Investigating the Temperature Shock of a Plate in the Framework of a Static Two-Dimensional Formulation of the Thermoelasticity Problem

Abstract

The paper investigates the stress–strain state of a homogeneous rectangular plate after a temperature shock. It is believed that the plate is the first approximation of the solar panel model of a small spacecraft. To study the stress–strain state of the plate, a two-dimensional thermoelasticity problem is posed. The problem has a static formulation, since it does not take into account the dynamics of the plate’s natural oscillations. These oscillations affect the stress–strain state through the initial deflection of the plate at the time of the temperature shock. This deflection changes the parameters of the temperature shock and does not allow the use of a one-dimensional formulation of the thermoelasticity problem. As a result of solving the static two-dimensional thermoelasticity problem, approximate solutions are obtained for the components of the plate point’s displacement vector after the temperature shock. An approximation of the temperature field is presented. A numerical simulation is carried out. The correspondence of the obtained approximate analytical dependencies of the components of the plate point’s displacement vector to the numerical simulation data is analyzed. The proposed method can be used to assess the significance of the influence of the small spacecraft’s solar panels temperature shock on the dynamics of its rotational motion.