We propose a procedure for the numerical-analytic solution of one-dimensional problems of thermoelasticity for bodies of simple geometry based on the representation of temperature dependences of the physicomechanical characteristics of materials in the form of piecewise constant functions of temperature and the application of the Kirchhoff substitution and the methods of generalized functions. This procedure enables us to study one-dimensional nonstationary thermal and quasistatic stress-strain states under the combined thermal and force action with controlled reliability.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ya. M. Grigorenko, A. T. Vasilenko, and N. D. Pankratova, Problems of the Theory of Elasticity of Inhomogeneous Bodies [in Russian], Naukova Dumka, Kiev (1991).
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford (1959).
Yu. M. Kolyano and A. N. Kulik, Temperature Stresses from Volume Sources [in Russian], Naukova Dumka, Kiev (1983).
R. M. Kushnir and V. S. Popovych, Thermoelasticity of Thermosensitive Bodies, in: Ya. I. Burak and R. M. Kushnir (editors), Modeling and Optimization in the Thermomechanics of Conducting Inhomogeneous Bodies [in Ukrainian], Vol. 3, Spolom, Lviv (2009).
A. V. Lykov, Theory of Heat Conduction, Vysshaya Shkola, Moscow (1967).
S. V. Maslenkov and E. A. Maslenkova, Steels and Alloys for High Temperatures: A Handbook [in Russian], Vol. 1, Metallurgiya, Moscow (1991).
Ya. S. Podstrigach, V. A. Lomakin, and Yu. M. Kolyano, Thermoelasticity of Bodies with Inhomogeneous Structures [in Russian], Nauka, Moscow (1984).
Y. Kiani and M. R. Eslami, “Geometrically nonlinear rapid heating of temperature-dependent circular FGM plates,” J. Therm. Stresses, 37, No. 12, 1495–1518 (2014).
V. Popovych, “Methods for the Determination of the Thermostressed State of Thermosensitive Solids under Complex Heat Exchange Conditions,” in: R. B. Hetnarski (editor), Encyclopedia of Thermal Stresses, Vol. 6, Springer (2014), pp. 2997–3008.
Author information
Authors and Affiliations
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 4, pp. 99–106, October–December, 2015.
Rights and permissions
About this article
Cite this article
Makhorkin, І.М., Mastykash, L.V. On One Numerical-Analytic Method for the Solution of One-Dimensional Quasistatic Problems of Thermoelasticity for Thermosensitive Bodies of Simple Geometry. J Math Sci 228, 122–132 (2018). https://doi.org/10.1007/s10958-017-3610-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-017-3610-2