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Plane Waves in Generalized Thermo-microstretch Elastic Solid with Thermal Relaxation Using Finite Element Method

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Abstract

The propagation of plane waves in a thermo-microstretch elastic solid half-space as proposed by Lord–Shulman as well as the classical dynamical coupled theory are discussed. The problem has been solved numerically using a finite element method. Numerical results for the displacement components, force stresses, temperature, couple stresses, and microstress distribution are obtained. The variations of the considered variables through the horizontal distance are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity for different values of the relaxation time.

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References

  1. Eringen A.C.: Ari Kitabevi Matbassi Istanbul 24, 1 (1971)

    Google Scholar 

  2. Eringen A.C.: J. Math. Mech. 15, 909 (1966)

    MathSciNet  MATH  Google Scholar 

  3. Eringen A.C.: Int. J. Eng. Sci. 28, 1291 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bofill F., Quintanilla R.: Int. J. Eng. Sci. 33, 2115 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  5. Iesan D., Quintanilla R.: Int. J. Eng. Sci. 43, 885 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Svanadze M., De Cicco S.: Int. J. Eng. Sci. 43, 417 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Iesan D., Scalia A.: Int. J. Eng. Sci. 44, 845 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Othman M.I.A., Lotfy Kh.: Multi. Model. Mater. Struct. 7, 43 (2011)

    Google Scholar 

  9. Eringen A.C.: Microcontinuum Field Theories I: Foundation and Solids. Springer, New York (1999)

    Book  Google Scholar 

  10. Iesau D., Nappa L.: Int. J. Eng. Sci. 39, 1815 (2001)

    Article  Google Scholar 

  11. Iesau D., Pompei A.: Int. J. Eng. Sci. 33, 399 (1995)

    Article  Google Scholar 

  12. De Cicco S.: Int. J. Eng. Sci. 41, 187 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  15. Muller I.M.: Arch. Ration. Mech. Anal. 41, 319 (1971)

    Article  Google Scholar 

  16. Green A.E., Laws N.: Arch. Ration. Mech. Anal. 45, 47 (1972)

    Article  MathSciNet  Google Scholar 

  17. Green A.E., Lindsay K.A.: J. Elast. 2, 1 (1972)

    Article  MATH  Google Scholar 

  18. E.S. Suhubi, Thermoelastic Solids, in Continuum Physics, ed. by A.C. Eringen (Academic Press, London, 1975)

  19. Kumar R., Singh B.: Proc. Ind. Acad. Sci. (Math. Sci.) 106, 183 (1996)

    Article  MATH  Google Scholar 

  20. Kumar R., Singh B.: Int. J. Eng. Sci. 36, 891 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  21. Othman M.I.A.: J. Therm. Stresses 25, 1027 (2002)

    Article  Google Scholar 

  22. Othman M.I.A., Singh B.: Int. J. Solids Struct. 44, 2748 (2007)

    Article  MATH  Google Scholar 

  23. Abbas I.A.: Forschung im Ingenieurwesen 71, 215 (2007)

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  26. Abbas I.A.: Forschung im Ingenieurwesen 72, 101 (2008)

    Article  Google Scholar 

  27. Abbas I.A., Othman M.I.A.: Int. J. Ind. Math. 1, 121 (2009)

    Google Scholar 

  28. Wriggers P.: Nonlinear Finite Element Methods. Springer, Berlin (2008)

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts–Khulais, King Abdulaziz University, Jeddah, Saudi Arabia

    Ibrahim A. Abbas

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

    Ibrahim A. Abbas

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

    Mohamed I. A. Othman

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

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Abbas, I.A., Othman, M.I.A. Plane Waves in Generalized Thermo-microstretch Elastic Solid with Thermal Relaxation Using Finite Element Method. Int J Thermophys 33, 2407–2423 (2012). https://doi.org/10.1007/s10765-012-1340-8

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  • DOI: https://doi.org/10.1007/s10765-012-1340-8

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