MATHEMATICAL MODELING OF DEFORMATION PROCESSES OF THERMOELASTIC PLATES TAKING INTO ACCOUNT TEMPERATURE
Keywords:
Hamilton principle, Bubnov Galerkin, Cauchy equations, Hooke's law, Maxwell's electromagnetic tensor, R-function, Gaussian, Iteration.Abstract
In the article, based on the Hamilton 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.
