Advertisement

Journal of Mathematical Sciences

, Volume 165, Issue 3, pp 355–370 | Cite as

Thermoelastic contact of half-spaces with equal thermal distortivities in the presence of a heat-permeable intersurface gap

  • R. M. Martynyak
  • K. A. Chumak
Article

We consider the interaction of elastic half-spaces with equal thermal distortivities in the presence of a heat-permeable medium in an intercontact gap caused by a recess on the surface of one of the bodies. Outside the gap, a perfect thermal and frictionless mechanical contact takes place between the bodies. Using the method of functions of intercontact gaps, the formulated contact problem is reduced to a singular integral equation for a derivative of the height of the gap, which is solved analytically, and to a Prandtl-type singular integro-differential equation for the difference of temperature of the surfaces in the region of the gap, for the solution of which we propose an analytic-numerical approach. Plots illustrate the influence of load and the thermal conductivity of the filler on the temperature difference between the edges of the gap, contact stresses, heat flows, and longitudinal strains between the half-spaces.

Keywords

Thermal Conductivity Heat Flow Contact Problem Longitudinal Strain Singular Integral Equation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K. L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge (1985).MATHGoogle Scholar
  2. 2.
    H. S. Kit, R. M. Martynyak, and I. M. Machishin, “The effect of a fluid in the contact gap on the stress state of conjugate bodies,” Int. Appl. Mech., 39, No. 3, 292–299 (2003).CrossRefGoogle Scholar
  3. 3.
    H. S. Kit, R. M. Martynyak, and B. E. Monastyrskyy, “Thermoelastic interaction of bodies in the presence of a surface circular recess with regard for the contact thermal resistance,” Teor. Prikl. Mekh., Issue 37, 19–27 (2003).Google Scholar
  4. 4.
    H. S. Kit, V. F. Emets’, and Ya. I. Kunets’, “A model of the elastodynamic interaction of a thin-walled inclusion with a matrix under antiplanar shear,” J. Math. Sci., 97, No. 1, 3810–3816 (1999).CrossRefGoogle Scholar
  5. 5.
    H. S. Kit, R. M. Martynyak, and B. E. Monastyrskyy, “Method of potentials in problems on the local absence of equilibrium,” Visn. Dnipropetr. Univ. Ser. Mekh., 1, Issue 4, 69–77 (2001).Google Scholar
  6. 6.
    A. A. Krishtafovich and R. M. Martynyak, “Lamination of anisotropic half-spaces in the presence of contact thermal resistance,” Int. Appl. Mech., 35, No. 2, 159–164 (1999).CrossRefGoogle Scholar
  7. 7.
    V. D. Kubenko, “Nonstationary plane elastic contact problem for matched cylindrical surfaces,” Int. Appl. Mech., 40, No. 1, 51–60 (2004).CrossRefGoogle Scholar
  8. 8.
    R. Martynyak, A. Kryshtafovych, and I. Machyshyn, “Unilateral contact of bodies with conforming surfaces under the action of heat sources and sinks,” Visn. L’viv. Univ., Ser. Mekh.-Mat., Issue 55, 169–173 (1999).Google Scholar
  9. 9.
    R. M. Martynyak, “The contact of a half-space and an uneven base in the presence of an intercontact gap filled by an ideal gas,” J. Math. Sci., 107, No. 1, 3680–3685 (2004).CrossRefGoogle Scholar
  10. 10.
    R. M. Martynyak, “Contact interaction between two half-spaces in the presence of a surface recess partially filled with an incompressible liquid,” Mater. Sci., 26, No. 2, 205–208 (1990).CrossRefGoogle Scholar
  11. 11.
    R. M. Martynyak, “Mechanothermodiffusion interaction of bodies with regard for the filler of intercontact gaps,” Mater. Sci., 36, No. 2, 300–304 (2000).CrossRefGoogle Scholar
  12. 12.
    R. M. Martynyak, Mechanothermodiffusion Interaction of Bodies with Contact Surface Heterogeneities and Defects [in Ukrainian], Doctoral-Degree Thesis (Physics and Mathematics), Lviv (2000).Google Scholar
  13. 13.
    R. M. Martynyak, “Instability of thermoelastic interaction between a half-space and a rigid base through a thin liquid layer,” J. Math. Sci., 99, No. 5, 1607–1615 (2000).CrossRefGoogle Scholar
  14. 14.
    R. M. Martynyak and B. S. Slobodyan, “Interaction of two bodies in case of capillaries in intercontact gap,” Mat. Met. Fiz.-Mekh. Polya, 49, No. 1, 164–173 (2006).MATHGoogle Scholar
  15. 15.
    A. B. Movchan and S. A. Nazarov, “The stress-strain state at a tip of a sharp inclusion,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 155–163 (1986).Google Scholar
  16. 16.
    N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Springer, Berlin (1977).Google Scholar
  17. 17.
    V. V. Panasyuk, M. P. Savruk, and Z. T. Nazarchuk, Method of Singular Integral Equations in Two-Dimensional Diffraction Problems [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
  18. 18.
    Ya. S. Pidstryhach, “Conditions of thermal contact of solid bodies,” Dopov. Akad. Nauk Ukr. RSR, No. 7, 872–874 (1963).Google Scholar
  19. 19.
    Ya. S. Pidstryhach, “Temperature field in a system of solid bodies conjugated with a thin interlayer,” Inzh.-Fiz. Zh., 6, No. 10, 129–136 (1963).Google Scholar
  20. 20.
    H. T. Sulym, Bases of the Mathematical Theory of Thermoelastic Equilibrium of Deformable Solids with Thin Inclusions [in Ukrainian], Doslidno-Vydavnychyi Tsentr NTSh, Lviv (2007).Google Scholar
  21. 21.
    R. N. Shvets and R. M. Martynyak, “Integral equations of the contact problem of thermoelasticity for rough bodies,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 11, 59–63 (1985).Google Scholar
  22. 22.
    R. N. Shvets and R. M. Martynyak, “Thermoelastic contact interaction of bodies in the presence of surface thermophysical irregularities,” J. Math. Sci., 62, No. 1, 2512–2517 (1992).CrossRefGoogle Scholar
  23. 23.
    R. M. Shvets and R. M. Martynyak, “Thermal-diffusion instability of the frictional contact of elastic bodies,” Mater. Sci., 30, No. 3, 377–379 (1995).CrossRefGoogle Scholar
  24. 24.
    A. Azarkhin and J. R. Barber, “Thermoelastic instability for the transient contact problem of two sliding half-planes,” J. Appl. Mech., 53, No. 3, 565–572 (1985).CrossRefGoogle Scholar
  25. 25.
    J. R. Barber, “Thermoelastic instabilities in the sliding of conforming solids,” Proc. Roy. Soc., A 312, 381–394 (1969).CrossRefGoogle Scholar
  26. 26.
    M. Ciavarella, A. Baldini, J. Barber, and A. Strozzi, “Reduced dependence on loading parameters in almost conforming contact,” Int. J. Mech. Sci., 48, 917–925 (2006).CrossRefGoogle Scholar
  27. 27.
    M. Comninou and J. Dundurs, “On lack of uniqueness in heat conduction through a solid to solid contact,” J. Heat Transfer., 102, 319–323 (1980).CrossRefGoogle Scholar
  28. 28.
    H. Kit, R. Martynyak, and B. Monastyrskyy, “Imperfect contact interaction of two half-spaces with allowance for interface thermal resistance,” in: Thermal Stresses-2003: Proc. of the 5th Int. Congress on Thermal Stresses (Blacksburg, USA, June 8–11, 2003), Vol. 2, (2003), pp. WA 9-1-1–9-1-4.Google Scholar
  29. 29.
    A. P. S. Selvadurai, “On an invariance principle for unilateral contact at a bimaterial elastic interface,” Int. J. Eng. Sci., 41, 721–739 (2003).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • R. M. Martynyak
    • 1
  • K. A. Chumak
    • 1
  1. 1.Pidstryhach Institute for Applied Problems of Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

Personalised recommendations