A method of numerical analysis of temperature fields and thermoelastoplastic stress–strain state of thin shells with assessment of strength under repeated loading is proposed. The modified constitutive equations of the theory of deformation along paths of small curvature are used, taking into account the perfect Bauschinger effect. A numerical example is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Z. Galishin, P. A. Steblyanko, and Yu. N. Shevchenko, “Determining nonstationary temperature fields in thin laminated shells of revolution subject to axisymmetric heating,” Mat. Probl. Tekhn. Mekh., No. 2(19), 3–12 (2012).
A. V. Lykov, Theory of Thermal Conduction [in Russian], Vysshaya Shkola, Moscow (1967).
N. N. Malinin, Strength of Turbo Machines [in Russian], Mashgiz, Moscow (1962).
Ya. M. Grigorenko and A. T. Vasilenko, Theory of Shells with Variable Stiffness, Vol. 4 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kyiv (1981).
Yu. N. Shevchenko and I. V. Prokhorenko, Theory of Elastoplastic Shells under Nonisothermal Loading, Vol. 3 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kyiv (1981).
Yu. N. Shevchenko and V. G. Savchenko, Thermoviscoplasticity, Vol. 2 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1987).
V. V. Novozhilov, Thin Shell Theory, Noordhoff, Groningen (1964).
G. S. Pisarenko, A. P. Yakovlev, and V. V. Matveev, Strength of Materials [in Russian], Naukova Dumka, Kyiv (1988).
V. P. Sdobyrev, “Long-term strength of EI 437B alloy in combined stress state,” Izv. AN SSSR, OTN, No. 4, 92–97 (1958).
Yu. N. Shevchenko, Thermoplasticity under Variable Loading [in Russian], Naukova Dumka, Kyiv (1970).
Yu. N. Shevchenko, M. E. Babeshko, and R. G. Terekhov, Thermoviscoelastoplastic Processes of Combined Deformation of Structural Members [in Russian], Naukova Dumka, Kyiv (1992).
Yu. N. Shevchenko, A. Z. Galishin, P. A. Steblyanko, M. V. Banias, P. G. Degtiarenko, and A. M. Tonkonozhenko, “Determining nonstationary temperature fields in thin laminated shells of revolution during combined heat exchange with the environment,” Mat. Probl. Tekhn. Mekh., No. 2(25), 85–90 (2014).
M. E. Babeshko, A. Z. Galishin, A. I. Semenets, and Yu. N. Shevchenko, “Influence of the stress mode on the strength of high-pressure vessels,” Int. Appl. Mech., 1, No. 3, 319–325 (2015).
M. E. Babeshko and V. G. Savchenko, “Analyzing processes of nonisothermal loading of shells of revolution with allowance for repeated plastic strain,” Int. Appl. Mech., 53, No. 6, 639–646 (2017).
M. E. Babeshko and V. G. Savchenko, “Method of solving the problem of thermoradiation plasticity for layered axisymmetric bodies made of isotropic and orthotropic materials,” Int. Appl. Mech., 57, No. 3, 306–319 (2021).
M. E. Babeshko and V. G. Savchenko, “Elastoplastic axisymmetric stress–strain state of thin shells made of materials with different compressive and tensile moduli,” Int. Appl. Mech., 57, No. 4, 414–423 (2021).
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, Oxford (1947).
R. Hill, The Mathematical Theory of Plasticity, Claredon Press, Oxford (1950).
M. E. Babeshko and V. G. Savchenko, “Technique of allowing for plastic strain under unloading in thermoplasticity problems for axisymmetric bodies,” Int. Appl. Mech., 55, No. 4, 416–425 (2019).
Yu. N. Shevchenko, N. F. Andrushko, M. E. Babeshko, M. V. Banyas, A. Z. Galishin, P. G. Dehtyarenko, V. G. Savchenko, A. V. Tonkonozhenko, and N. N. Tormakhov, “Development of mathematical models and computer technologies for the virtual destructive testing of shell structures,” Sci. Innov., 9, No. 6, 23–30 (2013).
Yu. N. Shevchenko, N. F. Andrushko, M. E. Babeshko, M. V. Banyas, A. Z. Galishin, P. G. Dehtyarenko, V. G. Savchenko, A. V. Tonkonozhenko, and N. N. Tormakhov, “Procedure of forecasting operation and extremal state of critical systems of the rocket technique under repeated thermo-force loading,” Sci. Innov., 11, No. 5, 25–36 (2015).
Yu. N. Shevchenko and V. G. Savchenko, “Three-dimensional problems of thermoviscoplasticity: focus on Ukrainian research (review),” Int. Appl. Mech., 52, No. 3, 217–271 (2016).
P. A. Steblyanko and Yu. N. Shevchenko, “Computational methods in stationary and nonstationary thermal-plasticity problems,” in: Encyclopedia of Thermal Stresses Vol. 2 C–D of 11-volume series, Springer, New York (2014), pp. 623–630.
M. Zyczkowski, Combined Loadings in the Theory of Plasticity, PWN, Warszawa (1981).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prykladna Mekhanika, Vol. 58, No. 6, pp. 70–83, November–December 2022
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Babeshko, M.O., Galishin, A.Z. & Savchenko, V.G. Stress State and Strength of Thin-Walled Structures Under Nonisothermal Reloading. Int Appl Mech 58, 683–694 (2022). https://doi.org/10.1007/s10778-023-01192-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-023-01192-3