Semi Analytical Analysis of FGM Thick-Walled Cylindrical Pressure Vessel with Longitudinal Variation of Elastic Modulus under Internal Pressure

Subject Areas : Engineering

M Shariati ¹ , H Sadeghi ² , M Ghannad ³ , H Gharooni ⁴

1 - Department of Mechanical Engineering, Ferdosi University
2 - Department of Mechanical Engineering, Shahrood University
3 - Department of Mechanical Engineering, Shahrood University
4 - Department of Mechanical Engineering, Shahrood University

Received: 2015-02-15 Accepted : 2015-04-03 Published : 2015-06-30

Keywords: Thick-walled cylinder, FGM, Exponential, Cylindrical pressure vessel, Longitudinal variations of elastic modulus,

Abstract :

In this paper, a numerical analysis of stresses and displacements in FGM thick-walled cylindrical pressure vessel under internal pressure has been presented. The elastic modulus is assumed to be varying along the longitude of the pressure vessel with an exponential function continuously. The Poisson’s ratio is assumed to be constant. Whereas most of the previous studies about FGM thick-walled pressure vessels are on the basis of changing material properties along the radial direction, in this research, elastic analysis of cylindrical pressure vessel with exponential variations of elastic modulus along the longitudinal direction, under internal pressure, have been investigated. For the analysis of the vessel, the stiffness matrix of the cylindrical pressure vessel has been extracted by the usage of Galerkin Method and the numerical solution for axisymmetric cylindrical pressure vessel under internal pressure have been presented. Following that, displacements and stress distributions depending on inhomogeneity constant of FGM vessel along the longitudinal direction of elastic modulus, are illustrated and compared with those of the homogeneous case. The values which have been used in this study are arbitrary chosen to demonstrate the effect of inhomogeneity on displacements and stress distributions. Finally, the results are compared with the findings of finite element method (FEM).

References:

[1] Fukui Y., Yamanaka N., 1992, Elastic analysis for thick-walled tubes of functionally graded materials subjected to internal pressure, JSME International Journal Series I 35(4): 891-900.
[2] Tutuncu N., Ozturk M., 2001, Exact solution for stresses in functionally graded pressure vessel, Composites Part B: Engineering 32: 683-686.
[3] Jabbari M., Sohrab pour S., Eslami M.R., 2002, Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, International Journal of Pressure Vessel and Piping 79: 493-497.
[4] Eipakchi H.R., Khadem S.E., Rahimi G.H., 2008, Axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure, Journal of Engineering Mechanics 134: 601-610.
[5] Eslami M.R., Babaei M.H., Poultangari R., 2005, Thermal and mechanical stresses in a functionally graded thick sphere, International Journal of Pressure Vessel and Piping 82: 522-527.
[6] Dai H.L., Fu Y.M., Dong Z.M., 2006, Exact solutions for functionally graded pressure vessels in a uniform magnetic field, International Journal of Solids and Structures 43: 5570-5580.
[7] Naghdabadi R., Kordkheili S.A., 2005, A finite element formulation for analysis of functionally graded plates and shells, ASME Journal of Applied Mechanics 74: 375-386.
[8] Hongjun X., Zhifei S., Taotao Z., 2006, Elastic analyses of heterogeneous hollow cylinders, 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: 140-147.
[10] Tutuncu N., 2007, Stresses in thick-walled FGM cylinders with exponentially-varying properties, Engineering Structures 29: 2032-2035.
[11] Ghannad M., Nejad M.Z., 2010, Elastic analysis of pressurized thick hollow cylindrical shells with clamped-clamped ends, Mechanika 5(85): 11-18.
[12] Ghannad M., Rahimi G.H., Zamani Nejad M., 2012, Determination of displacements and stresses in pressurized thick cylindrical shells with variable thickness using perturbation technique, Mechanika 18(1): 14-21.
[13] Gharooni H., Ghannad M., 2012, Analytical solution of rotary pressurized FGM cylinder by the usage of first order shear deformation theory, 11th Conference of Iranian Aerospace Society 15024: 195.
[14] Liu L., Li J., Ding M., Yang X., 2007, Development of SiC/(W, Ti)C gradient ceramic nozzle materials for sand blasting surface treatments, International Journal of Refractory Metals and Hard Materials 25(2): 130-137.
[15] Liu L., Deng J., 2008, Study on erosion wear mechanism of SiC/(W,Ti)C gradient ceramic nozzle material, Journal of Key Engineering Materials 375(376): 440-444.
[16] Asemi K., Salehi M., Akhlaghi M., 2011, Elastic solution of a two-dimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads, Acta Mechanica 217(1-2): 119-134.
[17] Masoud Asgari M., Akhlaghi M., 2010, Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with finite length, Archive of Applied Mechanics 80(4): 353-376.
[18] Ghannad M., Rahimi G.H., 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.