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Free Finite Rotations in Deformation of Thin Bodies

  • Leonid I. ShkutinEmail author
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)

Abstract

The term "thin bodies" includes shells, plates and rods. Such bodies are divided in two groups: shell-like and rod-like bodies. The first group includes shells, plates and thin-walled rods, and the second group includes beams and rods with rigid cross-sections. Two approaches to model thin bodies deformation are developed in the scientific literature: axiomatic and approximate. The axiomatic approach was developed by J.Bernoulli, L.Euler, and Cosserat brothers. The paper by J.Ericksen and C.Truesdell [1] stimulated a general interest to axiomatic models of the deformation in mechanics. The review of the relevant publications is given in the references [2–5].This lecture is devoted to construction and application of the approximate deformation models for rod-like and shell-like bodies.

Keywords

Finite rotations Rod-like structures Shell-like structures 

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References

  1. 1.
    Ericksen, J.L., Truesdell, C.: Exact theory of stress and strain in rods and shells. Arch. Rat. Mech. Anal. 1(1), 295–323 (1958)CrossRefGoogle Scholar
  2. 2.
    Shkutin, L.I.: Deformation Mechanics of Flexible Bodies. Nauka, Novosibirsk (1988)Google Scholar
  3. 3.
    Shkutin, L.I.: Generalized models of the Cosserat type for finite deformation analysis of thin bodies. J. Appl. Mech. Tech. Phys. 37(4), 400–410 (1996)CrossRefGoogle Scholar
  4. 4.
    Eremeyev, V.A., Zubov, L.M.: Mechanics of Elastic Shells. Nauka, Moscow (2008)Google Scholar
  5. 5.
    Pietraszkievicz, W., Eremeyev, V.A.: On natural strain measures of the non-linear micropolar continuum. Int. J. Solids Struct. 46, 774–787 (2009)CrossRefGoogle Scholar
  6. 6.
    Shkutin, L.I.: Numerical analysis of axisymmetric buckling of plates under radial compression. J. Appl. Mech. Tech. Phys. 45(1), 89–95 (2004)CrossRefGoogle Scholar
  7. 7.
    Shkutin, L.I.: Numerical analysis of axisymmetric buckling of a conical shell under radial compression. J. Appl. Mech. Tech. Phys. 45(5), 741–746 (2004)CrossRefGoogle Scholar
  8. 8.
    Shkutin, L.I.: Analysis of axisymmetric phase strains in plates and shells. J. Appl. Mech. Tech. Phys. 48(2), 285–291 (2007)CrossRefGoogle Scholar
  9. 9.
    Shkutin, L.I.: Axisymmetric deformation of plates and shells with phase transformations under thermal cycling. J. Appl. Mech. Tech. Phys. 49(2), 330–335 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Institute of Computational ModelingKrasnoyarskRussia

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