A thermal-magnetic-elastic problem for a thin current-carrying annular plate of varying thickness in a magnetic field is studied. The standard Cauchy form nonlinear differential equations, which include eight basic unknown variables in all, are obtained by the variable replacement method. Using the difference and quasi-linearization methods, the nonlinear partial differential equations are reduced to a sequence of quasi-linear differential equations, which can be solved by the discrete-orthogonalization method. The temperature field in a thin annular plate with varying thickness and the integral eigenvalues are found after considering Joule’s heat effect in an electromagnetic field and introducing the thermal equilibrium equation and generalized Ohm law. The change rules for stresses, displacements, and temperature in the thin annular plate with varying thickness with the electromagnetic parameters are discussed through the example calculation. The results show that the stresses, strains, and temperature can be controlled by changing the electromagnetic and mechanical parameters. The results presented are expected to be a theoretical reference for the thermo-magneto-elastic analysis of a thin current-carrying plate.
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Published in Prikladnaya Mekhanika, Vol. 57, No. 1, pp. 130–144, January–February 2021.
This research was partially supported by a grant from the National Natural Science Foundation of China, the Foundation of Key Laboratory of Nonlinear Continuum Mechanics, Institute of Mechanics of Chinese Academy of Sciences. The authors gratefully acknowledge these supports.
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Bian, Y.H., You, Q. Analysis of Thermal-Magnetic-Elastic Stresses and Strains in a Thin Annular Plate with Varying Thickness. Int Appl Mech 57, 111–121 (2021). https://doi.org/10.1007/s10778-021-01066-6
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DOI: https://doi.org/10.1007/s10778-021-01066-6