Skip to main content
SpringerLink
Log in

Thermomechanical Deformation in an Orthotropic Micropolar Thermoelastic Solid

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

The thermomechanical deformation in an orthotropic micropolar generalized thermoelastic half-space is investigated. Descarte’s method, along with the irreducible case of Cardon’s method, is used to obtain the roots of an eight-degree equation. Laplace and Fourier transform techniques are used to obtain the general solution for the set of boundary value problems. Particular types of boundary conditions have been taken to illustrate the utility of the approach. The transformed components of the stresses and temperature distribution have been obtained. A numerical inversion technique is employed to invert the integral transform, and the resulting quantities are presented graphically.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Eringen A.C., Suhubi E.S.: Int. J. Eng. Sci. 2, 189 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  2. Eringen A.C.: J. Math. Mech. 15, 909 (1996)

    MathSciNet  Google Scholar 

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

    Article  MATH  ADS  Google Scholar 

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

    Article  MATH  Google Scholar 

  5. Dhaliwal R., Sherief H.: Quart. Appl. Math. 23, 1 (1980)

    MathSciNet  Google Scholar 

  6. Wang C.Y., Achenbach J.D.: Wave Motion 16, 389 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  7. Wu K.C.: J. Acoust. Soc. Am. 109, 2625 (2001)

    Article  ADS  Google Scholar 

  8. W. Nowacki, “Couple stress in the theory of thermoelasticity,” in Proceedings of ITUAM Symposia, Vienna, ed. by H. Parkus, L.I. Sedov (Springer-Verlag, New York, 1966), pp. 259–278

  9. A.C. Eringen, Foundations of Micropolar Thermoelasticity, Course of Lectures No. 23, CSIM, Udine, Italy (Springer-Verlag, New York, 1970)

  10. Tauchert T.R., Claus W.D., Ariman T.: Int. J. Eng. Sci. 6, 36 (1968)

    Article  Google Scholar 

  11. Dost S., Tabarrok B.: Int. J. Eng. Sci. 16, 173 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  12. Chandrasekhariah D.S.: Int. J. Eng. Sci. 24, 1389 (1986)

    Article  Google Scholar 

  13. Martynenko M.D., Bosyakov S.M.: J. Eng. Phys. Thermophys. 73, 1004 (2000)

    Article  Google Scholar 

  14. M. Al. Hasan, J. Dyszlewicz, J. Therm. Stresses 24, 1007 (2000)

  15. M. Al. Hasan, J. Dyszlewicz, J. Therm. Stresses 24, 709 (2001)

  16. Tian-Min D.: Appl. Math. Mech. 23(2), 119 (2002)

    Article  Google Scholar 

  17. Martynenko M.D., Bosyakov S.M.: J. Eng. Phys. Thermophys. 75, 41 (2002)

    Article  Google Scholar 

  18. Kumar R., Ailawalia P.: Eur. J. Mech. A-Solids 25, 271 (2006)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. Kumar R., Ailawalia P.: Int. J. Solids Struct. 43, 2761 (2006)

    Article  MATH  Google Scholar 

  20. Kumar R., Ailawalia P.: Int. J. Solids Struct. 44, 4063 (2007)

    Google Scholar 

  21. Kumar R., Ailawalia P.: Int. J. Thermophys. 28, 342 (2007)

    Article  Google Scholar 

  22. Iesan D.: J. Eng. Math. 8, 107 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  23. Kumar R., Choudhary S.: Meccanica 38, 349 (2003)

    Article  MATH  Google Scholar 

  24. Kumar R., Choudhary S.: J. Sound Vibration 239, 467 (2001)

    Article  ADS  Google Scholar 

  25. Kumar R., Choudhary S.: Sadhana 29, 83 (2004)

    Article  MATH  Google Scholar 

  26. Bahar L.Y., Hetnarski R.B.: J. Therm. Stresses 1, 135 (1978)

    Article  Google Scholar 

  27. R. S. Dhaliwal, A. Singh, “Micropolar thermoelasticity”, in Thermal Stresses II, Mechanical and Mathematical Methods, Ser. 2, ed. by R. Hetarski (North-Holland, Amsterdam, 1987)

  28. Kumar R., Deswal S.: J. Sound Vibration 239, 467 (2001)

    Article  ADS  Google Scholar 

  29. Honig G., Hirdes V.: J. Comput. Appl. Math. 10, 113 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  30. Press W.H., Teukolshy S.A., Vellering W.T., Flannery B.P.: Numerical Recipes. Cambridge University Press, Cambridge (1986)

    Google Scholar 

  31. R. D. Gauthier, “Experimental investigations on micropolar media”, in Mechanics of Micropolar Media, ed. by O. Brulin, R.K.T Hsieh (World Scientific, Singapore, 1982)

  32. Ezzat M.A., Othman M.I., Smaan A.A.: Int. J. Eng. Sci. 39, 1383 (2001)

    Article  Google Scholar 

  33. Chandrasekhariah D.S., Srinath K.S.: J. Elast. 46, 19 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India

    Rajneesh Kumar & Rajani Rani Gupta

Authors
  1. Rajneesh Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rajani Rani Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rajneesh Kumar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kumar, R., Gupta, R.R. Thermomechanical Deformation in an Orthotropic Micropolar Thermoelastic Solid. Int J Thermophys 30, 693–709 (2009). https://doi.org/10.1007/s10765-008-0527-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10765-008-0527-5

Keywords

Search

Navigation