Mathematical Modeling of Thermo-Electro-Magnit-Elastic Deformation Processes of Thin Plates of Complex Constructive Form
Keywords:
Hamilton-Ostrogradsky principle, Bubnov Galerkin method, Cauchy relation, Hooke’s law, Maxwell’s electromagnetic tensor, ????-functionAbstract
In this work, a mathematical model of the thermo-electro-magnetic-elastic deformation process of thin plates with a complex shape was developed and calculation experiments were carried out using the Hamilton-Ostrogradsky variational principle. Based on the Kirchhoff-Liav hypothesis, the three-dimensional mathematical model was transferred to a two-dimensional view. Cauchy’s problem, physical law (Hook’s law), Lawrence force and Maxwell’s equations were used to find variational solutions of kinetic and potential energy and work done by external forces. The effects of electromagnetic field forces and temperature on the state of deformation stress of an electrically conductive plate were observed, as a result, the equation of motion in the form of a system of differential differential equations with initial and boundary conditions for displacement, i.e. mathematical model was developed. R-function, numerical methods (Bubnov-Galerkin, Newmark, Gauss and Gauss squares) were used to find the solutions of the unknown function, and a calculation algorithm was created. In the calculation experiments, numerical results were obtained by conducting calculation experiments based on the mechanical conditions of the plate and various conditions. A comparative analysis of the calculation results was presented.
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