Identification of the temperature field and stresses in a thermosensitive cylinder according to the surface strains
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IDENTIFICATION OF THE TEMPERATURE FIELD AND STRESSES IN A THERMOSENSITIVE CYLINDER ACCORDING TO THE SURFACE STRAINS R. M. Kushnir and A. V. Yasins’kyi
UDC 539.3
We identify the time dependence of temperature of a surface of a long hollow thermosensitive cylinder and its thermal and thermal stressed states according to the known temperature and strains on the other surface. The posed problem is reduced to the inverse problem of thermoelasticity. By using the solution of the direct problem of thermoelasticity, we perform the numerical verification of the proposed procedure of solution of the inverse problem.
The diagnostics of thermal and thermal stressed states of the parts of equipment of thermal power plants is often quite complicated because, for various structural, technological, and methodological reasons [1, 2], the thermal loading of the indicated parts can be found (measured) only for a part of their surfaces. Hence, the corresponding problems of heat conduction and thermoelasticity are underdetermined, which means that additional data are required for their solution. If the original problem is supplemented with the data on the parameters of the thermal process (temperature and heat flows) at some points of the analyzed element, then the problem of identification of the unknown thermal loading can be reduced to the solution of ill-posed inverse problems of heat conduction. The investigations based on this approach are systematized in the monographs [1–4]. The major part of the algorithms used for the construction of regularized solutions of the indicated inverse problems of heat conduction require additional data obtained at inner points of the body. However, the violation of the integrity of elements for the corresponding measurements is not always reasonable. Moreover, it is sometimes possible to perform the identification of all parameters of thermal loading for the inverse problem of heat conduction [5]. Thus, in view of the fact that the temperature and strain fields are correlated, it is reasonable to use additional data on the behavior of the parameters of mechanical processes (displacements, stresses, and strains) at some points of the analyzed element [5–8]. For a long hollow cylinder, the efficiency of this approach is experimentally demonstrated in [5]. It is shown that, for the identification of the heat flow on the inner surface of the cylinder, it suffices to know the behavior of temperature and strains on its outer surface. In [9–11], it is shown that, for cylindrical and spherical bodies, the application of additional data on the displacements of one surface of the body and reduction (on the basis of these data) of the problems of identification to the inverse problems of thermoelasticity lead to qualitatively new results, namely, the obtained inverse problems of thermoelasticity are, under certain conditions, well-posed in Tikhonov’s sense and, hence, can be solved by the methods used for the solution of well-posed problems. Note that the problems of identification of residual strains and
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