Skip to main content
SpringerLink
Log in

The stressed state of piecewise-homogeneous bodies subject to nonsteady thermal fields

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

The study of the distribution of thermal fields and the thermal stresses they generate, and the influence of these factors on the strength of piecewise-homogeneous bodies was begun and developed in the work of Ya. S. Pidstrigach, Yu. M. Kolyano, and their students [5, 12, 13]. In the present paper we use the theory of generalized functions to reduce the two-dimensional quasistatic problem of thermal stresses for piecewisehomogeneous bodies to solving systems of integral equations. The kernels of these equations are chosen as the corresponding Green's functions. We obtain a single system of integral equations for the entire region under consideration. To solve the system we apply the method of boundary elements [2]. On the basis of the results obtained we carry out a study of the thermostressed state of a half-plane with rectangular inclusions.

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

Literature Cited

  1. V. G. Balan and V. I. Lavrenyuk. “A study of the thermostressed state of piecewise-homogeneous bodies,” Preprint, Ukrainian Institute for Scientific Information, No. 1821 (1988).

  2. C. Brebbia, J. Telles, and L. Wrobel,The Boundary-element Method [Russian translation], Mir, Moscow (1987)

    Google Scholar 

  3. V. S. Vladimirov,The Equations of Mathematical Physics, Dekker, New York (1971).

    Google Scholar 

  4. V. Kech and P. Theodorescu,Introduction to the Theory of Generalized Functions with Applications in Engineering [Russian translation], Mir, Moscow (1978).

    Google Scholar 

  5. Yu. M. Kolyano, A. N. Kulik, and R. M. Kushnir, “On the formulation of the generalized coupling problem for the equations of thermoelasticity of piecewise-homogeneous bodies,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 2, 44–49 (1980).

    Google Scholar 

  6. V. I. Lavrenyuk, “On the solution of thermomechanical problems for piecewise-homogeneous bodies,” in:Mechanics of Inhomogeneous Structures: Proceedings of the First All-Union Conference [in Russian], Naukova Dumka, Kiev (1986), pp. 117–122.

    Google Scholar 

  7. V. A. Lomakin,Theory of Elasticity of Nonhomogeneous Bodies [in Russian], Moscow State University Press (1976).

  8. V. M. Maizel',The Temperature Problem of Elasticity Theory [in Russian], Ukrainian Academy of Sciences Press (1951).

  9. E. Melan and G. Parkus,Thermal stresses Caused by Steady Temperature Fields, [in Russian], Fizmatgiz, Moscow (1958).

    Google Scholar 

  10. W. Nowacki,Problems of Thermoelasticity [Russian translation], Mir, Moscow (1962).

    Google Scholar 

  11. W. Nowacki,Theory of Elasticity, [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  12. Ya. S. Podstrigach and Yu. M. Kolyano,Generalized Thermomechanics [in Russian], Naukova Dumka, Kiev (1976).

    Google Scholar 

  13. Ya. S. Podstrigach, V. A. Lomakin, and Yu. M. Kolyano,Thermoelasticity of Bodies of Inhomogeneous Structure [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  14. V. N. Tereshchenko, “Green's functions for the quasistatic problem of thermoelasticity,”Obchisl. Prikl. Mat., No. 77, 97–104 (1993).

    MATH  Google Scholar 

  15. V. M. Tereshchenko, “Green's functions for nonsteady problems of thermoelasticity,” Preprint No. 1462-Uk92, Kiev (1992).

Download references

Authors
  1. V. I. Lavrenyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. M. Tereshchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematichni Metodi i Fiziko-mekhnichni Polya, Vol. 40, No. 1, 1997, pp. 53–58.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lavrenyuk, V.I., Tereshchenko, V.M. The stressed state of piecewise-homogeneous bodies subject to nonsteady thermal fields. J Math Sci 88, 368–373 (1998). https://doi.org/10.1007/BF02365254

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02365254

Keywords

Search

Navigation