Journal of Computational Applied Mechanics

Elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties using power series method of Frobenius

Document Type : Research Paper

Authors

1 Mechanical Engineering Department, Yasouj University, P. O. Box: 75914-353, Yasouj, Iran.

2 Mechanical Engineering Department, Yasouj University, Yasouj, Iran

3 School of Mechanical Engineering, University of Tehran, Tehran, Iran.

Abstract

Based on the Frobenius series method, stresses analysis of the functionally graded rotating thick cylindrical pressure vessels (FGRTCPV) are examined. The vessel is considered in both plane stress and plane strain conditions. All of the cylindrical shell properties except the Poisson ratio are considered exponential function along the radial direction. The governing Navier equation for this problem is determined, by employing the principle of the two-dimensional elastic theories. This paper presents a closed-form analytical solution for the Navier equation of FGRTCPV as the novelty of the present paper. Moreover, a finite element (FE) model is developed for comparison with the results of the Frobenius series method. This comparison demonstrates that the results of the Frobenius series method are accurate. Finally, the effect of some parameters on stresses analysis of the FGRTCPV is examined. In order to investigate the inhomogeneity effect on the elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties, values of the parameters have been set arbitrary in the present study. The presented outcomes illustrate that the inhomogeneity constant provides a major effect on the mechanical behaviors of the exponential FG thick cylindrical under pressure.

Keywords

Main Subjects

[1]     K. Khorshidi, A. Bakhsheshy, Free Natural Frequency Analysis of an FG Composite Rectangular Plate Coupled with Fluid using Rayleigh–Ritz Method, Mechanics of Advanced Composite Structures‎, Vol. 1, No. 2, pp. 131-143, 2014.
[2]     A. M. Zenkour, Dynamical bending analysis of functionally graded infinite cylinder with rigid core, Applied Mathematics and Computation, Vol. 218, No. 17, pp. 8997-9006, 2012.
[3]     A. Hadi, A. Rastgoo, A. Daneshmehr, F. Ehsani, Stress and strain analysis of functionally graded rectangular plate with exponentially varying properties, Indian Journal of Materials Science, Vol. 2013, 2013.
[4]     M. Mohammadi, M. Safarabadi, A. Rastgoo, A. Farajpour, Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment, Acta Mechanica, Vol. 227, No. 8, pp. 2207-2232, 2016.
[5]     M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco pasternak foundation, Journal of Solid Mechanics, Vol. 6, pp. 98-121, 2014.
[6]     S. R. Asemi, M. Mohammadi, A. Farajpour, A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, Vol. 11, No. 9, pp. 1515-1540, 2014.
[7]     M. R. Farajpour, A. Rastgoo, A. Farajpour, M. Mohammadi, Vibration of piezoelectric nanofilm-based electromechanical sensors via higher-order non-local strain gradient theory, Micro & Nano Letters, Vol. 11, No. 6, pp. 302-307, 2016.
[8]     M. Mohammadi, A. Farajpour, M. Goodarzi, H. Mohammadi, Temperature effect on vibration analysis of annular graphene sheet embedded on visco-pasternak foundation, J. Solid Mech, Vol. 5, pp. 305-323, 2013.
[9]     B. S. Aragh, E. B. Farahani, A. N. Barati, Natural frequency analysis of continuously graded carbon nanotube-reinforced cylindrical shells based on third-order shear deformation theory, Mathematics and Mechanics of Solids, Vol. 18, No. 3, pp. 264-284, 2013.
[10]   J. Dryden, R. Batra, Material tailoring and moduli homogenization for finite twisting deformations of functionally graded Mooney-Rivlin hollow cylinders, Acta Mechanica, Vol. 224, No. 4, pp. 811-818, 2013.
[11]   A. Daneshmehr, A. Rajabpoor, A. Hadi, Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories, International Journal of Engineering Science, Vol. 95, pp. 23-35, 2015.
[12]   M. Z. Nejad, A. Hadi, Non-local analysis of free vibration of bi-directional functionally graded Euler–Bernoulli nano-beams, International Journal of Engineering Science, Vol. 105, pp. 1-11, 2016.
[13]   M. Z. Nejad, A. Rastgoo, A. Hadi, Exact elasto-plastic analysis of rotating disks made of functionally graded materials, International Journal of Engineering Science, Vol. 85, pp. 47-57, 2014.
[14]   M. Z. Nejad, A. Hadi, A. Rastgoo, Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory, International Journal of Engineering Science, Vol. 103, pp. 1-10, 2016.
[15]   M. Z. Nejad, A. Hadi, Eringen's non-local elasticity theory for bending analysis of bi-directional functionally graded Euler–Bernoulli nano-beams, International Journal of Engineering Science, Vol. 106, pp. 1-9, 2016.
[16]   M. Kahrobaiyan, M. Rahaeifard, S. Tajalli, M. Ahmadian, A strain gradient functionally graded Euler–Bernoulli beam formulation, International Journal of Engineering Science, Vol. 52, pp. 65-76, 2012.
[17]   Z. Mazarei, M. Z. Nejad, A. Hadi, Thermo-elasto-plastic analysis of thick-walled spherical pressure vessels made of functionally graded materials, International Journal of Applied Mechanics, Vol. 8, No. 04, pp. 1650054, 2016.
[18]   M. Z. Nejad, G. Rahimi, Deformations and stresses in rotating FGM pressurized thick hollow cylinder under thermal load, Scientific Research and Essays, Vol. 4, No. 3, pp. 131-140, 2009.
[19]   M. Jabbari, M. Z. Nejad, M. Ghannad, Thermo-elastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading, International journal of engineering science, Vol. 96, pp. 1-18, 2015.
[20]   M. Jabbari, M. Z. Nejad, M. Ghannad, Thermo-elastic analysis of axially functionally graded rotating thick truncated conical shells with varying thickness, Composites Part B: Engineering, Vol. 96, pp. 20-34, 2016.
[21]   M. Nejad, A. Rastgoo, A. Hadi, Effect of Exponentially-Varying Properties on Displacements and Stresses in Pressurized Functionally Graded Thick Spherical Shells with Using Iterative Technique, Journal of Solid Mechanics Vol, Vol. 6, No. 4, pp. 366-377, 2014.
[22]   M. Hosseini, M. Shishesaz, K. N. Tahan, A. Hadi, Stress analysis of rotating nano-disks of variable thickness made of functionally graded materials, International Journal of Engineering Science, Vol. 109, pp. 29-53, 2016.
[23]   C. Horgan, A. Chan, The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials, Journal of Elasticity, Vol. 55, No. 1, pp. 43-59, 1999.
[24]   N. Tutuncu, M. Ozturk, Exact solutions for stresses in functionally graded pressure vessels, Composites Part B: Engineering, Vol. 32, No. 8, pp. 683-686, 2001.
[25]   Z. Shi, T. Zhang, H. Xiang, Exact solutions of heterogeneous elastic hollow cylinders, Composite structures, Vol. 79, No. 1, pp. 140-147, 2007.
[26]   N. Tutuncu, Stresses in thick-walled FGM cylinders with exponentially-varying properties, Engineering Structures, Vol. 29, No. 9, pp. 2032-2035, 2007.
[27]   Y. Chen, X. Lin, Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials, Computational Materials Science, Vol. 44, No. 2, pp. 581-587, 2008.
[28]   R. Batra, G. Nie, Analytical solutions for functionally graded incompressible eccentric and non-axisymmetrically loaded circular cylinders, Composite Structures, Vol. 92, No. 5, pp. 1229-1245, 2010.
[29]   G. Nie, R. Batra, Exact solutions and material tailoring for functionally graded hollow circular cylinders, Journal of Elasticity, Vol. 99, No. 2, pp. 179-201, 2010.
[30]   G. Nie, R. Batra, Material tailoring and analysis of functionally graded isotropic and incompressible linear elastic hollow cylinders, Composite structures, Vol. 92, No. 2, pp. 265-274, 2010.
[31]   H. Çallioğlu, N. B. Bektaş, M. Sayer, Stress analysis of functionally graded rotating discs: analytical and numerical solutions, Acta Mechanica Sinica, Vol. 27, No. 6, pp. 950-955, 2011.
[32]   P. Fatehi, M. Z. Nejad, Effects of material gradients on onset of yield in FGM rotating thick cylindrical shells, International Journal of Applied Mechanics, Vol. 6, No. 04, pp. 1450038, 2014.
[33]   M. Z. Nejad, M. Jabbari, M. Ghannad, Elastic analysis of axially functionally graded rotating thick cylinder with variable thickness under non-uniform arbitrarily pressure loading, International Journal of Engineering Science, Vol. 89, pp. 86-99, 2015.
[34]   M. H. Sadd, 2009, Elasticity: theory, applications, and numerics, Academic Press,
[35]          M. Mohammadi, A. Farajpour, M. Goodarzi, F. Dinari, Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, No. 4, pp. 659-682, 2014.
[36]          M. Mohammadi, M. Goodarzi, M. Ghayour, S. Alivand, Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial in-plane pre-load via nonlocal elasticity theory, Journal of Solid Mechanics, Vol. 4, No. 2, pp. 128-143, 2012.
[37]          M. Mohammadi, A. Farajpour, M. Goodarzi, R. Heydarshenas, Levy type solution for nonlocal thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Journal of Solid Mechanics, Vol. 5, No. 2, pp. 116-132, 2013.
[38]          M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco pasternak foundation, Journal of Solid Mechanics, Vol. 6, pp. 98-121, 2014. 

Journal of Computational Applied Mechanics
Volume 48, Issue 1
June 2017
Pages 89-98
  • Receive Date: 20 May 2017
  • Revise Date: 08 June 2017
  • Accept Date: 19 June 2017