Solving the problem of geometrical nonlinear deformation of electro-magnetic thin plate with complex configuration and analysis of results

In this article the task of geometric nonlinear deformation of a thin plate of complex configuration is discussed taking into account the influence of the electromagnetic field forces. A mathematical model is obtained in the form of a system of partial differential equations with initial and boundary conditions for displacement according to the Hamilton-Ostrogradsky hypothesis using the Bund Kirgof-Love hypothesis, Cauchy relations, Hooke's law and the Lorentz degree, as well as the Maxwell electromagnetic tensor. For the numerical solution of the problem under study, a calculation algorithm is developed, the results are obtained and analyzed using together the method of analytical R-functions (RFM) of magnetoelastic plates of complex structural shape and the Bubnov-Galerkin variation method.

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