Skip to main content
SpringerLink
Log in

The Stress State of a Flexible Orthotropic Spherical Shell Subject to External Current and Mechanical Force in a Magnetic Field

  • Published:
International Applied Mechanics Aims and scope

A nonlinear axisymmetric problem of magnetoelasticity for an orthotropic spherical shell with orthotropic conductivity is considered. A system of nonlinear differential equations describing the stress–strain state of flexible orthotropic spherical shells in mechanical and magnetic fields is derived. The stress state of an orthotropic shell subject to time-dependent external current and mechanical force is numerically analyzed as an example

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. R. E. Bellman and R. E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems, Elsevier, New York (1965).

    MATH  Google Scholar 

  2. G. E. Bagdasaryan and Z. N. Danoyan, “Equations of motion for displacements of perfectly conductive elastic anisotropic materials in a magnetic field,” Mekh. Deform. Tverd. Tela, 3, 32–42 (1984).

    MATH  Google Scholar 

  3. V. I. Vol’man and Yu. V. Pimenov, Engineering Electrodynamics [in Russian], Svyaz’, Moscow (1971).

  4. Ya. M. Grigorenko and L. V. Mol’chenko, Fundamentals of the Theory of Plates and Shells [in Ukrainian], Lybid’, Kyiv (1993).

  5. Ya. M. Grigorenko and L. V. Mol’chenko, Fundamentals of the Theory of Plates and Shells with Elements of Magnetoelasticity (Textbook) [in Russian], IPTs Kievskii Universitet, Kyiv (2010).

  6. J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices, Clarendon Press, Oxford (1957).

    MATH  Google Scholar 

  7. Yu. I. Sirotin and M. P. Shaskol’skaya, Fundamentals of Crystal Physics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  8. A. F. Ulitko, L. V. Mol’chenko, and V. F. Koval’chuk, Magnetoelasticity under Dynamic Loading [in Ukrainian], Lybid’, Kyiv (1994).

    Google Scholar 

  9. L. V. Mol’chenko and I. I. Loos, “Influence of conicity on the stress–strain state of a flexible orthotropic conical shell in a nonstationary magnetic field,” Int. Appl. Mech., 46, No. 11, 1261–1267 (2010).

    Article  MathSciNet  Google Scholar 

  10. L. V. Mol’chenko, I. I. Loos, and R. Sh. Indiaminov, “Nonlinear deformation of conical shells in magnetic fields,” Int. Appl. Mech., 33, No. 3, 221–226 (1997).

    Google Scholar 

  11. L. V. Mol’chenko, I. I. Loos, and R. Sh. Indiaminov, “Determining the stress state of flexible orthotropic shell of revolution in magnetic field,” Int. Appl. Mech., 44, No. 8, 882–891 (2008).

    Article  MathSciNet  ADS  Google Scholar 

  12. N. M. Newmark, “A method of computation for structural dynamics,” J. Eng. Mech. Div., Proc. ASCE, 85, No. 7, 67–97 (1959).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Taras Shevchenko National University, 4 Glushkova Av., Kyiv, Ukraine, 03127

    L. V. Mol’chenko & I. I. Loos

Authors
  1. L. V. Mol’chenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. I. Loos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. V. Mol’chenko.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 49, No. 5, pp. 34–39, September–October 2013.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mol’chenko, L.V., Loos, I.I. The Stress State of a Flexible Orthotropic Spherical Shell Subject to External Current and Mechanical Force in a Magnetic Field. Int Appl Mech 49, 528–533 (2013). https://doi.org/10.1007/s10778-013-0587-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-013-0587-5

Keywords

Search

Navigation