Applications of differential transformation method to solve systems of ordinary and partial differential equations

Sarp, Ümit; Evirgen, Fırat; Ikikardes, Sebahattin

doi:10.25092/baunfbed.423145

Cited by 7 publications

(1 citation statement)

References 30 publications

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“…FGMs are co mposite materials made of ceramic and metal. The materialś properties of FG beams are assumed to vary continuously through the depth of the beam according to a power law as [1,2,5,13] ( ) = ( − ) (…”

Section: Figure 1 Fg Beam -Geometry and Coordinatesmentioning

confidence: 99%

A New Method of Resolution of the Bending of Thick FGM Beams Based on Refined Higher Order Shear Deformation Theory

Razouki¹,

Boutahar²,

Bikri³

2020

ujme

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The aim of this work is to study the static bending of functionally graded beams accounting higher order of shear deformat ion theory. The governing equations, derived from the virtual work principle, are a set of ordinary d ifferential equations describing a static bending of a thick beam. Thus, this paper presents the differential transform method used to solve the previous system of equations. The results obtained lay the foundation to determine the exact analytical solution for different boundary conditions and external loadings. The axial displacement and the bending and shear displacements, in the exact analytical form, of a thick clamped-clamped beam with functionally graded material under a unifo rm load will be fully developed. Moreover, normal and shear stresses will be analyzed. To confirm the efficiency of this work, a co mparison with the nu merical results provided by literature is performed. Through this work, the given analytical results provide engineers with an accurate tool to determine the analytical solution for the bending of plates and shells. In addition, the geometric and material parameters that appear clearly in the analytical results allow for a mo re optimized design of functionally graded material beams. This type of beams is frequently used in mechanical engineering fields such as aerospace engineering.

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Section: Figure 1 Fg Beam -Geometry and Coordinatesmentioning

confidence: 99%

A New Method of Resolution of the Bending of Thick FGM Beams Based on Refined Higher Order Shear Deformation Theory

Razouki¹,

Boutahar²,

Bikri³

2020

ujme

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Hybrid evolutionary padé approximation approach for numerical treatment of nonlinear partial differential equations

Nisar

Ali²,

Mahmood

et al. 2021

Alexandria Engineering Journal

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Sonlu bir bölge üzerinde Atangana-Baleanu türevli adveksiyon-difüzyon denklemine analitik çözümler

Avcı¹,

Yetim²

2018

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In this paper, an advection-diffusion equation with Atangana-Baleanu derivative is considered. Cauchy and Dirichlet problems have been described on a finite interval. The main aim is to scrutinize the fundamental solutions for the prescribed problems. The Laplace and the finite sin-Fourier integral transformation techniques are applied to determine the concentration profiles corresponding to the fundamental solutions. Results have been obtained as linear combinations of one or bi-parameterMittag-Leffler functions. Consequently, the effects of the fractional parameter and drift velocity parameter on the fundamental solutions are interpreted by the help of some illustrative graphics. Sonlu bir bölge üzerinde Atangana-Baleanu türevli adveksiyondifüzyon denklemine analitik çözümler Özet Bu çalışmada Atangana-Baleanu türevli bir adveksiyon-difüzyon denklemi ele alınmıştır. Cauchy ve Dirichlet problemleri sonlu bir aralıkta tanımlanmıştır. Asıl amaç, belirlenen problemler için temel çözümleri irdelemektir. Temel çözümlere karşılık gelen konsantrasyon profillerini belirlemek için Laplace ve sonlu sin-Fourier integral dönüşüm teknikleri uygulanmıştır. Sonuçlar, bir veya iki parametreli Mittag-* Derya AVCI, dkaradeniz@balikesir.edu.tr, https://orcid.org/0000-0003-3662-0474 Aylin YETİM, ayetim72@gmail.com, https://orcid.org/0000-0002-6961-9114 Leffler fonksiyonlarının lineer kombinasyonları olarak elde edilmiştir. Sonuç olarak, kesirli parametrenin ve sürüklenme hızı parametresinin çözümler üzerindeki etkileri bazı açıklayıcı grafikler yardımıyla yorumlanmıştır. Anahtar Kelimeler: Atangana-Baleanu türevi, adveksiyon-difüzyon denklemi, Laplace integral dönüşümü, Mittag-Leffler fonksiyonu, temel çözüm.

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Applications of differential transformation method to solve systems of ordinary and partial differential equations

Abstract: In this study, the numerical solutions of some systems of ordinary and partial differential equations have been analyzed by using the Differential Transformation

Cited by 7 publications

References 30 publications

A New Method of Resolution of the Bending of Thick FGM Beams Based on Refined Higher Order Shear Deformation Theory

A New Method of Resolution of the Bending of Thick FGM Beams Based on Refined Higher Order Shear Deformation Theory

Hybrid evolutionary padé approximation approach for numerical treatment of nonlinear partial differential equations

Sonlu bir bölge üzerinde Atangana-Baleanu türevli adveksiyon-difüzyon denklemine analitik çözümler

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