Continuum Mechanics and Thermodynamics

, Volume 30, Issue 3, pp 509–527 | Cite as

Determination of the thermal stress wave propagation in orthotropic hollow cylinder based on classical theory of thermoelasticity

Original Article
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Abstract

The thermoelasticity problem in a thick-walled orthotropic hollow cylinder is solved analytically using finite Hankel transform and Laplace transform. Time-dependent thermal and mechanical boundary conditions are applied on the inner and the outer surfaces of the cylinder. For solving the energy equation, the temperature itself is considered as boundary condition to be applied on both the inner and the outer surfaces of the orthotropic cylinder. Two different cases are assumed for solving the equation of motion: traction–traction problem (tractions are prescribed on both the inner and the outer surfaces) and traction–displacement (traction is prescribed on the inner surface and displacement is prescribed on the outer surface of the hollow orthotropic cylinder). Due to considering uncoupled theory, after obtaining temperature distribution, the dynamical structural problem is solved and closed-form relations are derived for radial displacement, radial and hoop stress. As a case study, exponentially decaying temperature with respect to time is prescribed on the inner surface of the cylinder and the temperature of the outer surface is considered to be zero. Owing to solving dynamical problem, the stress wave propagation and its reflections were observed after plotting the results in both cases.

Keywords

Classical thermoelasticity Orthotropic cylinder Hankel transform Stress wave 

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References

  1. 1.
    Yen, A.C., Kirmser, P.G.: On the thermal stresses in a finite circular cylinder. J. Eng. Math. 5(1), 19–32 (1971)CrossRefMATHGoogle Scholar
  2. 2.
    Kardomateas, G.A.: Thermoelastic stresses in a filament-wound orthotropic composite elliptic cylinder due to a uniform temperature change. IJSS 26(5–6), 527–537 (1990)MATHGoogle Scholar
  3. 3.
    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. Model. 31(9), 1807–1818 (2007)CrossRefMATHGoogle Scholar
  4. 4.
    Shahani, A.R., Momeni Bashusqeh, S.: Analytical solution of the thermoelasticity problem in a pressurized thick-walled sphere subjected to transient thermal loading. MMS 19(2), 135–151 (2014)MathSciNetMATHGoogle Scholar
  5. 5.
    Shahani, A.R., Momeni Bashusqeh, S.: Analytical solution of the coupled thermo-elasticity problem in a pressurized sphere. JThSt 36(12), 1283–1307 (2013)Google Scholar
  6. 6.
    Yee, K.-C., Moon, T.J.: Plane thermal stress analysis of an orthotropic cylinder subjected to an arbitrary, transient asymmetric temperature distribution. J. Appl. Mech. 69(5), 632–640 (2002)ADSCrossRefMATHGoogle Scholar
  7. 7.
    Wang, X.: Thermal shock in a hollow cylinder caused by rapid arbitrary heating. J. Sound Vib. 183(5), 899–906 (1995)ADSCrossRefMATHGoogle Scholar
  8. 8.
    Cho, H., Kardomateas, G.A., Valle, C.S.: Elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell. J. Appl. Mech. 65(1), 184–193 (1998)ADSCrossRefGoogle Scholar
  9. 9.
    Ding, H.J., Wang, H.M., Chen, W.Q.: A solution of a non-homogeneous orthotropic cylindrical shell for axisymmetric plane strain dynamic thermoelastic problems. J. Sound Vib. 263(4), 815–829 (2003)ADSCrossRefGoogle Scholar
  10. 10.
    Jabbari, M., Dehbani, H., Eslami, M.R.: An exact solution for classic coupled thermoelasticity in cylindrical coordinates. J. Press. Vessel Technol. 133(1), 1–10 (2011)Google Scholar
  11. 11.
    Goshima, T., Miyao, K.: Transient thermal stresses in a hollow cylinder subjected to y-ray heating and convective heat losses. NuEnD 125(2), 267–273 (1991)Google Scholar
  12. 12.
    Zhang, Q., Wang, Z.W., Tang, C.Y., Hu, D.P., Liu, P.Q., Xia, L.Z.: Analytical solution of the thermo-mechanical stresses in a multilayered composite pressure vessel considering the influence of the closed ends. Int. J. Press. Vessels Pip. 98(1), 102–110 (2012)CrossRefGoogle Scholar
  13. 13.
    Abd-Alla, A.M., Abd-Alla, A.N., Zeidan, N.A.: Transient thermal stresses in a transversely isotropic infinite circular cylinder. Appl. Math. Comput. 121(1), 93–122 (2001)MathSciNetMATHGoogle Scholar
  14. 14.
    Kouchakzadeh, M.A., Entezari, A.: Analytical solution of classic coupled thermoelasticity problem in a rotating disk. JThSt 38(1), 1269–1291 (2015)Google Scholar
  15. 15.
    Shahani, A.R., Sharifi torki, H.: Analytical solution of the thermoelasticity problem in thick-walled cylinder subjected to transient thermal loading. MME 16(10), 147–154 (2016). (in Persian)Google Scholar
  16. 16.
    Marin, M.: On weak solutions in elasticity of dipolar bodies with voids. JCoAM 82(1–2), 291–297 (1997)MathSciNetMATHGoogle Scholar
  17. 17.
    Marin, M.: Harmonic vibrations in thermoelasticity of microstretch materials. J. Vib. Acoust. 132(4), 1–6 (2010)CrossRefGoogle Scholar
  18. 18.
    Sharma, K., Marin, M.: Effect of distinct conductive and thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space. U.P.B. Sci. Bull. 75(2), 121–132 (2013)MathSciNetMATHGoogle Scholar
  19. 19.
    Decolon, C.: Analysis of Composite Structures. Hermes Penton Ltd, London (2002)MATHGoogle Scholar
  20. 20.
    Rand, O., Rovenski, V.: Analytical Methods in Anisotropic Elasticity. Springer, Birkhauser Boston (2004)MATHGoogle Scholar
  21. 21.
    Hahn, W.D., Necati O Zisik, A.: Heat Conduction, 3rd edn. Wiley, Hoboken (2012)CrossRefGoogle Scholar
  22. 22.
    Sneddon, I.N.: The Use of Integral Transform. Mc-Graw-Hill Book Company, New York (1972)MATHGoogle Scholar
  23. 23.
    Cinelli, G.: An extension of the finite hankel transform and applications. IJES 3, 539–559 (1965)MathSciNetMATHGoogle Scholar
  24. 24.
    Cho, H., Kardomateas, G.A.: Thermal shock stresses due to heat convection at a bounding surface in a thick orthotropic cylinderical shell. IJSS 38, 2769–2788 (2001)MATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.K.N. Toosi University of TechnologyTehranIran

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