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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
R. E. Miller and V. B. Shenoy, Nanotechnology 11, 139–147 (2000).
A. M. Krivtsov and N. F. Morozov, Dokl. Akad. Nauk 381(3), 345–347 (2001) [Phys.-Dokl. 46 (11), 825–827 (2001)].
A. V. Ankudinov, S. M. Bauer, S. V. Kashtanova, et al., Izv. Vyssh. Uchebn. Zaved. Sev.-Kavkaz. Region, Aktual’nye Probl. Mekh. Estestv. Nauki, 7–9 (2009).
A. V. Ankundinov, S. M. Bauer, A. M. Ermakov, et al., in Modern Problems of Continuum Mechanics. Conference Proceedings 1, 35–38.
P. E. Tovstik, Vestn. S.-Peterburg. Univ., Mat. Mekh. Astron., No. 3, 49 (2007).
V. A. Rodionova, B. F. Titaev, and K. F. Chernykh, Applied Theory of Anisotropic Plates and Shells (S.-Peterburg. Gos. Univ., St. Petersburg, 1996), pp. 40–80 [in Russian].
O. M. Palii and V. E. Spiro, Anisotropic Shells in Shipbuilding. Theory and Computation (Sudostroenie, Leningrad, 1977) [in Russian].
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.
About this article
Cite this article
Bauer, S.M., Ermakov, A.M., Kashtanova, S.V. et al. Application of nonclassical models of shell theory to study mechanical parameters of multilayer nanotubes. Vestnik St.Petersb. Univ.Math. 44, 13 (2011). https://doi.org/10.3103/S1063454111010055
- Cylindrical Shell
- Stress Strain State
- Displacement Component
- Shell Layer
- Shell Theory