Geodesic
On the analytical solution of one creep problem
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 3, pp. 282-294

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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.
Keywords: creep, long-term strength, damage parameter, binomial differential, initial problem, system of ordinary differential equations.
Mots-clés : fracture 
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     author = {E. B. Kuznetsov and S. S. Leonov},
     title = {On the analytical solution of one creep problem},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {282--294},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2018_20_3_a2/}
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E. B. Kuznetsov; S. S. Leonov. On the analytical solution of one creep problem. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 3, pp. 282-294. http://geodesic.mathdoc.fr/item/SVMO_2018_20_3_a2/