Advertisement

Solution of the Problem of Heat Conduction for the Transversely Isotropic Piecewise-Homogeneous Space with Two Circular Inclusions

  • O. F. Kryvyi
  • Yu. O. Morozov
Article
  • 1 Downloads

The nonaxisymmetric problem of heat conduction for a piecewise-homogeneous transversely isotropic space with two (thermally active and thermally insulated) internal inclusions located parallel to the plane of conjugation of two different transversely isotropic half spaces is reduced to a system of two two-dimensional singular integral equations. The solution of this system is constructed in the form of series in Jacobi polynomials. As a result, we obtain the dependences of the temperature distribution on the thermophysical properties of materials and on the distances between the inclusions and the interface of the half spaces. The quantitative and qualitative specific features of the temperature field in the neighborhood of inclusions are analyzed.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. V. Efimov, A. F. Krivoi, G. Ya. Popov, “Problems on the stress concentration near a circular imperfection in a composite elastic medium,” Izv. Ros. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 42–58 (1998); English translation: Mech. Solids, 33, No. 2, 35–49 (1998).Google Scholar
  2. 2.
    H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford (1959).zbMATHGoogle Scholar
  3. 3.
    H. S. Kit and R. M. Andriichuk, “Influence of a stationary heat source on the stress state of a half space with rigidly, smoothly, or flexibly fastened boundary,” Mat. Met. Fiz.-Mekh. Polya, 58, No. 4, 78–86 (2015); English translation: J. Math. Sci., 228, No. 2, 91–104 (2018).Google Scholar
  4. 4.
    H. S. Kit and R. M. Andriichuk, “The problem of stationary heat conduction for a piecewise homogeneous space under the conditions of heat release in a circular region,” Prykl. Probl. Mekh. Mat., Issue 10, 115–122 (2012).Google Scholar
  5. 5.
    H. S. Kit and O. P. Sushko, “Problems of stationary heat conduction and thermoelasticity for a body with a heat permeable disk-shaped inclusion (crack),” Mat. Met. Fiz.-Mekh. Polya, 52, No. 4, 150–159 (2009); English translation: J. Math. Sci., 174, No. 3, 309–321 (2011).Google Scholar
  6. 6.
    H. S. Kit and O. P. Sushko, “Axially symmetric problems of stationary heat conduction and thermoelasticity for a body with thermally active or thermally insulated disk inclusion (crack),” Mat. Met. Fiz.-Mekh. Polya, 53, No. 1, 58–70 (2010); English translation: J. Math. Sci., 176, No. 4, 561–577 (2011).Google Scholar
  7. 7.
    H. S. Kit and O. P. Sushko, “Distribution of stationary temperature and stresses in a body with heat-permeable disk inclusion,” Met. Rozv'yaz. Prikl. Probl. Mekh. Deform. Tverd. Tila, Issue 10, 145–153 (2009).Google Scholar
  8. 8.
    H. S. Kit and O. P. Sushko, “Stationary temperature field in a semiinfinite body with thermally active or thermally insulated disk inclusion,” Fiz.-Mat. Model. Inform. Tekhnol., Issue 13, 67–80 (2011).Google Scholar
  9. 9.
    O. F. Kryvyi, “Mutual influence of an interface tunnel crack and an interface tunnel inclusion in a piecewise homogeneous anisotropic space,” Mat. Met. Fiz.-Mekh. Polya, 56, No. 4, 118–124 (2013); English translation: J. Math. Sci., 208, No. 4, 409–416 (2015).CrossRefGoogle Scholar
  10. 10.
    O. F. Kryvyi, “Delaminated interface inclusion in a piecewise homogeneous transversely isotropic space,” Fiz.-Khim. Mekh. Mater., 50, No. 2, 77–84 (2014); English translation: Mater. Sci., 50, No. 2, 245–253 (2014).MathSciNetCrossRefGoogle Scholar
  11. 11.
    O. F. Kryvyy, “Interface circular inclusion under mixed conditions of interaction with a piecewise-homogeneous transversely isotropic space,” Mat. Met. Fiz.-Mekh. Polya, 54, No. 2, 89–102 (2011); English translation: J. Math. Sci., 184, No. 1, 101–119 (2012).Google Scholar
  12. 12.
    O. F. Kryvyy, “Singular integral relations and equations for a piecewise-homogeneous transversely isotropic space with interphase defects,” Mat. Met. Fiz.-Mekh. Polya, 53, No. 1, 23–35 (2010); English translation: J. Math. Sci., 176, No. 4, 515–531 (2011).Google Scholar
  13. 13.
    A. F. Krivoi and Yu. A. Morozov, “Solution of the heat-conduction problem for two coplanar cracks in a composite transversely isotropic space,” Visn. Donets. Nats. Univ. Ser. A. Pryrod. Nauky, No. 1, 76–83 (2014).Google Scholar
  14. 14.
    A. F. Krivoi and Yu. A. Morozov, “Solution of the problem of heat conduction for a piecewise homogeneous orthotropic space with interface defects,” Visn. Odes. Nats. Univ. Mat. Mekh., 17, Issue 3(15), 107–119 (2012); http://liber.onu.edu.ua/pdf/T17%20v3(15).pdf.
  15. 15.
    G. Ya. Popov, Concentration of Elastic Stresses Near Stamps, Cuts, Thin Inclusions, and Reinforcements [in Russian], Nauka, Moscow (1982).Google Scholar
  16. 16.
    O. Kryvyy, “The discontinuous solution for the piece-homogeneous transverse isotropic medium,” Oper. Theory: Adv. Appl., 191, 395–406 (2009).MathSciNetzbMATHGoogle Scholar
  17. 17.
    R. Kushnir and B. Protsiuk, “A method of Green’s functions for quasistatic thermoelasticity problems in layered thermosensitive bodies under complex heat exchange,” Oper. Theory: Adv. Appl., 191, 143–154 (2009).MathSciNetzbMATHGoogle Scholar
  18. 18.
    J. A. Nairn, “Modeling imperfect interfaces in the material-point method using multimaterial methods,” Comput. Model. Eng. Sci., 92, No. 3, 271–299 (2013); http://www.techscience.com/doi/10.3970/cmes.2013.092.271.html.MathSciNetzbMATHGoogle Scholar
  19. 19.
    H. Pan, T. Song, and Z. Wang, “Thermal fracture model for a functionally graded material with general thermomechanical properties and collinear cracks,” J. Therm. Stresses, 39, No. 7, 820–834 (2016).CrossRefGoogle Scholar
  20. 20.
    V. Petrova and S. Schmauder, “FGM/homogeneous bimaterials with systems of cracks under thermomechanical loading: Analysis by fracture criteria,” Eng. Fract. Mech., 130, 12–20 (2014).CrossRefGoogle Scholar
  21. 21.
    V. Petrova and S. Schmauder, “Thermal fracture of a functionally graded/homogeneous bimaterial with system of cracks,” Theor. Appl. Fract. Mech., 55, No. 2, 148–157 (2011).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • O. F. Kryvyi
    • 1
  • Yu. O. Morozov
    • 2
  1. 1.“Odesa Maritime Academy” National UniversityOdessaUkraine
  2. 2.Odessa National Polytechnic UniversityOdessaUkraine

Personalised recommendations