Non-stationary axially symmetric goal of thermo-elasticity for a fixed rigid circular multi-layer plate

Abstract

Abstract. This paper considers axially symmetric goal of thermoselasticity for a fixed rigid circular multi-layer isotropic plate with nonstationary heat flows on its front faces. The mathematical model is presented in the form of a not self-adjoint system that includes differential motion equations and a linear equation of the thermal-elastic state in a three-dimensional model. A new closed solution in an unconnected setting is built by the method of finite integral transformation. At the same time, a standardization procedure is conducted at each stage of the solution, which allows to implement an appropriate conversion algorithm. The calculated ratios provide an opportunity to perform a qualitative and quantitative analysis of the associated temperature and mechanical fields and also to examine stress-strain behaviour of the multi-layer systems both under the local thermal shock, which is observed, for example, in the interaction with the laser beam and in the case of uneven unsteady surface heating, which is frequent during the operation of protective construction structures.