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

Bauer, S. M. and Ermakov, A. M. and 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). Article 13. ISSN 1063-4541

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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Permanent restricted access to Published version, in accordance with the copyright policy of the publisher. 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.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Agricultural, Civil and Environmental Engineering
Date Deposited: 26 Oct 2016 02:43
Last Modified: 09 Feb 2017 05:46
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations
09 Engineering > 0913 Mechanical Engineering > 091308 Solid Mechanics
Identification Number or DOI: 10.3103/S1063454111010055
URI: http://eprints.usq.edu.au/id/eprint/29894

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