Materials Science

, Volume 40, Issue 3, pp 365–375 | Cite as

Centrally symmetric quasistatic problem of thermoelasticity for a temperature sensitive body

  • V. S. Popovych
  • H. T. Sulym


The perturbation method is used to construct the general solution of a centrally symmetric quasistatic problem of elasticity under the assumption that all thermomechanical characteristics of a body are functions of temperature. As special cases, we obtain the solutions of the corresponding problems of thermoelasticity for hollow and continuous balls and a space containing a spherical cavity. We also perform the numerical analysis of the temperature field and the stress-strain state induced by this field in the space with spherical cavity free of external loads. Note that the process of convective heat exchange with an ambient medium of constant temperature is realized through this cavity.


Constant Temperature General Solution Temperature Field Heat Exchange Convective Heat 
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  1. 1.
    Lomakin, V. A. 1976Theory of Elasticity for Inhomogeneous BodiesMoscow UniversityMoscow[in Russian]Google Scholar
  2. 2.
    Kolyano, Y. M. 1992Methods of Heat Conduction and Thermoelasticity for Inhomogeneous BodiesNaukova DumkaKiev[in Russian]Google Scholar
  3. 3.
    Popovych, V. S., Harmatii, H. Y. 1993Numerical-Analytic Methods for the Construction of Solutions of the Problems of Heat Conduction for Temperature-Sensitive Bodies Under the Conditions of Convective Heat TransferUkrainian Academy of SciencesLviv[in Ukrainian], Preprint No. 13-93, Pidstryhach Institute for Applied Problems in Mechanics and MathematicsGoogle Scholar
  4. 4.
    Postol’nik, Y. S., Ogurtsov, A. P. 2000Nonlinear Applied ThermomechanicsNMTs VO MONTsKiev[in Ukrainian]Google Scholar
  5. 5.
    Postol’nik, Y. S., Ogurtsov, A. P. 2002Metallurgical ThermomechanicsSystemni TekhnologiiDnipropetrovs’k[in Ukrainian]Google Scholar
  6. 6.
    Nowinski, J. 1962Transient thermoelastic problem for an infinite medium with a spherical cavity exhibiting temperature-dependent propertiesJ. Appl. Mech.29197205Google Scholar
  7. 7.
    Parkus, H. 1963Instationäre WärmespannungenFizmatgizMoscowRussian translationGoogle Scholar
  8. 8.
    Nowacki, W. 1962Zagadnienia TermosprężystościIzd. Akad. Nauk SSSRMoscow[Russian translation]Google Scholar
  9. 9.
    Fikhtengol’ts, G. M. 1969A Course of Differential and Integral CalculusNaukaMoscow[in Russian]Google Scholar
  10. 10.
    V. S. Popovych and H. Yu. Harmatii, “Nonstationary problem of heat conduction for a temperature sensitive space containing a spherical cavity,” Matem. Met. Fiz.-Khim. Polya, Issue 37, 100–104 (1994).Google Scholar
  11. 11.
    Abramowitz, M.Stegun, I. A. eds. 1979Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical TablesNaukaMoscow[Russian translation]Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • V. S. Popovych
    • 1
    • 2
  • H. T. Sulym
    • 1
    • 2
  1. 1.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian Academy of SciencesLviv
  2. 2.Franko Lviv National UniversityLviv

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