The research of stress-strained conditions of aviation and power industrial facilities refers to the problems of mechanics of a solid deformed body. In this case the ultimate goal of the research may be different: determination of the stress-strain state of specific objects; identification of mechanical characteristics of materials. But if we assume that the study of the stress-strain state of a body with known all other initial data is the subject of a direct problem, then the definition of any parameter of the system by known characteristics stress-strain state can be attributed to the class of inverse problems of the mechanics of a deformed solid. New inverse thermoelasticity problems for thin ring have been formulated in which unknown thermal loading (temperature of boundary surface and intensity of frictional heat flux) has been determined using additionally given vertical displacements of one of the outer boundary surfaces. The functional spaces, for which the problems are well-posed, have been found. The method for solving the problems has been suggested and numerically verified with the use of the solution of the direct problem. This paper deals with the determination of heating temperatures and temperature distributions on the upper surface of a thin ring. The expressions of the heating temperatures and temperature distributions have been obtained in series form, involving Bessel's functions with the help of the integral transform technique. Thermoelastic deformations have been discussed and illustrated numerically with the help of temperature and determined. In the framework of the nonlinear theory of thin rings on the basis of the inverse problem method was formulated a model of deformation of the observed thin-walled ring with loads, boundary conditions, geometric parameters to be determined. The basis of the model is the parametrization of a direct problem of nonlinear theory thin-walled elements using the boundary elements method г and the variational formulation of the identification problem, which provides for minimization of the residual functional reflecting the deviation of stress-strain state parameters obtained as a result of observation from those calculated on the basis of an approximate solution.

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