Task solving organization of the inverse thermoelasticity problem for a rectangular plates
The approach for solving the inverse problem of thermoelasticity, based on the method of the functions of influence, is proposed. The use of the functions of influence makes it possible to represent the temperature and the thermal voltage depending on the same desired vector. The numerical results of the identification of the thermal load measured with the error of thermal stress, which is characterized by a random quantity distributed under the normal law. The approach considered in this article is adapted to the problems of determining the non-stationary temperature and thermo-stressed states of isotropic two-layer hollow long cylinders and balls in the absence of information on the thermal load on one of the boundary surfaces. Under the well-known behavior in time of temperature and radial displacements of another boundary surface on the basis of the proposed method, problems are formulated, which are reduced to the inverse thermoelasticity problems, which are described by the Volterr integral equations of the first kind of convolution. Thermoelastic deformations have been discussed and illustrated numerically with the help of temperature and determined. The study of the kernels of the obtained integral equations for the considered bodies showed that they are additionally defined, monotonically increasing and have a root feature in the interval, i.e., they are Abel type integral equation. The functional spaces, for which the problems are well-posed, have been found. According to the results, obtained analytically, we can conclude, that the conditions for agreeing the values of the initial temperature, given radial displacements and pressures inside and outside the system at the initial moment of time are fulfilled. The basis of the model is the parametrization of a direct problem of nonlinear theory thin-walled elements using the boundary elements method ã 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 observationfrom those calculated on the basis of an approximate solution.
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