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Thermomagnetoelastic Deformation of a Flexible Orthotropic Conical Shell with Electrical Conductivity and Joule Heat Taken into Account

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We proposed a theory and a method for solving geometrically nonlinear problems for thermomagnetoelastic orthotropic shells taking into account Joule heat in the microsecond range. The problem fora flexible orthotropic conical shell is solved numerically taking into account orthotropic conductivity and Joule heat.

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References

  1. S. A. Ambartsumyan, G. E. Bagdasaryan, and M. V. Belubekyan, Magnetoelasticity of Thin Shells and Plates [in Russian], Nauka, Moscow (1977).

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

  3. V. D. Budak, L. V. Mol’chenko, and A. V. Ovcharenko, Numerical and Analytical Solution of Boundary-Value Problems of Magnetoelasticity [in Russian], Ilion, Nikolaev (2016).

  4. V. D. Budak, L. V. Mol’chenko, and A. V. Ovcharenko, Nonlinear Magnetoelastic Shells [in Russian], Ilion, Nikolaev (2016).

  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. 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. A. Sommerfeld, Electrodynamics, Academic Press, New York (1964).

  8. L. D. Landau, and E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, Oxford (1984).

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

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

  11. I. E. Tamm, Fundamentals of the Theory of Electricity, Mir, Moscow (1976).

  12. L. A. Shapovalov, “On simple equations of the geometrically nonlinear theory of thin shells,” Inzh. Zh. Mekh. Tverd. Tela, No. 1, 56–62 (1968).

  13. Y. H. Bian, “Analysis of nonlinear stresses and strains in a thin current-carrying elastic plate,” Int. Appl. Mech., 51, No. 1, 108–120 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  14. R. Elhajjar, V. La Saponara, and A. Muliana, Smart Composites. Mechanics and Design, CRS Press, Boca Raton (2013).

  15. A. Ya. Grigorenko, S. A. Pankrat’ev, and S. N. Yaremchenko, “Solution of stress-strain problems for complex-shaped plates in a refined formulation,” Int. Appl. Mech., 53, No. 3, 326–333 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  16. K. Hutter, A. A. F. Van de Ven, and A. Ursescu, Electromagnetic Field Matter Interactions in Thermoelastic Solids and Viscous Fluids, Springer, Berlin (2007).

  17. C. Hwu, Anisotropic Elastic Plates, Springer, Boston (2010).

  18. S. A. Kaloerov, “Determining the intensity factors for stresses electric-flux and electric-field strength in multiply connected electroelastic anisotropic media,” Int. Appl. Mech., 43, No. 6. 631–637 (2007).

  19. L. V. Mol’chenko, L. N. Fedorchenko, and L. Ya. Vasilieva, “Nonlinear theory of magnetoelasticity of shells of revolution with Joule heat taken into account,” Int. Appl. Mech., 54, No. 3, 306–314 (2018).

    Article  ADS  MathSciNet  Google Scholar 

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

  21. L. V. Mol’chenko and I. I. Loos, “Thermomagnetoelastic deformation of flexible isotropic shells of revolution subject to joule heating,” Int. Appl. Mech., 55, No. 1, 68–78 (2019).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

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Authors and Affiliations

  1. Mykolaiv V. O. Sukhomlynskyi National University, 24 Nikolska St., Mykolaiv, Ukraine, 54030

    L. V. Mol’chenko & I. I. Loos

Authors
  1. L. V. Mol’chenko
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  2. I. I. Loos
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Correspondence to L. V. Mol’chenko.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 55, No. 5, pp. 89–100, September–October 2019.

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Mol’chenko, L.V., Loos, I.I. Thermomagnetoelastic Deformation of a Flexible Orthotropic Conical Shell with Electrical Conductivity and Joule Heat Taken into Account. Int Appl Mech 55, 534–543 (2019). https://doi.org/10.1007/s10778-019-00975-x

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  • DOI: https://doi.org/10.1007/s10778-019-00975-x

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