Plane thermoelastic deformation of a multilayer plate with elastic links between its layers

Abstract

Тhe method of the solution of the stationary plane thermoelastic problem of a multilayer plate with elastic links between its layers is proposed. It is assumed that tangential (normal) elastic links between two neighboring layers exist if the difference between the horizontal (vertical) displacements of points of the upper boundary of the lower layer and of the corresponding points of the lower boundary of the upper layer are proportional to the tangential (normal) stresses on their boundary. It is assumed that the conditions of perfect thermal contact are satisfied on their common boundaries. The technique is based on a compliance functions method and a Fourier transformation method. The Fourier transforms of displacements, stresses, and functions used to describe temperature and flow at the points of a layer can be represented in the form of linear combinations of the auxiliary functions. The auxiliary functions are connected with the Fourier transforms of displacements, stresses, and functions used to describe temperature and flow at the points of the upper boundary of the corresponding layer. For considered problem six auxiliary functions can be found from boundary conditions. Using the conditions on the common boundaries of the layers and the boundary conditions the recurrent formulas for finding other auxiliary functions are constructed. We’ve proved that the auxiliary functions are dependent. This dependence can be represented in the matrix form using so-called compliance functions. We’ve constructed the recurrence relations for the compliance functions of the termoelastic plate. The algorithm for solving the considered problem is formulated. For a two-layer plate subjected to the action of thermal load the influence of the coefficients of elastic links, the coefficients of thermal expantion and the coefficients of thermal conductivity on the distribution of the normal stresses and the tangential stresses on its common boundary is investigated. The proposed method allows to analyze the influence of the mechanical and temperature characteristics of the layers on the distribution of stresses and displacements in the layers of the plate with any finite number of the layers.