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IssuesArchive of Issues2005-3pp.41-45

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N. G. Ryabenkov and R. F. Faizullina, "An asymptotic method in the plane elastic body deformation theory," Mech. Solids. 40 (3), 41-45 (2005)
Year 2005 Volume 40 Number 3 Pages 41-45
Title An asymptotic method in the plane elastic body deformation theory
Author(s) N. G. Ryabenkov (Kazan)
R. F. Faizullina (Kazan)
Abstract An approach to expansion of the stress state of a plane elastic body into a series in terms of a small parameters is proposed. By asymptotic integration, the classical three-dimensional elasticity equations are solved, and the capabilities of the proposed approach for development of deformation models for plates and binding layers are illustrated.
References
1.  A. L. Goldenveizer, "Derivation of an approximate plate bending theory by asymptotic integration of the elasticity equations," PMM [Applied Mathematics and Mechanics], Vol. 26, No. 4, pp. 660-686, 1962.
2.  L. A. Agalovyan, "On the boundary layer interaction with the internal stress-strain state of a strip," Izv. AN ArmSSR, No. 5, pp. 30, 48-62, 1977.
3.  V. M. Mal'kov, "Linear theory of a thin layer of a low-compressibility material," Doklady AN SSSR, Vol. 293, No. 1, pp. 52-54, 1987.
4.  V. V. Bolotin, "Basic equations of reinforced materials," Mekhanika Polimerov, No. 2, pp. 27-38, 1965.
5.  M. Goland, and E. Reissner, "The stresses in cemented joints," J. Appl. Mech., Vol. 11, No. 1, pp. A17-A27, 1944.
6.  Yu. P. Artyukhin, "Stresses in cemented joints," in Investigations on the Theory of Plates and Shells [in Russian], pp. 3-27, Izd-vo KGU, Kazan, 1975.
7.  N. G. Ryabenkov, "Asymptotic solution of elasticity problems for a thin binder layer," in Proceedings of the 18th Int. Conference on the Theory of Shells and Plates. Volume 2 [in Russian], pp. 142-145, Izd-vo SGTU, Saratov, 1997.
8.  N. G. Ryabenkov, "A version of the asymptotic approach in the thin layer elasticity," in Proceedings of the 20th Int. Conference on the Theory of Shells and Plates [in Russian], pp. 254-261, Izd-vo NNGU, Nizhni Novgorod, 2002.
Received 13 May 2003
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