An alternative numerical solution of thick-walled cylinders and spheres made of functionally graded materials

Chen, Y.Z.; Lin, X. Y.

doi:10.1016/j.commatsci.2010.02.033

Cited by 50 publications

(24 citation statements)

References 10 publications

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“…(11) and its corresponding non-dimensional boundary and initial conditions given in Eq. (12), the non-dimensional dynamic radial displacement u(ξ, τ) is first divided into a quasi-static part u st (ξ, τ) and a dynamic part u dy (ξ, τ). The quasi-static part u st (ξ, τ) satisfies the static-state equilibrium equation and the imposed boundary tractions.…”

Section: Solution Methodsmentioning

confidence: 99%

“…Now, it is necessary to determine the initial conditions on Ω i (τ ) in terms of the given initial conditions (12). It follows from Eq.…”

Section: Dynamic Part Of Radial Displacementmentioning

confidence: 99%

“…This has led to many investigations on FGM cylindrical structures in recent years . In this regard, a high volume of research has been devoted to seeking analytical solutions for the FGM and multilayered cylinders under steady-state loading [3][4][5][6][7][8][9][10][11][12] .…”

Section: Introductionmentioning

confidence: 99%

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Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

Nikkhah

Honarvar

Dehghan

2011

Appl. Math. Mech.-Engl. Ed.

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An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson's ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler's equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material (FGM) hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.

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Section: Solution Methodsmentioning

confidence: 99%

“…Now, it is necessary to determine the initial conditions on Ω i (τ ) in terms of the given initial conditions (12). It follows from Eq.…”

Section: Dynamic Part Of Radial Displacementmentioning

confidence: 99%

See 1 more Smart Citation

Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

Nikkhah

Honarvar

Dehghan

2011

Appl. Math. Mech.-Engl. Ed.

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show abstract

“…(12) The only nontrivial equilibrium equation is [5], (13) Similarly, according to stress equilibrium equations, the governing equation of displacement becomes (14) with boundary conditions that come from radial stress, (15) where obtained as below depends on the r. Subscript s represents spherical vessel.…”

Section: Basic Formulation Of Spherical Pressure Vesselmentioning

confidence: 99%

The Effect of the Poisson Ratio on Stresses of Heterogeneous Pressure Vessels

Eker

Yarımpabuç²,

Çelebi³

2018

European Mechanical Science

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Functionally graded materials (FGM) belong to advanced composite materials class whose mechanical properties vary continuously from one surface to another at macro level. Thick walled annular structures are widely used in industry as nuclear reactors, long pipes used for carrying gases/oil, pressure vessels etc. Elastic analysis of FG thick walled cylindrical and spherical pressure vessels subjected only to internal pressure are studied. The material properties (Young' s modulus-Poisson' s ratio) are assumed to obey the power-law function through the wall thickness. Under these assumptions the governing equations of the FG vessels become a two-point boundary value problem. The analytical solution of such an equation can not be obtained except for simple grading functions. Complementary Functions Method is performed to solve governing equation in order to obtain displacement and stress distributions depending on inhomogeneity parameters.

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“…[17], dış basınç altındaki kademelendirilmiş küresel basınç kabı için çözümler sunmuşlardır. Bir diğer çalışmada, Chen ve Lin [18], dış basıncın fonksiyonel olarak kademelendirilmiş kapta oluşturduğu yer değiştirme bileşenlerine etkilerini, sayısal bir model kullanarak incelemiştir. Sadece iç yüzeyi fonksiyonel olarak kademelendirilmiş bir malzeme ile kaplanan kalın duvarlı küresel kabın deformasyon davranışı Atashipour ve ekibi [19] tarafından incelenmiştir.…”

Section: Introductionunclassified

Analysis on multi-layered and functionally graded spherical pressure vessels

Arslan¹

2017

Pamukkale J Eng Sci

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An alternative numerical solution of thick-walled cylinders and spheres made of functionally graded materials

Cited by 50 publications

References 10 publications

Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

The Effect of the Poisson Ratio on Stresses of Heterogeneous Pressure Vessels

Analysis on multi-layered and functionally graded spherical pressure vessels

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