MATHEMATİCAL MODELING OF NONLİNEAR DEFORMATİON PROCESSES OF THIN MAGNETELASTIC PLATES OF COMPLEX CONSTRUCTIVE FORM

In the article, based on the Hamilton-Ostrogradsky variational principle, a mathematical model of the process of geometric nonlinear deformation of thin magnetoelastic plates with a complex structural shape was developed and calculations were performed. In this case, the three-dimensional mathematical model was transferred to a two-dimensional view using the Kirchhoff-Liav hypothesis. Cauchy's relationship, Hooke's law, Lawrence's force, and Maxwell's electromagnetic tensor were used to determine kinetic and potential energy and work done by external forces. The effects of the electromagnetic field on the deformation stress state of the magnetoelastic plate were observed. As a result, a mathematical model in the form of a system of partial differential equations with initial and boundary conditions was created. To solve the equation, a calculation algorithm was developed using the R-function, Bubnov-Galerkin, Newmark, Gaussian, Gaussian squares, and Iteration numerical methods. Calculations were carried out in various mechanical states of the magnetoelastic plate, its boundaries were fixed, one side was hinged and the other side was free, and numerous results were obtained. A comparative analysis of the results of the calculations was presented.