The derivation and a method of solution of the nonlinear equations of thermomagnetoelasticity of flexible orthotropic shells of revolution taking into account orthotropic conductivity and Joule heat are presented. The thermomagnetoelasticity of a flexible orthotropic ring plate is analyzed using an axisymmetric problem statement.
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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, Elsevier, New York (1965).
V. D. Budak, L. V. Mol’chenko, and A. V. Ovcharenko, Numerical-Analytical Solution of Boundary-Value Problems of Magnetoelasticity of Flexible Shells [in Ukrainian], Ilion, Mykolaiv (2016).
V. D. Budak, L. V. Mol’chenko, and A. V. Ovcharenko, Nonlinear Magnetoelastic Shells [in Russian], 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 [in Russian], VPTs Kyivs’kyi 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., No. 19, 32–47 (1979).
L. D. Landau, and E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, Oxford (1984).
J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices, Clarendon Press, Oxford (1957).
L. I. Sedov, A Course in Continuum Mechanics, Vol. 2, Wolters-Noordhoff, Groningen (1972).
Yu. I. Sirotin and M. P. Shaskol’skaya, Fundamentals of Crystal Physics [in Russian], Nauka, Moscow (1979).
J. A. Stratton, Electromagnetic Theory, McGraw-Hill, New York (1941).
I. E. Tamm, Fundamentals of the Theory of Electricity, Mir, Moscow (1979).
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).
R. V. Dinzhos, V. P. Privalko, and E. G. Privalko, “Enthalpy relaxation in the cooling/heating cycles of polyamide 6/organoclay nanocomposites. I. Non-isothermal crystallization,” J. Macromolecular Sci., Part B. Phys., B44, 421–430 (2005).
V. P. Privalko, R. V. Dinzhos, and E. G. Privalko, “Enthalpy relaxation in the cooling/heating cycles of polyamide 6/organoclay nanocomposites. II. Melting behavior,” J. Macromolecular Sci., Part B. Phys., B44, 431–443 (2005).
R. Elhajjar, V. Saponara, and A. Muliana, Smart Composites. Mechanics and Design, CRC Press, New York (2013).
K. Hutter, A. A. F. Ven, and A. Ursescu, Electromagnetic Field Matter Interactions in Thermoelastic Solids and Viscous Fluids, Springer, Berlin (2006).
L. V. Mol’chenko, L. N. Fedorchenko, and L. Ya. Vasil’eva, “Nonlinear theory of magnetoelasticity of shells of revolution with Joule heat taken into account,” Int. Appl. Mech., 54, No. 3, 306–314 (2018).
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).
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).
L. V. Mol’chenko and I. I. Loos, “Asymmetric deformation of sells of revolution of variable stiffness in a nostationary magnetic field,” Int. Appl. Mech., 55, No. 3, 311–320 (2019).
L. V. Mol’chenko, I. I. Loos, and V. N. Darmosyuk, “Thermomagnetoelastic deformation of flexible orthotropic shells of revolution of variable stiffness with joule heat taken into account,” Int. Appl. Mech., 56, No. 4, 498–511 (2020).
F. C. Moon, Magneto-Solid Mechanics, Wiley, New York (1984).
N. M. Newmark, “A method of computation for structural dynamics,” J. Eng. Mech. Div. Proc. ASCE., 85, No. 7, 67–97 (1959).
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Translated from Prikladnaya Mekhanika, Vol. 57, No. 2, pp. 107–126, March–April 2021.
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Mol’chenko, L.V., Loos, I.I. Magnetoelastic Deformation of Flexible Orthotropic Ring Plate with Orthotropic Conductivity and Joule Heat. Int Appl Mech 57, 217–233 (2021). https://doi.org/10.1007/s10778-021-01075-5
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DOI: https://doi.org/10.1007/s10778-021-01075-5