Identification of the thermal and thermostressed states of a two-layer cylinder from surface displacements

Abstract

The problem of identifying the law of time variation in the temperature of one boundary surface of a two-layer cylinder and its thermal and thermostressed state from the temperature and radial displacement of the other surface is formulated and solved. The inverse problem of thermoelasticity to which the problem posed is reduced is analyzed for well-posedness. The solution of the direct problem of thermoelasticity is used to numerically test the technique of solving the inverse problem Keywords: two-layer cylinder, identification, inverse problem of thermoelasticity, well-posedness, numerical testingIntroduction. The experimental analysis of the thermal and thermostressed states of parts of operating heat-and-power equipment is often complicated by the fact that the thermal load on a part can only be determined on some portion of its boundary surface for design, technological, or methodical reasons [11,12]. Therefore, the problems of heat transfer and thermoelasticity are ill-posed, and additional data are needed to solve them. If the original problem is supplemented with information on the behavior of thermal parameters (temperature, heat flow) at some point(s) of a part, then the thermal load can be identified by solving ill-posed inverse problems of heat transfer. The studies based on such an approach are systematized in the monographs [5,11,12,23]. Most algorithms used in these studies to construct regularized solutions to inverse heat-transfer problems assume that additional data are obtained (measured) at an internal point(s) of the body. However, it is not always justified to disturb an operative part to make such measurements. Moreover, it may even be impossible to determine all the characteristics of thermal load in the inverse heat-transfer problem [13]. In this connection, the recent studies [13,14,16,24] identified the thermal and thermostressed states of a body using data on the behavior of mechanical parameters (displacements, strains, stresses) at some point as additional information. The temperature of the boundary surface of a thick layer was determined in [14,16] within the framework of a one-dimensional dynamic problem of thermoelasticity. The heat flow on the inside surface of a long hollow cylinder was determined in [13,22] from the temperature and strains on the outside surface. It was shown in [9, 10] that the use of additional information on the behavior of the displacements of the boundary surface to reduce the identification problem to the inverse problem of thermoelasticity leads to a qualitatively new result-the resulting inverse problems of thermoelasticity are under certain conditions well-posed in the sense of Tikhonov [7] and, hence, can be solved using methods intended for well-posed problems. It was proved in [22] that the problem of identifying the thermostressed state of an elastic body from displacements and temperature on a portion of its boundary surface has a unique solution.The present paper addresses the inverse problem of thermoelasticity to which we reduce the problem o...

Inverse Thermoelastic Analysis of a Cylindrical Tribo-Couple

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“…Assume the unknown temperature t 1 (η) to be a continuous function on the interval [0, τ], i.e., t 1 (η) ∈ C [0,τ] , to construct a solution to Equation (16). Let us represent the time interval [0, τ m ] by the mesh consisting of m intervals of the length h = τ m /m and represent the sought-out function on each of these intervals by a linear spline…”

“…For non-stationary processes, these conditions usually express the fitting between the input data at the initial moment of time or interrelation of the mechanical components on the surfaces of the solid [ 1 , 10 ]. Some methods for solving one- and two-dimensional inverse thermoelasticity problems have been addressed in [ 11 , 12 , 13 , 14 , 15 , 16 ].…”

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Effect of Material Properties in the Direct and Inverse Thermomechanical Analyses of Multilayer Functionally Graded Solids

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