We solve a quasistatic problem of thermoelasticity for an infinitely long cylindrical shell made of a material with low shear stiffness. The shell is subjected to the action of local heat sources whose power varies as a function of time. We perform the numerical analysis of temperature fields, annular forces, and axial moments for various practically important modes of heating of the shells.
Similar content being viewed by others
References
H. Bateman and A. Erdélyi, Tables of Integral Transforms, Vol. 1, McGraw-Hill, New York (1954).
V. V. Bolotin, “Equations for the non-stationary temperature fields in thin shells in the presence of sources of heat,” Prikl. Mat. Mekh., 24, No. 2, 361–363 (1960); English translation: J. Appl. Math. Mech., 24, No. 2, 515–519 (1960).
V. K. Hanulich, O. V. Maksymuk, and N. V. Hanulich, “Quasistatic problem of thermoelasticity for a cylindrical shell with heat sources and heat exchange,” Mat. Met. Fiz.-Mekh. Polya, 58, No. 1, 154–161 (2015); English translation: J. Math. Sci., 222, No. 2, 194–204 (2017).
N. V. Hanulich, “Cylindrical shell of finite length with low shear stiffness under the action of local heat sources,” Mat. Met. Fiz.-Mekh. Polya, 59, No. 4, 82–90 (2016); English translation: J. Math. Sci., 238, No. 2, 97–107 (2019).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Nauka, Moscow (1971).
H. B. Dwight, Tables of Integrals and Other Mathematical Data, The Macmillan Company, New York (1961).
A. V. Maksymuk and N. V. Hanulich, “Thermoelasticity of a cylindrical shell with low shear stiffness in a local temperature field,” Mat. Met. Fiz.-Mekh. Polya, 58, No. 3, 26–34 (2015); English translation: J. Math. Sci., 226, No. 1, 28–40 (2017).
B. L. Pelekh, Theory of Shells with Finite Shear Stiffness [in Russian], Naukova Dumka, Kiev (1973).
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions [in Russian], Nauka, Moscow (1983).
V. N. Faddeeva and N. M. Terent’ev, Tables of Values of the Probability Integral of Complex Argument [in Russian], Gostekhteoretizdat, Moscow–Leningrad (1954); English translation: Pergamon, Oxford (1961).
O. Maksymuk and N. Ganulich, “On the calculation of thermoelastic processes in a cylindrical shell with local heat sources,” Math. Model. Comput., 4, No. 2, 162–170 (2017).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 62, No. 2, pp. 62–73, April–June, 2019.
Rights and permissions
About this article
Cite this article
Maksymuk, О.V., Hanulich-Manukian, N.V. Thermoelastic Behavior of an Infinitely Long Cylindrical Shell Compliant to Shear under The Action Of Heat Sources Of Variable Power. J Math Sci 261, 70–84 (2022). https://doi.org/10.1007/s10958-022-05738-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-022-05738-7