MSC2010 34A12, 34A34
On the analytical solution of one creep problem
E. B. Kuznetsov1, S. S. Leonov2
| Annotation | The analytical solution of one initial value problem for the system of two ordinary differential equations describing the fracture process of metal structures in deflected mode at creep conditions is considered in the paper. Similar problems arise when calculating the strength characteristics and estimating residual deformations in the design of nuclear reactors, in building and aerospace industries and in mechanical engineering. The solvability of the creep constitutive equations’ system is of great practical importance. The possibility of obtaining an exact analytical solution makes it possible to significantly simplify both the identification of creep characteristics and the process of model examination. Necessary and sufficient integrability conditions imposed on the parameters of the model are obtained for the initial problem using Chebyshev's theorem on the integration of a binomial differential. The recommendations for the numerical solution of the considered problem are given. |
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| Keywords | creep, fracture, long-term strength, damage parameter, binomial differential, initial problem, system of ordinary differential equations |
1Evgenii B. Kuznetsov, Professor, Department of Dynamic Systems Modeling, Moscow Aviation Institute (4 Volokolamskoye highway, Moscow 125993, Russia), Dr. Sci. (Physics and Mathematics), ORCID: https://orcid.org/0000-0002-9452-6577, kuznetsov@mai.ru
2Sergey S. Leonov, Associate Professor, Department of Dynamic Systems Modeling, Moscow Aviation Institute (4 Volokolamskoye highway, Moscow 125993, Russia), Ph.D. (Physics and Mathematics), ORCID: https://orcid.org/0000-0001-6077-0435, powerandglory@yandex.ru
Citation: E. B. Kuznetsov, S. S. Leonov, "[On the analytical solution of one creep problem]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,20:3 (2018) 282–294 (In Russian)
DOI 10.15507/2079-6900.20.201803.282-294
