Evaluation of the Mechanical Parameters of Nanotubes by Means of Nonclassical Theories of Shells

  • Svetlana M. BauerEmail author
  • Andrei M. Ermakov
  • Stanislava V. Kashtanova
  • Nikita F. Morozov
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)


In [3] the stiffness of bridges and cantilevers made of natural chrysotile asbestos nanotubes has been studied by means of scanning probe microscopy. The stiffness is defined as a ratio of the value of the local load (applied to the tube) to the value of the displacement. Nanotubes with different fillers are analyzed. Experiments show that the stiffness of the tube depends on the materials for filling. The tubes with water are softer and the tubes filled with mercury are more rigid than tubes without filling materials. It was shown in [3] that the classical theory of bending can not explain the experimental results, but the experimental results well agree with the Timoshenko-Reissner theory (at least qualitatively), when the interlaminar shear modulus of elasticity changes for different filling materials. When additional factors such as lamination of structure and cylindrical anisotropy are taken into account the theory of Rodionova-Titaev-Chernykh (RTC) permits to obtain much more reliable results. In this work the authors also applied another nonclassical shell theory, namely the shell theory of Paliy-Spiro (PS) developed for shells with moderate thickness. The comparison of nonclassical shell theories (RTCh and PS) with experimental data and FEM calculations are presented.


Theory of anisotropic shells Shell theory of Paliy-Spiro Shell theory of Rodionova-Titaev-Chernykh 


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  1. 1.
    Miller, R.E., Shenoy, V.B.: Size dependent elastic properties of nano-sized structural elements. Nanotechnology, 11(3) 139–147 (2000)CrossRefGoogle Scholar
  2. 2.
    Krivtsov, A.M., Morozov, N.F.: Anomalies in mechanical characteristics of nanometer-size objects. Doklady Physics, 46(11) 825–827 (2001)CrossRefGoogle Scholar
  3. 3.
    Ankudinov, A.V., Bauer, S.M., Kashtanova, S.V., Morozov, N.F., Nyapshaev, I.A.: A study of mechanical stiffness of a solitary asbestos nanotubes (in Russian). Bulletin of Higher Educational Institutions. The North Caucasus Region. Series Natural Sciences. 7-9 (2009)Google Scholar
  4. 4.
    Ankudinov, A.V., Bauer, S.M., Ermakov, A.M., Kashtanova, S.V., Morozov, N.F.: On mechanical properties of asbestos nanotubes (in Russian). XIV International Conference Modern Problems of the Mechanics of Solid Media., Azov, Russia, 2010. Conference Proceedings, Vol. 1, Pp. 35-38Google Scholar
  5. 5.
    Tovstik, P.E.: On the asymptotic character of the approximate models of beams, plates and shells (in Russian). Vestn. S. Peterburg. Univ., Mat. Mekh. Astron., 49, 49-54 (2007)Google Scholar
  6. 6.
    Rodionova, V.A., Titaev, B.F., Chernykh, K.F.: Applied Theory of Anisotropic Plates and Shells (in Russian). St. Peterburg University Press, St. Petersburg (1996)Google Scholar
  7. 7.
    Paliy, O.M., Spiro, V.E.: Anisotropic Shells in Shipbuilding. Theory and Analysis (in Russian). Sudostroenie, Leningrad (1977)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Svetlana M. Bauer
    • 1
    Email author
  • Andrei M. Ermakov
    • 1
  • Stanislava V. Kashtanova
    • 1
  • Nikita F. Morozov
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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