The problem of thermoelasticity in terms of stresses for an inhomogeneous hollow long cylinder with an arbitrary dependence of the physicomechanical characteristics of the material on the radial coordinate is reduced to the solution of a Fredholm equation of the second kind for radial stress. We obtain this equation by direct integration of the equations of equilibrium and continuity and solve it by reducing to a system of algebraic equations. The results of calculations are compared with the known exact solutions of the problem of thermoelasticity for individual dependences of the characteristics of the material on the radial coordinate. We determine the characteristics of materials, the temperature field, and loading guaranteeing the equality of the radial stress in the cylinder to zero.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 3, pp. 141–147, July–October, 2013.
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Kalynyak, B.M. Fredholm Equations of the Second Kind for Radial Stresses Aimed at the Determination of the Thermoelastic State of an Inhomogeneous Hollow Long Cylinder. J Math Sci 205, 659–666 (2015). https://doi.org/10.1007/s10958-015-2273-0
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DOI: https://doi.org/10.1007/s10958-015-2273-0