachir,Abderrahmene, Sahli,Smail, Benbarek,Benaoumeur, Aour Techno-Press 2019 Advances in computational design Vol.4 No.3

The sealing cement of total hip arthroplasty is the most widely used binder in orthopedic surgery for anchoring implants to their recipient bones. Nevertheless, this latter remains a fragile material with weak mechanical properties. Inside this material cracks initiate from cavities. These cracks propagate under the effect of fatigue and lead to the failure of this binder and consequently the loosening of the prosthesis. In this context, this work consists to predict the position of cracks initiation and their propagations path using the Extended Finite Element Method (XFEM). The results show that cracks can only be initiated from a sharp edges of an ellipsoidal cavity which the ratio of the minor axis over the major axis is equal to 0.1. A maximum crack length of 19 ?m found for a cavity situated in the proximal zone position under a static loading. All cracks propagate in same(almost) way regardless of the cavity(site of initiation) position and its inclination in the proximal zone.

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.

Optimization of Phenolic Compound Recovery and Antioxidant Activity of Light and Dark Dried Fig (Ficus carica L.) Varieties

Mostapha Bachir Bey,Hayette Louaileche,Salima Zemouri 한국식품과학회 2013 Food Science and Biotechnology Vol.22 No.6

The optimum conditions for extraction of totalphenolic contents (TPC) and for enhancing the antioxidantactivity from light and dark dried figs were determined. The effects of the solvent nature (acetone, ethanol, methanol,or water), solvent concentration (20-80%), acetic acidconcentration (0-2%), extraction temperature (25-70oC),extraction time (0.5-4 h), sample to solvent ratio (1/25-1/100), and number of extractions (1, 2, and 3) weredetermined. The TPC was used to identify antioxidantcompounds. 2,2-diphenyl-1-picrylhydrazyl (DPPH) wasused to evaluate antioxidant activity. All extraction parametershad significant effects (p<0.05) on the TPC and theantioxidant activities. The best conditions were obtainedwith double extraction using 60% acetone withoutacidification, at 40oC for 120 min, and with a 1/75 solid tosolvent ratio. These conditions resulted in TPC concentrationsof 469.46 (light variety) and 399.79 mg of gallic acid(GAE)/100 g (dark variety), and antioxidant activities of96.47 and 102.28 mg of GAE/100 g, respectively.

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.