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Generalized Thermoelasticity of Thermal-Shock Problem in a Non-homogeneous Isotropic Hollow Cylinder with Energy Dissipation

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Abstract

A solution of a thermal-shock problem of generalized thermoelasticity of a non-homogeneous isotropic hollow cylinder using a finite-element method is developed. The formulation is applied to the generalized thermoelasticity based on the Green and Naghdi (GN) theory of type II and type III by an appropriate choice of parameters. The problem has been solved numerically using a finite-element method. Numerical results for the distributions of displacement, temperature, radial stress, and hoop stress are represented graphically. The results indicate that the effects of non-homogeneity are very pronounced. The effects of non-homogeneity are presented with the two types of the Green and Naghdi theory.

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References

  1. Biot M.: J. Appl. Phys. 27, 240 (1956)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Lord H., Shulman Y.: J. Mech. Phys. Solids 15, 299 (1967)

    Article  ADS  MATH  Google Scholar 

  3. Green A.E., Lindsay K.A.: J. Elasticity 2, 1 (1972)

    Article  MATH  Google Scholar 

  4. Ignaczak J.: Shock Vib. Dig. 13, 3 (1981)

    Article  Google Scholar 

  5. L. Bahar, R. Hetnarski, in Proceedings 6th Canadian Congress on Applied Mechanics (University of British Columbia, Vancouver, 1977), p. 17

  6. L. Bahar, R. Hetnarski, in Proceedings of 15th Midwest Mechanic Conference (University of Illinois, Chicago, 1977), p. 161

  7. Erbay S., Suhubi E.S.: J. Therm. Stresses 9, 279 (1986)

    Article  Google Scholar 

  8. Furukawa T., Noda N., Ashida F.: JSME Int. J. 31, 26 (1990)

    Google Scholar 

  9. Sharma J.N., Chand D.: Int. J. Eng. Sci. 30, 223 (1992)

    Article  MATH  Google Scholar 

  10. Chandrasekharaiah D.S., Murthy H.N.: J. Therm. Stresses 16, 55 (1993)

    Article  Google Scholar 

  11. Misra J.C., Chattopadhyay N.C., Samanta S.C.: Comp. Struc. 52, 705 (1994)

    Article  MATH  Google Scholar 

  12. Othman M.I.A.: Int. J. Solids Struct. 41, 2939 (2004)

    Article  MATH  Google Scholar 

  13. Othman M.I.A., Song YQ: Appl. Math. Modell. 32, 483 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Othman M.I.A.: Can. J. Phys. 81, 1403 (2003)

    Article  ADS  Google Scholar 

  15. El-Maghraby N.M., Youssef H.: Appl. Math. Comp. 156, 577 (2004)

    Article  MATH  Google Scholar 

  16. D.E. Carlson, in Handbuch der Physik, via/2 (Springer, Berlin, 1972), p. 297

  17. Hetnarski R.B., Ignazack J.: J. Therm. Stresses 22, 451 (1999)

    Article  Google Scholar 

  18. Green A.E., Naghdi P.M.: Proc. R. Soc. London, Ser. A 432, 171 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Green A.E., Naghdi P.M.: J. Therm. Stresses 15, 253 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  20. Green A.E., Naghdi P.M.: J. Elast. 31, 189 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  21. Chandrasekharaiah D.S., Srinath K.S.: J. Therm. Stresses 16, 55 (1993)

    Article  Google Scholar 

  22. Othman M.I.A., Song Y.Q.: Acta Mech. 184, 189 (2006)

    Article  MATH  Google Scholar 

  23. Othman M.I.A., Song Y.Q.: Int. J. Solids Struct. 44, 5651 (2007)

    Article  MATH  Google Scholar 

  24. Zienkiewicz O.C., Taylor R.L.: The Finite Element Method. Fluid Dynamics, 5th edn. Butterworth–Heinemann, Oxford (2000)

    Google Scholar 

  25. Abbas I.A.: Forsch. Ing. 71, 215 (2007)

    Article  Google Scholar 

  26. Youssef H., Abbas I.A.: Comput. Methods Sci. Tech. 13, 95 (2007)

    Google Scholar 

  27. Abbas I.A, Abd-allah A.N.: Arch. Appl. Mech. 78, 283 (2008)

    Article  ADS  MATH  Google Scholar 

  28. Misra J.C., Samanta S.C., Chakraborty A.K., Misra S.C.: Int. J. Eng. Sci. 29, 1505 (1991)

    Article  MATH  Google Scholar 

  29. Reddy J.N.: An Introduction to the Finite Element Method, 2nd edn. McGraw-Hill, New York (1993)

    Google Scholar 

  30. Cook R.D., Malkus D.S., Plesha M.E.: Concepts and Applications of Finite Element Analysis, 3rd edn. Wiley, New York (1989)

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt

    Mohamed I. A. Othman

  2. Department of Mathematics, Faculty of Sciences and Arts-Khulais, King AbdulAziz University, Jeddah, Saudi Arabia

    Ibrahim A. Abbas

  3. Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt

    Ibrahim A. Abbas

Authors
  1. Mohamed I. A. Othman
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  2. Ibrahim A. Abbas
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Correspondence to Mohamed I. A. Othman.

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Othman, M.I.A., Abbas, I.A. Generalized Thermoelasticity of Thermal-Shock Problem in a Non-homogeneous Isotropic Hollow Cylinder with Energy Dissipation. Int J Thermophys 33, 913–923 (2012). https://doi.org/10.1007/s10765-012-1202-4

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  • DOI: https://doi.org/10.1007/s10765-012-1202-4

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