Skip to main content
SpringerLink
Log in

Method for direct integration of the equations of an axisymmetric problem on thermoelasticity in stresses for unbounded regions

  • Published:
International Applied Mechanics Aims and scope

Abstract

We consider a method for direct integration of equilibrium and consistency equations for axisymmetric quasistatic thermoelasticity problems in regions with unbounded radial coordinates. Relations between stress tensor components are obtained. We derive a system of two integro-differential equations in stresses and an equivalent system of differential equations. We present solutions for the thermoelasticity problem and integral equilibrium conditions for the first stress invariant for a space, half-space, and unbounded layer.

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. B. Boli and J. Weiner,The Theory of Thermal Stress [Russian translation], Mir, Moscow (1964).

    Google Scholar 

  2. V. M. Vigak,Control of Thermal Stress and Displacement [in Russian], Nauk. Dumka, Kiev (1988).

    Google Scholar 

  3. V. M. Vigak, “Solution of plane problem of thermoelasticity for a rectangular region,”Dop. NAN Ukrainy, No. 12, 58–62 (1994).

    Google Scholar 

  4. V. M. Vigak, “Structure of solution of plane problem of elasticity for a rectangular region,”Dop. NAN Ukrainy, No. 10, 41–45 (1995).

    Google Scholar 

  5. V. M. Vigak, “Solutions of stress problems of the theory of elasticity and thermoelasticity,” in:Integral Transformations and their Applications to Boundary-Value Problems [in Ukrainian], Issue 9, 34–122 (1995).

  6. V. M. Vigak, “Direct method of integration of equations of plane problems of elasticity and thermoelasticity,”Dop. NAN Ukrainy, No. 12, 62–67 (1998).

    Google Scholar 

  7. V. M. Vigak, “Direct method of integration of equations of plane problems of elasticity and thermoelasticity for orthotropic materials,”Mat. Metody i Fiz.-Mekh. Polya, No. 1 (40), 24–29 (1997).

    Google Scholar 

  8. A. D. Kovalenko,Fundamental Thermoelasticity [in Russian], Nauk. Dumka, Kiev (1981).

    Google Scholar 

  9. M. A. Koltunov, Yu. N. Vasil'ev, and V. A. Chernykh,Elasticity and Stability of Cylindrical Bodies [in Russian], Vyssh. Shk., Moscow (1975).

    Google Scholar 

  10. A. I. Lur'e,Three-Dimensional Problems in the Theory of Elasticity [in Russian], Gosizdat Tekhn. Theoret. Lit., Moscow (1955).

    Google Scholar 

  11. P. F. Papkovich,The Theory of Elasticity [in Russian], Oborongiz, Moscow-Leningrad (1939).

    Google Scholar 

  12. I. Sneddon,The Fourier Transform [Russian translation], Izd. Inostr. Lit., Moscow (1955).

    Google Scholar 

  13. Kh. Khan,The Theory of Elasticity [Russian translation], Mir, Moscow (1988).

    Google Scholar 

Download references

Authors
  1. V. M. Vigak
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Ya. S. Podstrigach Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, L'vov, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 49–56, March, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vigak, V.M. Method for direct integration of the equations of an axisymmetric problem on thermoelasticity in stresses for unbounded regions. Int Appl Mech 35, 262–268 (1999). https://doi.org/10.1007/BF02682121

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02682121

Keywords

Search

Navigation