Journal of Mathematical Sciences

, Volume 183, Issue 2, pp 177–189 | Cite as

Thermostressed state of a composite plate with heat exchange under the action of a uniformly distributed heat source

  • N. O. Horechko
  • R. M. Kushnir

An analytic-numerical approach to the construction of solutions of two-dimensional (in spatial coordinates) quasistatic problems of thermoelasticity for piecewise-homogeneous bodies is proposed. Using this approach, we represent the solution of the thermoelasticity problem for a composite unbounded plate heated by the environment and a uniformly distributed heat source in the form of series in multiple error integrals. On the basis of these results, the corresponding heat and thermoelastic states of this composite plate are computed.


Heat Exchange Composite Plate Stress Function Thermoelasticity Problem Thermomechanical Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. O. Horechko and R. M. Kushnir, “Computation of the quasistatic thermostressed state of contacting semibounded bodies,” Mat. Met. Fiz.-Mekh. Polya, 48, No. 3, 82–87 (2005).Google Scholar
  2. 2.
    N. O. Horechko and R. M. Kushnir, “Analysis of the nonstationary thermoelastic state of a tribosystem in the process of braking,” Fiz.-Khim. Mekh. Mater., 42, No. 5, 81–86 (2006); English translation : Mater. Sci., 42, No. 5, 665–672 (2006).CrossRefGoogle Scholar
  3. 3.
    V. A. Ditkin and A. P. Prudnikov, Integral Transformations and Operational Calculus [in Russian], Nauka, Moscow (1974).Google Scholar
  4. 4.
    R. M. Kushnir and Yu. A. Muzychuk, “On the determination of temperature stresses in composite plates,” Mat. Met. Fiz.-Mekh. Polya, Issue 16, 44–48 (1982).Google Scholar
  5. 5.
    R. Kushnir and N. Horechko, “Determination of a transient thermostressed state of a composite plate with heat exchange,” in: Abstracts of the Second International Scientific Conference “Contemporary Methods of Mechanics and Mathematics” (Lviv, May 25–29, 2008), Vol. 1, Lviv (2008), pp. 174–176.Google Scholar
  6. 6.
    Ya. S. Podstrigach and Yu. M. Kolyano, Transient Temperature Fields and Stresses in Thin Plates [in Russian], Naukova Dumka, Kyiv (1972).Google Scholar
  7. 7.
    Ya. S. Podstrigach, V. A. Lomakin, and Yu. M. Kolyano, Thermoelasticity of Bodies of Inhomogeneous Structure [in Russian], Naukova Dumka, Kyiv (1984).Google Scholar
  8. 8.
    A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions [in Russian], Fizmatlit, Moscow (2003).Google Scholar
  9. 9.
    M. Abramowitz and I. A. Stegun (editors), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards, Washington (1964).Google Scholar
  10. 10.
    P. K. Suetin, Classic Orthogonal Polynomials [in Russia], Nauka, Moscow (1979).Google Scholar
  11. 11.
    T. Atarashi and S. Minagawa, “Transient coupled-thermoelastic problem of heat conduction in a multilayered composite plate,” Int. J. Eng. Sci., 30, No. 10, 1543–1550 (1992).CrossRefGoogle Scholar
  12. 12.
    S. K. Bhullara and J. L. Wegnera, “Some transient thermoelastic plate problems,” J. Therm. Stresses, 32, No. 8, 768–790 (2009).CrossRefGoogle Scholar
  13. 13.
    M. R. Hetnarski and M. R. Eslami, Thermal Stresses—Advanced Theory and Applications, Springer, New York (2008).Google Scholar
  14. 14.
    Y. Tokovyy and C.-C. Ma, “Analytic solutions to the 2D elasticity and thermoelasticity problems for inhomogeneous planes and half-planes,” Arch. Appl. Mech., 79, No. 5, 441–456 (2009).MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  • N. O. Horechko
    • 1
  • R. M. Kushnir
    • 1
  1. 1.LvivUkraine

Personalised recommendations