Coupled Non-Stationary Thermoelastic Fields In A Rigidly Fixed Round Plate

The mathematical formulation of thermoelasticity problems includes coupled non-self-adjoint differential equations of motion and heat conduction. The problem of integrating them and constructing a general solution leads, as a rule, to the study of only the heat conduction equation or to the analysis of thermoelasticity problems in an unconnected formulation. However, for a better assessment of thermomechanical fields, it becomes necessary to construct coupled analytical solutions in a three-dimensional formulation. Therefore, the development of effective analytical methods and algorithms for calculating elastic systems is currently one of the urgent problems of modern science. In this problem, a mathematical calculation model is developed and a closed solution of the coupled axisymmetric non -stationary problem of the theory of thermoelasticity for a rigidly fixed isotropic plate is constructed. Design ratios are obtained by the method of finite biorthogonal transformations and are valid for an external temperature effect arbitrary in time (boundary conditions for thermal conductivity of the 1st kind). Software that allows to analyze the effect of coupled thermoelastic fields on the temperature field and the stress-strain state of the structure has been developed. Numerical analysis of the results shows that for a given external temperature effect, the rigidity of an elastic system (physical and mechanical characteristics and geometric dimensions) has a significant effect on its thermoelastic field. The developed calculation algorithm finds its application in the design of enclosing structures in the form of single-layer and multi-layer plates.