Eid, Rajeh

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Eid, R
R., Eid
Rajeh, Eid
R.,Eid
Eid, Rajeh
Eid,R.
E., Rajeh
E.,Rajeh
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Doçent Doktor
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rajeh.eid@atilim.edu.tr
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Scholarly Output

5

Articles

3

Citation Count

82

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1

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2005 - 200922010 - 20193
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Now showing 1 - 5 of 5
  • Thumbnail Image
    Master Thesis
    Poısson denkleminin sonlu elemanlar çözümü
    (2019) Eid, Rajeh; Eid, Rajeh; Mathematics
    Bu tez çalışmasında Sonlu elemanlar yöntemi (FEM) iki boyutlu (2D) poisson denklemini çözmek için uygulanmıştır.([8]). Algoritmamızı oluşturmak için şekil fonksiyonu kullandık. Bu çalışmada kullandığımız şekil fonksiyonları, doğrusal ve ikinci dereceden interpolasyon fonksiyonları olarak seçilmiştir([2],[9]). Doğrusal şekil fonksiyonunu 3 düğümlü üçgen, ve 4 düğümlü dikdörtgen elemanlara uygularken, ikinci dereceden fonksiyon 6 düğümlü üçgen ve dikdörtgen elemanlara uygulanmıştır. Daha sonra incelenen problemin yaklaşık çözümünü hesaplamak için sonlu elemanlar metodunu uyguladık. Çözümün doğruluğunu göstermek için lineer ve kuadratik şekil fonksiyonları kullanılarak sayısal sonuçlar elde edilmiştir. Çözümün verimliliği, Sonlu elemanlar yöntemi kullanılarak bulunan sonuçların, tam çözümle karşılaştırılarak gözlemlenmiştir.
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    Article
    Citation Count: 5
    Higher order isoparametric finite element solution of Stokes flow
    (Elsevier Science inc, 2005) Eid, Rajeh; Mathematics
    A finite element method of the penalization type, using higher order shape functions with rectangular elements, is presented for the solution of the Stokes flow. The fluid is viscous and the flow is slow, steady and incompressible. The solution has been obtained in terms of velocity field while the pressure terms are eliminated using the penalty function approach. The degree of the finite element approximation can be increased as much as one needs with this higher order shape function formulation. The method is tested in a lid-driven square cavity and it is found that there is a relationship between the viscosity and penalty parameter. From one solution one can obtain all the other solutions only by arranging one of the parameters since the product of these parameters has been shown that is a fixed constant. Selected graphs of the velocity field are given showing these behaviors. (C) 2004 Elsevier Inc. All rights reserved.
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    Review
    Citation Count: 11
    A freely damped oscillating fractional dynamic system modeled by fractional Euler-Lagrange equations
    (Sage Publications Ltd, 2018) Eid, Rajeh; Baleanu, Dumitru; İrfanoğlu, Bülent; Irfanoglu, Bulent; Mathematics; Department of Mechatronics Engineering
    The behaviors of some vibrating dynamic systems cannot be modeled precisely by means of integer representation models. Fractional representation looks like it is more accurate to model such systems. In this study, the fractional Euler-Lagrange equations model is introduced to model a fractional damped oscillating system. In this model, the fractional inertia force and the fractional damping force are proportional to the fractional derivative of the displacement. The fractional derivative orders in both forces are considered to be variable fractional orders. A numerical approximation technique is utilized to obtain the system responses. The discretization of the Coimbra fractional derivative and the finite difference technique are used to accomplish this approximation. The response of the system is verified by a comparison to a classical integer representation and is obtained based on different values of system parameters.
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    Article
    Citation Count: 49
    On fractional Schrodinger equation in α-dimensional fractional space
    (Pergamon-elsevier Science Ltd, 2009) Eid, Rajeh; Muslih, Sami I.; Baleanu, Dumitru; Rabei, E.; Mathematics
    The Schrodinger equation is solved in a-dimensional fractional space with a Coulomb potential proportional to 1/r(beta-2), 2 <= beta <= 4. The wave functions are studied in terms of spatial dimensionality alpha and beta and the results for beta = 3 are compared with those obtained in the literature. (C) 2008 Elsevier Ltd. All rights reserved.
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    Article
    Citation Count: 17
    Development of Decision Support Model for Selecting a Maintenance Plan Using a Fuzzy MCDM Approach: A Theoretical Framework
    (Hindawi Ltd, 2018) Eid, Rajeh; Eid, Rajeh; Rouyendegh (B Erdebilli), Babak Daneshvar; Mathematics
    In complex decision making, using multicriteria decision-making (MCDM) methodologies is the most scientific way to ensure an informed and justified decision between several alternatives. MCDMs have been used in different ways and with several applications that proved their efficiency in achieving this goal. In this research, the advantages and disadvantages of the different MCDM methodologies are studied, along with the different techniques implemented to increase their accuracy and precision. The main aim of the study is to develop a hybrid MCDM process that combines the strengths of several MCDM methods and apply it to choose the best fit maintenance policy/strategy for industrial application. Moreover, fuzzy linguistic terms are utilized in all of the used MCDM techniques in order to eliminate the uncertainty and ambiguity of the results. Through an extensive literature review performed on studies that have used MCDM methods in a hybrid context and using fuzzy linguistic terms, a model is developed to use fuzzy DEMATEL-AHP-TOPSIS hybrid technique. The model with its application is the first of its kind, which combines the strengths of fuzzy DEMATEL in establishing interrelationships between several criteria, as well as performing a pairwise comparison between the criteria for prioritization using the fuzzy AHP method. Thereafter, the alternatives are compared using fuzzy TOPSIS method by establishing negative and positive solutions and calculating the relative closeness for each of the alternatives. Furthermore, six main criteria, twenty criteria, and five alternatives are selected from the literature for the model application.