Displacements and Stresses in Rotating FGM Pressurized Thick Hollow cylindrical Shells Based on HSDT

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Abstract

This article presents an elastic analysis and a closed form analytical solution for rotating functionally graded thick-walled hollow cylindrical shells subjected to constant internal and/or external pressure. Regarding the problem which could not be solved through elasticity theory, the solution based on the higher-order shear deformation theory (HSDT) is suggested. The material is assumed to be isotropic heterogeneous with constant Poisson’s ratio and radially varying elastic modulus and density continuously along the thickness with a power function. Based on HSDT, and the virtual work principle, the general governing differential equations of axisymmetric rotating pressurized thick cylindrical shells made up of functionally graded materials (FGM) have been derived. Following that, the set of non-homogenous linear differential equations with constant coefficients for the cylinder with clamped-clamped ends was solved analytically, and the effect of loading and inhomogeneity on the stresses and displacements was investigated. The results are compared with the findings of both shear deformation theory (SDT) and finite element method (FEM). Finally the effects of higher-order approximations on the stresses and displacements have been studied.

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References

[1] Mirsky I, Hermann G (1958) Axially motions of thick cylindrical shells. J of Applied Mechanics-Transactions of the ASME 25: 97–102.
[2] Reddy JN, Liu CF (1985) A higher-order shear deformation theory of laminated elastic shells. International J. of Engineering Science 23: 319–330.
[3] Greenspon JE (1960) Vibration of a thick-walled cylindrical shell, comparison of the exact theory with approximate theories. J. of the Acoustical Society of America 32(5): 571–578.
[4] Fukui Y, Yamanaka N (1992) Elastic analysis for thick-walled tubes of functionally graded materials subjected to internal pressure. JSME Ser. I 35(4): 891–900.
[5] Simkins TE (1994) Amplifications of flexural waves in gun tubes. J of Sound and Vibration 172(2): 145–154.
[6] Eipakchi HR, Rahimi GH, Khadem SE (2003) Closed form solution for displacements of thick cylinders with varying thickness subjected to nonuniform internal pressure. J Structural Engineering and Mechanics 16(6): 731–748.
[7] Eipakchi HR, Khadem SE, Rahimi GH (2008) Axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure. J Engineering Mechanics 134: 601–610.
[8] Hongjun X, Zhifei S, Taotao Z (2006) Elastic analyses of heterogeneous hollow cylinders. J of Mechanics, Research Communications 33(5): 681–691.
[9] Zhifei S, Taotao Z, Hongjun X (2007) Exact solutions of heterogeneous elastic hollow cylinders. Composite Structures 79(1): 140–147.
[10] Tutuncu N (2007) Stresses in thick-walled FGM cylinders with exponentially-varying properties. J Engineering Structures 29: 2032–2035.
[11] قناد م، رحیمی غ­.ح، اسماعیل­زاده خادم س (1389) حلّ عمومی استوانه­های جدارکلفت متقارن محوری از مواد ناهمگن FG بر مبنای تئوری الاستیسیته­ مستوی. مکانیک مدرس 10(3): 31-43.
[12] قناد م، رحیمی غ­.ح، اسماعیل­زاده خادم س (1389) حلّ عمومی استوانه­های جدارکلفت متقارن محوری از مواد ناهمگن FG بر مبنای تئوری تغییر شکل برشی. مکانیک مدرس 10(4): 15-26.
[13] Zamaninejad M, Rahimi GH, Ghannad M (2009) Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system. Mechanika 3(77): 18–26.
[14] Zamani nejad M, Rahimi GH (2009) Deformations and stresses in rotating FGM pressurized thick hollow cylinder under thermal load. Scientific Research and Essay 4(3): 131–140.
[15] Ghannad M, Nejad MZ (2010) Elastic analysis of pressurized thick hollow cylindrical shells with clamped-clamped ends. Mechanika 5(85): 11–18.
[16] Eipakchi HR (2010) Third-order shear deformation theory for stress analysis of a thick conical shell under pressure. J of Mechanics of Materials and Structures 5(1): 1–17.
 [17] قارونی ح، قناد م (1390) حلّ تحلیلی استوانه­­ چرخان FGM تحت فشار به­کمک نظریه­ تغییر شکل برشی مرتبه­ی اول. مجموعه مقالات یازدهمین کنفرانس انجمن هوافضای ایران، تهران، دانشگاه هوایی شهید ستاری.
[18] Ghannad M, Gharooni H (2012) Displacements and stresses in pressurized thick FGM cylinders with varying properties of power function based on HSDT. J of Solid Mechanics 4(3): 237–251.
[19] Ghannad M, Rahimi GH, Zamani Nejad M (2013) Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials. Composites: Part B 45: 388–396.
Journal of Solid and Fluid Mechanics
Volume 4, Issue 1 - Serial Number 1
March and April 2014
Pages 65-78

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