ABSTRACT
The particular interest in the mechanics of deformable solid are the problems
associated with the bends of flexible plates and various flexible shells working in
non-uniform temperature field. Such problems are commonly encountered in applied
problems of the construction, oil-field, mechanical engineering, water and air
transport. During mathematical review of such kind of problems you have to deal
with systems of linear differential equations with variable coefficients and nonlinear
differential equations, and making analytical solution of which represents
considerable mathematical difficulties. Analytical solutions of such problems can be
made by the method of partial discretization, the method that has been derived by
one of the authors of this article based on the theory of generalized functions.
The paper considers the problem of thermoelasticity of inhomogeneous circular
flexible plate in the axially symmetric temperature field by taking into account the
influence of bending tension and change of elastic properties of plate material along
its thickness. The problem of compound bending of inhomogeneous circular plate
exposed to the action of lateral load, under temperature changes in thickness of the
plate with the influence of bending tension come to the investigation of decoupled
system of differential equations, obtaining of analytical solution of which using the
existing mathematical apparatus was not possible.