Axisymmetric thermoelastic deformation of a multilayer plate with imperfect thermal contact of its layers

Abstract

An axisymmetric stationary problem of thermoelasticity for a multilayer plate with imperfect thermal contact between its layers is solved by using the method of compliance functions along with the Hankel transform. It is assumed that the conditions of perfect mechanical contact are satisfied on their common boundaries. The Hankel transforms of displacements, stresses, and temperature at the points of the layer can be represented in the form of the linear combinations of the six auxiliary functions. The auxiliary functions are connected with the Hankel transforms of displacements, stresses, temperature and flow at the points of the upper boundary of the corresponding layer. For the problem considered six auxiliary functions can be found from the boundary conditions. Using the conditions on the common boundaries of the layers and entering a dummy layer the recurrent formulas for finding other auxiliary functions are constructed. The auxiliary functions of each layer are dependence. This dependence is represented in the matrix form using so-called compliance functions. The recurrence relations for the compliance functions of the thermoelastic multilayer plate are constructed. The algorithm for solving the сonsidered problem is formulated. The numerical calculations are made for a two-layer plate subjected to the action of the thermal loads. The influence of the coefficient of thermal resistance on the distribution of temperature at the points of the lower boundary of the upper layer and at the points of the upper boundary of the lower layer is analyzed. Also the influence of this coefficient on the distribution of normal stresses at the common boundary of layers is analyzed.