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Two-dimensional dynamic analysis of thermal stresses in a finite-length FG thick hollow cylinder subjected to thermal shock loading using an analytical method

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Abstract

This work is aiming to present an analytical method to study the dynamic behavior of thermoelastic stresses in a finite-length functionally graded (FG) thick hollow cylinder under thermal shock loading. The thermo-mechanical properties are assumed to vary continuously through the radial direction as a nonlinear power function. Using Laplace transform and series solution, the thermoelastic Navier equations in displacement form are solved analytically. The solution of the displacement field in the FG cylinder is obtained in the Laplace domain. Also, the fast Laplace inverse transform method (FLIT) is employed to transfer the results from Laplace domain to time domain. The effects of thermal shock loading on the dynamic characteristics of the FG thick hollow cylinder are studied in various points across the thickness of cylinder for various grading patterns of FGMs. A good agreement can be seen in the comparison of the obtained results based on the presented analytical method with published data.

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References

  1. Wang, X.: Thermal shock in a hollow cylinder caused by rapid arbitrary heating. J. Sound Vib. 788–895 (1995)

  2. Zibdeh H.S., Farran J.M.A.: Stress analysis in composite hollow cylinders due to an asymmetric temperature distribution. J. Pressure Vessel Technol. 117, 59–65 (1995)

    Article  Google Scholar 

  3. Ootao Y., Tanigawa Y.: Three-dimensional transient piezothermoelasticity in functionally graded rectangular plate bonded to a piezoelectric plate. Int. J. Solids Struct. 37, 4377–4401 (2000)

    Article  MATH  Google Scholar 

  4. Luping X.A., Kewei D.: Three-dimensional thermoelastic solution for laminated cantilever cylindrical shell. Aerosp. Sci. Technol. 5, 339–346 (2001)

    Article  MATH  Google Scholar 

  5. Yee K.C., Moon T.J.: Plane thermal stress analysis of an orthotropic cylinder subjected to an arbitrary, transient, asymmetric temperature distribution. Trans. ASME 69, 632–640 (2002)

    Article  MATH  Google Scholar 

  6. Chen W., Bian Z., Ding H.: Three-dimensional analysis of a thick FGM rectangular plate in thermal environment. J. Zhejiang Univ. Sci. 4(1), 1–7 (2003)

    Article  Google Scholar 

  7. Ruhi M., Angoshtari A., Naghdabadi R.: Thermoelastic analysis of thick-walled finite length cylinders of functionally graded materials. J. Therm. Stresses. 28(4), 391–408 (2005)

    Article  MATH  Google Scholar 

  8. Ootao Y., Tanigawa Y.: Two-dimensional thermoelastic analysis of a functionally graded cylindrical panel due to nonuniform heat supply. Mech. Res. Commun. 32, 429–443 (2005)

    Article  MATH  Google Scholar 

  9. Ootao Y., Tanigawa Y.: Transient thermoelastic problem of a functionally graded cylindrical panel due to nonuniform heat supply. J. Therm. Stresses. 30(5), 441–457 (2007)

    Article  Google Scholar 

  10. Jacob L.P., Senthil S.V.: An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells. Int. J. Solids Struct. 43, 1131–1158 (2006)

    Article  MATH  Google Scholar 

  11. Jabbari M., Bahtui A., Eslami M.R.: Axisymmetric mechanical and thermal stresses in thick long FGM cylinders. J. Therm. Stresses. 29(7), 643–663 (2006)

    Article  Google Scholar 

  12. Jabbari M., Bahtui A., Eslami M.R.: Axisymmetric mechanical and thermal stresses in thick short length FGM cylinders. J. Press. Vessels Pip. 86, 296–306 (2009)

    Article  Google Scholar 

  13. Shao Z.S.: Mechanical and thermal stresses of a functionally graded circular hollow cylinder with finite length. J. Press. Vessels Pip. 82, 155–163 (2005)

    Article  Google Scholar 

  14. Shao Z.S., Wang T.J.: Three-dimensional solutions for the stress fields in functionally graded cylindrical panel with finite length and subjected to thermal/mechanical loads. Int. J. Solids Struct. 43, 3856–3874 (2006)

    Article  MATH  Google Scholar 

  15. Shao Z.S., Wang T.J., Ang K.K.: Transient thermomechanical stresses of functionally graded cylindrical panels. AIAA J. 45(10), 2487–2496 (2007)

    Article  Google Scholar 

  16. Shao Z.S., Ang K.K., Reddy J.N., Wang T.J.: Nonaxisymmetric thermomechanical analysis of functionally graded hollow cylinders. J. Therm. Stresses 31(6), 515–536 (2008)

    Article  Google Scholar 

  17. Hosseini S.M., Akhlaghi M., Shakeri M.: Dynamic response and radial wave propagation velocity in thick hollow cylinder made of functionally graded materials. Eng. Comput. 24(3), 288–303 (2007)

    Article  MATH  Google Scholar 

  18. Hosseini S.M., Akhlaghi M., Shakeri M.: Transient heat conduction in functionally graded thick hollow cylinders by analytical method. Heat Mass Transf. 43, 669–675 (2007)

    Article  Google Scholar 

  19. Asgari M., Akhlaghi M., Hosseini S.M.: Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading. Acta Mech. 208, 163–180 (2009)

    Article  MATH  Google Scholar 

  20. Shahani A.R., Nabavi S.M.: Analytical solution of the quasi-static thermoelasticity problem in a pressurized thick-walled cylinder subjected to transient thermal loading. Appl. Math. Modell. 31, 1807–1818 (2007)

    Article  MATH  Google Scholar 

  21. Wang X., Sudak L.J.: Three-dimensional analysis of multi-layered functionally graded anisotropic cylindrical panel under thermomechanical loading. Mech. Mater. 40, 235–254 (2008)

    Article  Google Scholar 

  22. Tahani M., Mirzababaee S.M.: Nonlinear analysis of functionally graded plates in cylindrical bending under thermomechanical loadings based on a layerwise theory. Eur. J. Mech. A Solids 28, 248–256 (2009)

    Article  MATH  Google Scholar 

  23. Shariyat M.: A nonlinear hermitian transfinite element method for tansient behavior analysis of hollow functionally graded cylinders with temperature-dependent materials under thermo-mechanical loads. J. Press. Vessels Pip. 86, 280–289 (2009)

    Article  Google Scholar 

  24. Shariyat M., Lavasani S.M.H., Khaghani M.: Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders, using a second-order point-collocation method. Appl. Math. Modell. 34, 898–918 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  25. Hosseini S.M., Akhlaghi M.: Analytical solution in transient thermo-elasticity of functionally graded thick hollow cylinders (pseudo-dynamic analysis). Math. Methods Appl. Sci. 32, 2019–2034 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  26. Hosseini S.M., Abolbashari M.H.: General analytical solution for elastic radial wave propagation and dynamic analysis of functionally graded thick hollow cylinders subjected to impact loading. Acta Mech. 212, 1–19 (2009)

    Article  Google Scholar 

  27. Tahani M., Hosseini S.M., Safari A., Todoroki A.: Transient and dynamic stress analysis of functionally graded thick hollow cylinder subjected to thermal shock loading using an analytical method. JSME Int J. Ser. A. 4, 1346–1359 (2010)

    Google Scholar 

  28. Durbin F.: Numerical inversion of laplace transforms: an efficient improvement to Dubner and Abate’s method. Comput. J. 17, 371–376 (1974)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Ali Safari & Masoud Tahani

  2. Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Seyed Mahmoud Hosseini

Authors
  1. Ali Safari
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  2. Masoud Tahani
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  3. Seyed Mahmoud Hosseini
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Correspondence to Seyed Mahmoud Hosseini.

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Safari, A., Tahani, M. & Hosseini, S.M. Two-dimensional dynamic analysis of thermal stresses in a finite-length FG thick hollow cylinder subjected to thermal shock loading using an analytical method. Acta Mech 220, 299–314 (2011). https://doi.org/10.1007/s00707-011-0478-y

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  • DOI: https://doi.org/10.1007/s00707-011-0478-y

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