A computational algorithm for calculating the effect of the electromagnetic fields to thin complex configured plates Fakhriddin Nuraliev Tashkent University of Information Technologies named after Muhammad al-Khwarizmi Tashkent, Uzbekistan email address nuraliev2001@mail.ru Shohruh Safarov Scientic and Innovation Center of Information and Communication Technologies at Tashkent University of Information Technologies named after Muhammad Al-Khwarizmi Tashkent, Uzbekistan email address shohfar@gmail.com Mahkam Artikbayev Scientic and Innovation Center of Information and Communication Technologies at Tashkent University of Information Technologies named after Muhammad Al-Khwarizmi Tashkent, Uzbekistan email address m.artiqbaev@mail.ru Abstract—A nonlinear mathematical model of a flexible magneto-elastic plate (in motion subject to forces) is developed on the Lagrange principle. A computational algorithm is presented to estimate the geometry of magnetic plates. The algorithm is based on R-Function and Galerkin methods. These methods are used to develop a computational scheme. The cases of simple and complex structures of magneto-elastic flexible plates are considered and solutions are obtained under specific boundary conditions. These conditions are defined with some concrete requirements of engineering. Index Terms—Lagrange, RFM, Galerkin, Iteration, Gauss, algorithm, mathematical model. I. I NTRODUCTION Nowadays, a tremendous attention is devoted to the investi- gation of the effects of magneto-elastic objects on physical fields. Important results are published in [1]. In [1], Chen J.Y., Pan E., and Heyliger P.R analyzed the static deforma- tion of a spherically anisotropic and multilayered magneto- electro-elastic hollow sphere. They developed analytical so- lutions for the general static deformation of the spherical anisotropic and multilayered magneto-electro-elastic (MEE) hollow sphere. The method in [1] consisted of expressing the general solution in each layer in terms of the spherical system of vector functions. Another procedure based on the transformation of two variables was also considered to achieve the analytical results. Using this later procedure, the spherical system of vector functions automatically separates the static deformation into two independent sub-problems (both LM- type and N-type problems). The LM-type is associated with the spheroidal deformation and is further coupled with the electric and magnetic fields. The N-type is associated with the torsional deformation and is purely elastic and independent of the electric and magnetic fields. To solve the multilayer spherical problem, a matrix method of multiplication has been introduced. The method calculates the exponential material for each layer of the matrix. By assuming the condition of continuity on the interface between the adjacent spherical shells, the solution can be simply propagated from the inner surface to the outer surface of the layered and hollow MEE sphere so that specific boundary value problems can be solved. Three-layer sandwich hollow sphere with different layers under different boundary conditions was studied as numerical examples [1]. Subhaschandra Kattimani [2] investigates on the Geometrically nonlinear vibration of magneto-electro-elastic plates of multiferroic composite plates and shells. The layer wise shear deformation theory is incorporated for the geo- metrically nonlinear vibration (GNV) analysis of multiferroic composite plates and doubly curved shells [2]. According to [2], the coupled constitutive equations which involve ferroelas- tic, ferroelectric and ferromagnetic properties of multiferroic composite materials along with the total potential energy principle are utilized to derive the finite element formulation for the multiferroic or magneto-electro-elastic (MEE) plates. In [2], the electric and magnetic potentials are assumed to vary