We propose a procedure of getting analytic expressions for the description of axisymmetric stationary thermal fields, axisymmetric static or quasistatic stress and strain fields in long hollow multilayer cylinders made of thermally sensitive materials with constant normal loads and arbitrary classical conditions of heat exchange specified on the bounding surfaces. The problem of construction of the solution of the problem of heat conduction is reduced to the determination of one constant of integration and all other constants from a nonlinear algebraic equation are determined via the indicated constant. The problem of thermoelasticity is thus reduced to the solution of a system of Volterra integral equations of the second kind with the corresponding integral conditions. As a result of application of the proposed methods for the solution of the system of integral equations, we deduce formulas for the evaluation of the characteristics of the stress-strain state in the form of functional dependences on temperature, mass forces, thicknesses of the layers, surface loads and the temperature dependences of the mechanical characteristics of the materials of layers.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 57, No. 2, pp. 169–186, April–June, 2014.
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Popovych, V.S., Kalynyak, B.M. Mathematical Modeling and Methods for the Determination of the Static Thermoelastic State of Multilayer Thermally Sensitive Cylinders. J Math Sci 215, 218–242 (2016). https://doi.org/10.1007/s10958-016-2833-y
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DOI: https://doi.org/10.1007/s10958-016-2833-y