Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

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IssuesArchive of Issues2004-1pp.127-131

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N. V. Minaeva, "Nearly axisymmetric stress-strain state of an elastic-plastic pipe," Mech. Solids. 39 (1), 127-131 (2004)
Year 2004 Volume 39 Number 1 Pages 127-131
Title Nearly axisymmetric stress-strain state of an elastic-plastic pipe
Author(s) N. V. Minaeva (Voronezh)
Abstract We consider the stress-strain state of an elastic-plastic pipe under internal and external pressure. The cross-section of the pipe is close to a circular ring and its divergence from the ring is characterized by two small parameters. The solution is sought in the form of series in terms of powers of these parameters. We find a condition which ensures these series to be of Taylor type.
References
1.  D. D. Ivlev and L. V. Ershov, Perturbation Method in the Theory of Elastic-Plastic Deformations [in Russian], Nauka, Moscow, 1978.
2.  D. D. Ivlev and L. V. Ershov, "Buckling of a thick-walled pipe under internal pressure," Izv. AN SSSR. OTN, No. 8, pp. 149-152, 1957.
3.  L. S. Leibenzon, "Application of harmonic functions to the problem of stability of spherical and cylindrical shells," in L. S. Leibenzon, Selected Works. Volume 1 [in Russian], Izd-vo AN SSSR, Moscow, 1951.
4.  A. Yu. Ishlinskii, "Problems of stability of equilibrium of elastic media from the standpoint of mathematical elasticity," Ukr. Matem. Zh., Vol. 6, No. 2, pp. 140-146, 1954.
5.  A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow, 1976.
6.  M. A. Naimark, Linear Differential Operators, Nauka, Moscow, 1968.
7.  M. A. Artemov and N. V. Minaeva, "On the existence of states of systems with distributed parameters," Mathematical Modelling of Systems [in Russian], pp. 8-12, Izd-vo Voronezhsk. Un-ta, 1998.
Received 24 April 2001
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