Determining the temperature field and thermomechanical characteristics of a material, which ensure zero radial stresses in a long hollow cylinder inhomogeneous in the radial direction
DOI:
https://doi.org/10.15407/dopovidi2015.06.046Keywords:
absence of stresses, exact solutions, functional-graded materials, hollow cylinder, integral equations, inverse problem, thermo-elasticity, thermo-mechanical characteristics of materialsAbstract
A method to determine the temperature field and thermo-mechanical characteristics of a material, providing zero radial stresses along a radius in the inhomogeneous long hollow cylinder is proposed. The solution of the corresponding nonclassical steady uncoupled thermoelasticity problem is reduced to solving a Fredholm integral equation of the second kind relative to the temperature. Exact analytical expressions for the temperature field and the concentration of one ingredient of a two-component functionally graded material providing the zero radial and hoop stresses in limits of a simple-mixture model in the absence of mass forces and the axial loading are obtained. The numerical calculations of temperature fields and thermo-mechanical characteristics for real materials are presented.
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Abrinia K., Naee H., Sadeghi F., Djavanroodi F. Amer. J. oAppl. Sci., 2008, 5, No 7: 852–859.
Bohidar S.K., Sharma R., Mishra P.R. Intern. J. Research (IJR), 2014, 1, No 7: 289–301.
Functionally graded materials in the 21 st cent.: a workshop on trends and forecasts, ed. by Kiyoshi Ichikawa, 2001, 16.
Pidstryhach Ya. S. Selected works, Kyiv: Naukova Dumka, 1995 (in Ukrainian).
Vihak V.M. Optimal control of thermal stresses and displacements, Kyiv: Naukova Dumka, 1988 (in Russian).
Kushnir R.M., Popovych V. S., Yasinskyy A.V. Optimization and identification in thermo-mechanics of inhomogeneous bodies, L'viv: SPOLOM, 2011 (in Ukrainian).
Kalynyak B.M. J. of Math. Sciences, 2015, No 3: 659–666. https://doi.org/10.1007/s10958-015-2273-0
Kanwal R. P. Linear integral equations: theory and technique, New York, London, Toronto, Sydney, San-Francisco: Academic Press, 1971.
Shen H.-S. Functionally graded materials: nonlinear analysis of plates and shells, Boca Raton: CRC Press, 2009. https://doi.org/10.1201/9781420092578
Corless R.M., Gonnet G.H., Hare D. E.G., Jeffrey D. J., Knuth D. E. Advances in Comput. Math., 1996, 5: 329–359. https://doi.org/10.1007/BF02124750
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