Skip to main content
SpringerLink
Log in

Some non-classical thermoelasticity problems for a rectangular parallelepiped

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

In the Cartesian system of coordinates, thermoelastic equilibrium of an isotropic homogeneous rectangular parallelepiped is considered. On the lateral faces of a parallelepiped either symmetry or anti-symmetry conditions are defined while the top and bottom faces are free of stress. The problem is that to define the temperature on the top and bottom faces of a parallelepiped so that the normal displacement or the tangential displacements would take a priori fixed values on some two planes parallel to the bases. The problems are solved analytically using the method of separation of variables. The problems are non-classical, but they differ from other non-classical problems known in literature and are of a practical importance.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Khachikyan AS (2006) On harmonic and biharmonic problems for equations with nonclassical boundary conditions, (Russian). Izv Nats Akad Nauk Armen Mekh 59(4):24–31

    MathSciNet  Google Scholar 

  2. Sarkisyan VG (2007) A plane elasticity problem with non-classical boundary conditions. Actual problems of continuum mechanics. Proceedings of International Conference devoted to the 95th anniversary of Academician NAN of Armenia N. Kh. Arutyunyan, Yrevan, pp 373–376

  3. Agalovyan LA (2002) The solution asymptotics of classical and nonclassical, static and dynamic boundary-value problems for thin bodies. J Int Appl Mech 38(7):765–782. doi:10.1023/A:1020877123771

    Article  Google Scholar 

  4. Gordeziani DG (1984) A class of nonlocal boundary value problems in elasticity theory and shell theory, (Russian) Theory and numerical methods of calculating plates and shells. Tbilis Gos Univ II:106–127 (Russian)

    MathSciNet  Google Scholar 

  5. Obolashvili EI (1987) Solution of nonlocal problems in plane elasticity theory, (Russian) Current problems in mathematical physics. Tbilis Gos Univ II:295–302 (Russian)

    MathSciNet  Google Scholar 

  6. Bitsadze AV (1984) On the theory of nonlocal boundary value problems, (Russian). Dokl Akad Nauk SSSR 277(1):17–19

    MathSciNet  Google Scholar 

  7. Avalishvili G, Avalishvili M, Gordeziani D (2011) On integral nonlocal boundary value problems for some partial differential equations. Bull Georgian Natl Acad Sci (N.S.) 5(1):31–37

    MATH  MathSciNet  Google Scholar 

  8. Avalishvili G, Avalishvili M, Gordeziani D (2010) On some non-classical two-dimensional models for thermoelastic plates with variable thickness. Bull Georgian Natl Acad Sci (N.S.) 4(2):27–34

    MATH  MathSciNet  Google Scholar 

  9. Sladek J, Sladek V, Baant ZP (2003) Non-local boundary integral formulation for softening damage. Int J Numer Meth Eng 57(1):103–116

    Article  MATH  Google Scholar 

  10. Dehghan Mehdi (2002) Numerical solution of a non-local boundary value problem with Neumann’s boundary conditions. Commun Numer Methods Eng 19(1):1–12

    Article  MathSciNet  Google Scholar 

  11. Gordeziani D, Gordeziani E, Davitashvili T, Meladze G (2010) About the solution of some nonlocal boundary and initial-boundary value problems. GESJ Comput Sci Telecommun 3(26):161–169 (Russian)

    Google Scholar 

  12. Chirita S (2012) On the final boundary value problems in linear thermoelasticity. Meccanica 47(8):2005–2011

    Article  MathSciNet  Google Scholar 

  13. Khomasuridze N (1998) Thermoelastic equilibrium of bodies in generalized cylindrical coordinates. Georgian Math J 5(6):521–544

    Article  MATH  MathSciNet  Google Scholar 

  14. Khomasuridze N (2001) Thermoelastic stress of multilayer cylindrical bodies. J Therm Stress 24:919–936

    Article  Google Scholar 

  15. Khomasuridze NG (2007) On the symmetry principle in continuum mechanics, (Russian). Prikl Mat Mekh 71(1):23–32 Translation in J. Appl. Math. Mech., vol. 71, no. 1, pp. 20–29

    MATH  MathSciNet  Google Scholar 

  16. Boley BA, Weiner JH (1985) Theory of thermal stresses. Krieger Publishing Company, Malabar

    Google Scholar 

Download references

Acknowledgments

This work was supported by Shota Rustaveli National Scientific Foundation, AR/91/5-109/11.

Author information

Authors and Affiliations

  1. I.Vekua Institute of Applied Mathematics of Iv. Javakhisvili Tbilisi State University, 2 University St, 0186, Tbilisi, Georgia

    N. Khomasuridze, R. Janjgava & N. Zirakashvili

  2. University Of Georgia, 77a Kostava Street, 0171, Tbilisi, Georgia

    R. Janjgava & N. Zirakashvili

Authors
  1. N. Khomasuridze
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Janjgava
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Zirakashvili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Khomasuridze.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khomasuridze, N., Janjgava, R. & Zirakashvili, N. Some non-classical thermoelasticity problems for a rectangular parallelepiped. Meccanica 49, 1337–1342 (2014). https://doi.org/10.1007/s11012-014-9897-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-014-9897-x

Keywords

Search

Navigation