Application of nonclassical models of shell theory to study mechanical parameters of multilayer nanotubes

Article

Bauer, S. M., Ermakov, A. M., Kashtanova, S. V. and Morozov, N. F.. 2011. "Application of nonclassical models of shell theory to study mechanical parameters of multilayer nanotubes." Vestnik: Mathematics (St. Petersburg University). 44 (1), p. Article 13. https://doi.org/10.3103/S1063454111010055
Article Title

Application of nonclassical models of shell theory to study mechanical parameters of multilayer nanotubes

ERA Journal ID32483
Article CategoryArticle
AuthorsBauer, S. M. (Author), Ermakov, A. M. (Author), Kashtanova, S. V. (Author) and Morozov, N. F. (Animator)
Journal TitleVestnik: Mathematics (St. Petersburg University)
Vestnik: Mathematics (St. Petersburg University) (Vestnik: Mathematics (Sankt-Peterburgskii Universitet))
Journal Citation44 (1), p. Article 13
Year2011
Place of PublicationNew York, USA
ISSN1025-3106
1063-4541
1934-7855
Digital Object Identifier (DOI)https://doi.org/10.3103/S1063454111010055
Web Address (URL)http://link.springer.com/article/10.3103/S1063454111010055
Abstract

Stress-strain state of multilayer anisotropic cylindrical shells under a local pressure is studied. Such a problem may model the bending of an asbestos nanotube under the action of a research probe. In earlier works, these authors showed that the application of classical shell theories yields results far from experimental data. More accurate results are obtained by taking into account additional factors, such as the change of the transverse displacement magnitude (according to the Timoshenko-Reissner theory) or the layered structure of asbestos and cylindrical anisotropy (according to the Rodinova-Titaev-Chernykh theory). In the present paper, yet another shell theory, the Palii-Spiro theory, is applied to solve the problem; this theory was developed for shall of average thickness and is based on the following assumptions: (a) the rectilinear fibers of the shell perpendicular to its middle surface before deformation remain rectilinear after deformation; (b) the cosine of the angle between the shell of such fibers and the middle surface of the deformed shell equals the averaged angle of the transverse displacement.

Deformation field are studied with the use of nonclassical (the Rodinova-Titaev-Chernykh and Palii-Spiro) shell theories; a comparison with results obtained for three-dimensional models with the use of the Ansys 11 package is performed.

Original Russian Text © S.M. Bauer, A.M. Ermakov, S.V. Kashtanova, N.F. Morozov, 2011, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2011, No. 1, pp. 23–31.

ANZSRC Field of Research 2020490303. Numerical solution of differential and integral equations
490410. Partial differential equations
401707. Solid mechanics
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Byline AffiliationsSaint Petersburg State University, Russia
Institution of OriginUniversity of Southern Queensland
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