Skip to main content
SpringerLink
Log in

Stress State of a Transversely Isotropic Medium with an Arbitrarily Oriented Spheroidal Inclusion

  • Published:
International Applied Mechanics Aims and scope

Abstract

The stress-concentration problem for an elastic transversely isotropic medium containing an arbitrarily oriented spheroidal inclusion (inhomogeneity) is solved. The stress state in the elastic space is represented as the superposition of the principal state and the perturbed state due to the inhomogeneity. The problem is solved using the equivalent-inclusion method, the triple Fourier transform in space variables, and the Fourier-transformed Green function for an infinite anisotropic medium. Double integrals over a finite domain are evaluated using the Gaussian quadrature formulas. In special cases, the results are compared with those obtained by other authors. The influence of the geometry and orientation of the inclusion and the elastic properties of the medium and inclusion on the stress concentration is studied

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, New York (1970).

    Google Scholar 

  2. A. Ya. Aleksandrov and V. S. Vol’pert, “Some stress-concentration problems for an ellipsoidal cavity in a transversely isotropic body,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 1, 115’121 (1970).

  3. A. Ya. Aleksandrov and Yu. I. Solov’ev, Three-Dimensional Problems in the Theory of Elasticity [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  4. V. T. Golovchan, “Solution of triply periodic problems in the statics of an elastic body with spherical inclusions,” Int. Appl. Mech., 22, No.7, 623’631 (1986).

    Google Scholar 

  5. A. K. Malmeister, V. P. Tamusz, and G. A. Teters, Resistance of Rigid Polymeric Materials [in Russian], Zinatne, Riga (1972).

    Google Scholar 

  6. Yu. N. Nemish, “Development of analytical methods in three-dimensional problems of the statics of anisotropic bodies (review),” Int. Appl. Mech., 36, No.2, 135’173 (2000).

    Google Scholar 

  7. A. G. Nikolaev and V. S. Protsenko, “The first and second axisymmetric problems in the theory of elasticity for doubly connected domains bounded by spherical and spheroidal surfaces,” Prikl. Mat. Mekh., 24, No.1, 65’74 (1990).

    Google Scholar 

  8. Yu. N. Podil’chuk, Boundary-Value Static Problems for Elastic Bodies, Vol. 1 of the six-volume series Three-Dimensional Problems of the Theory of Elasticity and Plasticity [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  9. Yu. N. Podil’chuk, “Exact analytical solutions of three-dimensional boundary-value static problems for canonical transversely isotropic body (review),” Prikl. Mekh., 33, No.10, 3’30 (1997).

    Google Scholar 

  10. G. Ya. Popov, Elastic Stress Concentration near Punches, Notches, Thin Inclusions, and Reinforcements [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  11. A. F. Ulitko, Vector Eigenfunctions in Three-Dimensional Elastic Problems [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  12. J. D. Eshelby, “The continuum theory of lattice defects,” in: F. Seitz and D. Turnbull (eds.), Progress in Solid State Physics, Vol. 3, Acad. Press, New York (1956), pp. 79’303.

    Google Scholar 

  13. D. M. Barnett, “The precise evaluation of derivatives of the anisotropic elastic Green’s functions, ” Phys. Stat. Sol. (b), 49, 741’748 (1972).

    Google Scholar 

  14. A. H. Elliott, “Three-dimensional stress distributions in hexagonal aelotropic crystals,” Proc. Cambr. Phil. Soc., 44, Pt. 4, 522’533 (1948).

    Google Scholar 

  15. V. S. Kirilyuk, “Interaction of an ellipsoidal inclusion with an elliptic crack in an elastic material under triaxial tension,” Int. Appl. Mech., 39, No.6, 704’712 (2003).

    Google Scholar 

  16. V. S. Kirilyuk, “The stress state of an elastic medium with an elliptic crack and two ellipsoidal inclusions,” Int. Appl. Mech., 39, No.7, 829’839 (2003).

    Google Scholar 

  17. T. Mura, Micromechanics of Defects in Solids, Martinus Nijhoff, Boston’London (1987).

    Google Scholar 

  18. Yu. N. Podil’chuk and O. G. Dashko, “The stress’strain state of an elastic ferromagnetic medium with an ellipsoidal inclusion in a homogeneous magnetic field,” Int. Appl. Mech., 39, No.7, 802’811 (2003).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    V. S. Kirilyuk & O. I. Levchuk

Authors
  1. V. S. Kirilyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. I. Levchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 33–40, February 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kirilyuk, V.S., Levchuk, O.I. Stress State of a Transversely Isotropic Medium with an Arbitrarily Oriented Spheroidal Inclusion. Int Appl Mech 41, 137–143 (2005). https://doi.org/10.1007/s10778-005-0069-5

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-005-0069-5

Keywords

Search

Navigation