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Commutation Relations for Operators
Ahmed Bachir,Ali A. Hashem 경북대학교 자연과학대학 수학과 2004 Kyungpook mathematical journal Vol.44 No.1
In this paper, we present a new class of finite operators and give an extension of the orthogonality results to certain finite operators, also we will generalize some commutativity results.
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.
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.
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.
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.
Positive answer to the conjecture by Fong and Istratescu
Salah Mecheri,Ahmed Bachir 대한수학회 2005 대한수학회보 Vol.42 No.4
In this note we give a positive answer to the conjectureby Fong and Istratescu.
POSITIVE ANSWER TO THE CONJECTURE BY FONG AND ISTRATESCU
MECHERI SALAH,BACHIR AHMED Korean Mathematical Society 2005 대한수학회보 Vol.42 No.4
In this note we give a positive answer to the conjecture by Fong and Istratescu.
Ismail Bensaid,Ahmed Bekhadda,Bachir Kerboua,Cheikh Abdelmadjid 한국풍공학회 2018 Wind and Structures, An International Journal (WAS Vol.27 No.6
In this research work, nonlinear thermal buckling behavior of functionally graded (FG) plates is explored based a new higher-order shear deformation theory (HSDT). The present model has just four unknowns, by using a new supposition of the displacement field which enforces undetermined integral variables. A shear correction factor is, thus, not necessary. A power law distribution is employed to express the disparity of volume fraction of material distributions. Three kinds of thermal loading, namely, uniform, linear, and nonlinear and temperature rises over z-axis direction are examined. The non-linear governing equations are resolved for plates subjected to simply supported boundary conditions at the edges. The results are approved with those existing in the literature. Impacts of various parameters such as aspect and thickness ratios, gradient index, type of thermal load rising, on the non-dimensional thermal buckling load are all examined.
Hafid Khetir,Mohamed Bachir Bouiadjra,Mohammed Sid Ahmed Houari,Abdelouahed Tounsi,S. R. Mahmoud 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.64 No.4
In this paper, a new nonlocal trigonometric shear deformation theory is proposed for thermal buckling response of nanosize functionally graded (FG) nano-plates resting on two-parameter elastic foundation under various types of thermal environments. This theory uses for the first time, undetermined integral variables and it contains only four unknowns, that is even less than the first shear deformation theory (FSDT). It is considered that the FG nano-plate is exposed to uniform, linear and sinusoidal temperature rises. Mori-Tanaka model is utilized to define the gradually variation of material properties along the plate thickness. Nonlocal elasticity theory of Eringen is employed to capture the size influences. Through the stationary potential energy the governing equations are derived for a refined nonlocal four-variable shear deformation plate theory and then solved analytically. A variety of examples is proposed to demonstrate the importance of elastic foundation parameters, various temperature fields, nonlocality, material composition, aspect and side-to-thickness ratios on critical stability temperatures of FG nano-plate.
Bensaid, Ismail,Bekhadda, Ahmed,Kerboua, Bachir Techno-Press 2018 Advances in nano research Vol.6 No.3
Present investigation deals with the free vibration characteristics of nanoscale-beams resting on elastic Pasternak's foundation based on nonlocal strain-gradient theory and a higher order hyperbolic beam model which captures shear deformation effect without using any shear correction factor. The nanobeam is lying on two-parameters elastic foundation consist of lower spring layers as well as a shear layer. Nonlocal strain gradient theory takes into account two scale parameters for modeling the small size effects of nanostructures more accurately. Hamilton's principal is utilized to derive the governing equations of embedded strain gradient nanobeam and, after that, analytical solutions are provided for simply supported conditions to solve the governing equations. The obtained results are compared with those predicted by the previous articles available in literature. Finally, the impacts of nonlocal parameter, length scale parameter, slenderness ratio, elastic medium, on vibration frequencies of nanosize beams are all evaluated.