Applied Mathematics and Mechanics

, Volume 38, Issue 4, pp 479–494 | Cite as

Three-dimensional magneto-thermo-elastic analysis of functionally graded cylindrical shell

  • A. Mehditabar
  • G. H. Rahimi
  • S. Ansari Sadrabadi
Article
First Online:
Received:
Revised:
  • 76 Downloads

Abstract

The present paper presents the three-dimensional magneto-thermo-elastic analysis of the functionally graded cylindrical shell immersed in applied thermal and magnetic fields under non-uniform internal pressure. The inhomogeneity of the shell is assumed to vary along the radial direction according to a power law function, whereas Poisson’s ratio is supposed to be constant through the thickness. The existing equations in terms of the displacement components, temperature, and magnetic parameters are derived, and then the effective differential quadrature method (DQM) is used to acquire the analytical solution. Based on the DQM, the governing heat differential equations and edge boundary conditions are transformed into algebraic equations, and discretized in the series form. The effects of the gradient index and rapid temperature on the displacement, stress components, temperature, and induced magnetic field are graphically illustrated. The fast convergence of the method is demonstrated and compared with the results obtained by the finite element method (FEM).

Key words

magneto-thermo-elastic functionally graded material (FGM) cylindrical shell differential quadrature method (DQM) 

Chinese Library Classification

O343.6 

2010 Mathematics Subject Classification

35K55 35D05 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Xing, Y. and Liu, B. A differential quadrature analysis of dynamic and quasi-static magnetothermo-elastic stresses in a conducting rectangular plate subjected to an arbitrary variation of magnetic field. International Journal of Engineering Science, 48, 1944–1960 (2010)CrossRefMATHGoogle Scholar
  2. [2]
    Farid, M., Zahednejad, P., and Malekzadeh, P. Three-dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation using a hybrid semi-analytic, differential quadrature method. Materials and Design, 31, 2–13 (2010)CrossRefGoogle Scholar
  3. [3]
    Xin, L., Dui, G., Yang, S., and Zhou, D. Solution for behavior of a functionally graded thick-walled tube subjected to mechanical and thermal loads. International Journal of Mechanical Science, 98, 70–79 (2015)CrossRefGoogle Scholar
  4. [4]
    Alibeigloo, A. Elasticity solution of functionally graded carbon-nanotube-reinforced composite cylindrical panel with piezoelectric sensor and actuator layers. Composite: Part B, 87, 182–187 (2015)Google Scholar
  5. [5]
    Jabbari, M., Nejad, M. Z., and Ghannad, M. Thermo-elastic analysis of functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading. International Journal of Engineering Science, 96, 1–8 (2015)MathSciNetCrossRefGoogle Scholar
  6. [6]
    Kiani, K. Thermo-mechanical analysis of functionally graded plate-like nanorotors: a surface elasticity model. International Journal of Mechanical Sciences, 106, 39–49 (2016)CrossRefGoogle Scholar
  7. [7]
    Jamaludin, S. N. S., Basri, S., Hussain, A., Al-Othmany, D. S., Mustapha, F., and Nuruzzaman, D. M. Three-dimensional finite element modeling of thermomechanical problems in functionally graded hydroxyapatite/titanium plate. Mathematical Problems in Engineering, 2014, 1–12 (2014)CrossRefGoogle Scholar
  8. [8]
    Prakash, T. and Ganapathi, M. Asymmetric flexural vibration and thermo-elastic stability of FGM circular plates using finite element method. Composite: Part B, 37, 642–649 (2006)CrossRefGoogle Scholar
  9. [9]
    Feng, S. Z., Cui, X. Y., Li, G. Y., Feng, H., and Xu, F. X. Thermo-mechanical analysis of functionally graded cylindrical vessels using edge-based smoothed finite element method. International Journal of Pressure Vessels and Piping, 111-112, 302–309 (2013)CrossRefGoogle Scholar
  10. [10]
    Ching, H. K. and Yen, S. C. Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads. Composite: Part B, 36, 223–240 (2005)CrossRefGoogle Scholar
  11. [11]
    Chen, Y. Z. and Lin, X. Y. Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials. Computational Materials Science, 44, 581–587 (2008)CrossRefGoogle Scholar
  12. [12]
    Zafarmand, H. and Kadkhodayan, M. Three dimensional elasticity solution for static and dynamic analysis of multi-directional functionally graded thick sector plates with general boundary conditions. Composite: Part B, 69, 592–602 (2015)CrossRefGoogle Scholar
  13. [13]
    Jabbari, M., Sohrabpour, S., and Eslami, M. R. Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads. International Journal of Pressure and Vessels, 79, 493–497 (2002)CrossRefMATHGoogle Scholar
  14. [14]
    Loghman, A. and Pars, H. Exact solution for magneto-thermo-elastic behavior of double-walled cylinder made of an inner FGM and an outer homogeneous layer. International Journal of Mechanical Sciences, 88, 93–99 (2014)CrossRefGoogle Scholar
  15. [15]
    Mehditabar, A. Three-dimensional magneto-thermo-elastic analysis of functionally graded truncated conical shells. International Journal of Engineering, 26, 1445–1460 (2013)Google Scholar
  16. [16]
    Zenkour, A. M. and Abbas, I. A. Electro-magneto-thermo-elastic response of infinite functionally graded cylinders without energy dissipation. Journal of Magnetic Materials, 395, 123–129 (2015)CrossRefGoogle Scholar
  17. [17]
    Zhang, L. and Li, X. W. Buckling and vibration analysis of functionally graded magneto-electrothermo- elastic circular cylindrical shells. Applied Mathmatical Modelling, 37, 2279–2292 (2013)CrossRefMATHGoogle Scholar
  18. [18]
    Ezzat, M. and Atef, H. M. Magneto-electro viscoelastic layer in functionally graded materials. Composite: Part B, 42, 832–841 (2011)CrossRefGoogle Scholar
  19. [19]
    Kumar, R., Sharma, N., and Lata, P. Thermomechanical interactions in transversely isotropic magneto-thermo-elastic medium with vacuum and with and whithout energy dissipation with combined effects of rotation, vacuum and two temperature. Applied Mathematical Modelling, 40, 1–16 (2016)MathSciNetCrossRefGoogle Scholar
  20. [20]
    Rad, A. B. and Shariyat, M. Thermo-magneto-elasticity analysis of variable thickness annular FGM plates with asymmetric shear and normal loads and non-uniform elastic foundations. Archives of Civil and Mechanical Engineering, 16, 448–466 (2016)CrossRefGoogle Scholar
  21. [21]
    John, K. Electromagnetics, McGraw-Hill Book Company, Inc., New York (1941)MATHGoogle Scholar
  22. [22]
    Strang, G. Introduction to Applied Mathematics, Wellesley-Cambridge Press, Massachusetts (1986)MATHGoogle Scholar
  23. [23]
    Jane, K. C. and Wu, Y. H. A generalized thermo-elasticity problem of multilinear conical shells. International Journal of Solids and Structures, 41, 2205–2233 (2004)CrossRefMATHGoogle Scholar
  24. [24]
    Shu, C. Differential Quadrature and Its Application in Engineering, Springer-Verlag, London (2000)CrossRefMATHGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • A. Mehditabar
    • 1
  • G. H. Rahimi
    • 1
  • S. Ansari Sadrabadi
    • 1
  1. 1.Department of Mechanical Engineering, School of Mechanical EngineeringTarbiat Modares UniversityTehranIran

Personalised recommendations