Skip to main content
Log in

Analogy between elastic and thermoelastic problems for symmetrically loaded isotropic and transverally isotropic media

  • Published:
International Applied Mechanics Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. A. E. Andrikov, Three-Dimensional Problems of the Theory of Cracks [in Russian], Nauk. Dumka, Kiev (1982).

    Google Scholar 

  2. A. E. Andrikov, V. V. Panasyuk, and M. M. Stadnik, “Fracture of bittle prismatic bars weakened by internal circular cracks,” Probl. Prochn., No. 10, 37 (1972).

  3. E. V. Gobson, Theory of Spherical and Ellipsoidal Functions [Russian translation], Izd. Inostr. Lit., Moscow (1956).

    Google Scholar 

  4. G. S. Kim, M. V. Hai, and L. P. Laushnik, “First fundamental problem of the theory of elasticity for a solid with penny-shaped cracks,” Mat. Metod. Fiz.-Mekh. Polya, No. 7, 26 [sic].

  5. Yu. M. Kobzar', “Representation of solutions of static equations of the thermoelasticity of a transversally-isotropic solid,” Proceedings of Eleventh Scientific Conference of Young Scientists of the Institute of Mechanics, Academy of Sciences of Ukraine (Kiilov, May 27–30, 1986), VINITI Dep. No. 5507-B, July 27 (1986).

  6. N. S. Koshlyakov, É. B. Gliner, and M. M. Smirnov, Partial Differential Equations in Mathematical Physics [in Russian], Vyssh. Shk., Moscow (1970).

    Google Scholar 

  7. I. G. Petrovskii, Lectures on Partial Differential Equations [in Russian], Gostekhizdat, Moscow-Leningrad (1950).

    Google Scholar 

  8. Yu. N. Podil'chuk, “Thermoelastic deformation of a transversally isotropic parabolic cylinder,” Prikl. Mekh.,25, No. 7, 3 (1989).

    Google Scholar 

  9. M. M. Stadnik and V. P. Silovanyuk, “Tension of prismatic bars with circular cracks,” Fiz. Khim. Mekh. Mater.,14, No. 6, 84 (1978).

    Google Scholar 

  10. A. I. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics, Pergamon Press, Oxford (1963).

    Google Scholar 

  11. Y. A. Elliott, “Three-dimensional stress distributions in hexagonal aelotropic crystals,” Proc. Cambr. Phil. Soc.,44, No. 4, 522 (1948).

    Google Scholar 

  12. G. R. Irvin, “Crack-extension front for a part-through crack in a plate,” Trans. ASME, Ser. E, J. Appl. Mech., No. 29, 651 (1962).

  13. M. Isida, K. Hirota, H. Noguchi, and T. Yoshida, “Two parallel elliptic cracks in an infinite solid subjected to tension,” Int. J. Fract.,27, No. 1, 31 (1985).

    Google Scholar 

  14. E. N. Mastrojannis, L. M. Keer, and T. Mura, “Stress intensity factor for a plane crack under normal pressure,” Int. J. Fract.,15, No. 3, 247 (1979).

    Google Scholar 

  15. E. N. Mastrojannis and T. Mura, “On the problem of two coplanar cracks inside an infinite isotropic solid,” Int. J. Numer. Meth. Eng.,19, No. 1, 27 (1983).

    Google Scholar 

  16. M. K. Kassir and G. C. Sig, Three-Dimensional Crack Problems (Mechanics of Fracture. 2), Nordhoff, Leyden (1975).

    Google Scholar 

  17. M. K. Kassir and G. C. Sig, “Three-dimensional thermoelastic problems of planes of discontinuities or cracks in solids,” in: W. A. Shaw (ed.), Developments in Theoretical and Applied Mechanics. Vol. 3, Pergamon Press, Oxford (1967), pp. 117–146.

    Google Scholar 

  18. Z. Olesiak and I. N. Sneddon, “The distribution of thermal stress in an infinite elastic solid containing a penny-shaped crack,” Arch. Ration. Mech. Analysis,4, 238 (1959).

    Google Scholar 

  19. H. Sekine and T. Mura, “Weakening of an elastic solid by a periodic array of penny-shaped crack,” Int. J. Solids Struct.,15, No. 6, 493 (1979).

    Google Scholar 

  20. I. N. Sneddon, “The distribution of stress in the neighborhood of a crack in an elastic solid,” Proc. Roy. Soc. London. Ser. A,187, 229 (1946).

    Google Scholar 

Download references

Authors

Additional information

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 12, pp. 51–60, December, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kirilyuk, V.S. Analogy between elastic and thermoelastic problems for symmetrically loaded isotropic and transverally isotropic media. Int Appl Mech 31, 1004–1011 (1995). https://doi.org/10.1007/BF00847260

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00847260

Keywords

Navigation