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.
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S. A. Ambartsumyan, G. E. Bagdasaryan, and M. V. Belubekyan, Magnetoelasticity of Thin Shells and Plates [in Russian], Nauka, Moscow (1977).
R. E. Bellman and R. E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems, Mir, Moscow (1968).
V. D. Budak, L. V. Mol’chenko, and A. V. Ovcharenko, Nonlinear Magnetoelastic Shells [in Russian], Monograph, Ilion, Nikolaev (2016).
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).
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).
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).
I. E. Tamm, Electromagnetic Theory [in Russian], Nauka, Moscow (1976).
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).
R. Elhajjar, V. Saponara, and A. Muliana, Smart Composites. Mechanics and Design, CRC Press, New York (2013).
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).
K. Hutter, A. F. Van de Ven, and A. Ursescy, Electromagnetic Field Matter Interactions in Thermoelastic Solids and Viscous Fluids, Springer, Berlin (2007).
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).
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).
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).
F. C. Moon, Magneto-Solid Mechanics, John Wiley & Sons Inc., New York (1984).
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Translated from Prikladnaya Mekhanika, Vol. 55, No. 1, pp. 78–90, January–February, 2019.
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Mol’chenko, L.V., Loos, I.I. Thermomagnetoelastic Deformation of Flexible Isotropic Shells of Revolution Subject to Joule Heating. Int Appl Mech 55, 68–78 (2019). https://doi.org/10.1007/s10778-019-00935-5
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DOI: https://doi.org/10.1007/s10778-019-00935-5