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Thermomagnetoelastic Deformation of Flexible Isotropic Shells of Revolution Subject to Joule Heating

  • L. V. Mol’chenkoEmail author
  • I. I. Loos
Article

The equations of thermomagnetoelasticity for shells of revolution subject to Joule heat in a non-stationary magnetic field are derived. The thermomagnetoelasticity of a truncated conic shell is analyzed using an axisymmetric problem statement and allowing for Joule heat.

Keywords

magnetic field Joule heat Lorentz force conical shell 

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References

  1. 1.
    S. A. Ambartsumyan, G. E. Bagdasaryan, and M. V. Belubekyan, Magnetoelasticity of Thin Shells and Plates [in Russian], Nauka, Moscow (1977).Google Scholar
  2. 2.
    R. E. Bellman and R. E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems, Mir, Moscow (1968).Google Scholar
  3. 3.
    V. D. Budak, L. V. Mol’chenko, and A. V. Ovcharenko, Nonlinear Magnetoelastic Shells [in Russian], Monograph, Ilion, Nikolaev (2016).Google Scholar
  4. 4.
    S. K. Godunov, “Numerical solution of boundary-value problems for systems of linear ordinary differential equations,” Usp. Mat. Nauk, 16, No. 5, 171–174 (1961).MathSciNetGoogle Scholar
  5. 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).Google Scholar
  6. 6.
    V. I. Dresvyannikov, “Nonstationary problems of the mechanics of elastoplastic conductive bodies subject to strong impulsive magnetic fields,” Prikl. Probl. Prochn. Plast., 19, 32–47 (1979).Google Scholar
  7. 7.
    I. E. Tamm, Electromagnetic Theory [in Russian], Nauka, Moscow (1976).Google Scholar
  8. 8.
    Bian Yu-Hong “Analysis of nonlinear stresses and strains in a thin current-carrying elastic plate,” Int. Appl. Mech., 51, No. 1, 108–120 (2015).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    R. Elhajjar, V. Saponara, and A. Muliana, Smart Composites. Mechanics and Design, CRC Press, New York (2013).CrossRefGoogle Scholar
  10. 10.
    A. E. Green and P. M. Naghdi, “On electromagnetic effects in the theory of shells and plates,” Phil. Trans. Roy. Soc., A309, 559–610 (1983).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    K. Hutter, A. F. Van de Ven, and A. Ursescy, Electromagnetic Field Matter Interactions in Thermoelastic Solids and Viscous Fluids, Springer, Berlin (2007).Google Scholar
  12. 12.
    L. V. Mol’chenko and I. I. Loos, “The stress state of a flexible orthotropic spherical shell subject to external current and mechanical force in a magnetic field,” Int. Appl. Mech., 49, No. 5, 528–533 (2013).ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    L. V. Mol’chenko, I. I. Loos, and L. M. Fedorchenko, “Deformation of a flexible orthotropic spherical shell of variable tiffness in a magnetic field,” Int. Appl. Mech., 52, No. 1, 56–61 (2016).ADSCrossRefzbMATHGoogle Scholar
  14. 14.
    L. V. Mol’chenko, L. N. Fedorchenko, and L. Yu. Vasilieva, “Nonlinear theory of magnetoelasticity of shells of revolution with Joule heat taken into account,” Int. Appl. Mech., 54, No. 3, 306–314 (2018).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    F. C. Moon, Magneto-Solid Mechanics, John Wiley & Sons Inc., New York (1984).Google Scholar

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

Authors and Affiliations

  1. 1.Mykolaiv V. A. Sukhomlynskyi National UniversityMykolaivUkraine

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