Calculation Results of the Task of Geometric Nonlinear Deformation of Electro-magneto-elastic Thin Plates in a Complex Configuration

Abstract

In the article a mathematical model based on the Hamilton-Ostrogradsky variational principle is presented. Using the Kirkhgoff-Lyav hypothesis, the mathematical model in three-dimensional form is transformed into a two-dimensional model. The variational representation of potential and kinetic energy as well as the variation of work done by external forces, Cauchy relations, Hooke’s law, and Lorentz force and Maxwell’s electromagnetic forces are determined using the tensor view. In this case, the effects of the electromagnetic field on the deformation stress state of the magnetoelastic plate are considered. The result was a mathematical model in the form of a system of high-order differential equations with special derivatives with initial and boundary conditions relative to the displacement. To solve the problem, a computational algorithm was developed, for which a practical software tool was created, computational experiments were conducted, and the results obtained were analyzed.