MATHEMATICAL MODELING OF NONLINEAR DEFORMATION PROCESSES OF THIN MAGNETELASTIC PLATES OF COMPLEX CONSTRUCTIVE FORM - Shohruh Safarov Sharofovich; Mahkamov Anvarjon Abdujabborovich (Web of Journals Publishing, 2024)
The article is devoted to the development of a mathematical model of the process of geometric nonlinear deformation of thin magnetoelastic plates of a complex structural shape based on the Hamilton-Ostrogradsky variational principle, and conducting computational experiments. In this case, the three-dimensional mathematical model was transferred to a two-dimensional view using the Kirchhoff-Liav hypothesis. The effects of the electromagnetic field on the deformation stress state of the magnetoelastic plate were observed using the Lorentz force and the Maxwell electromagnetic tensor representation, resulting in a mathematical model in the form of a system of differential differential equations with initial and boundary conditions for displacement. was created. To solve the equation, a calculation algorithm was developed using R-function, Bubnov-Galerkin, Newmark, Gaussian, Gaussian squares, and Iteration numerical methods, and numerical results were obtained. A comparative analysis of the results of the calculations was presented.
Keywords: Hamilton-Ostrogradsky principle, Bubnov Galerkin, Cauchy relation, Hooke's law, Maxwell's electromagnetic tensor, R-function, Gauss, Iteration.