Large Rotations in Structural Mechanics — Overview

  • N. Büchter
  • E. Ramm
Part of the International Centre for Mechanical Sciences book series (CISM, volume 328)


Some basic aspects on the handling of finite rotations in structural mechanics are presented in this overview.

Different possibilities to choose the three independent rotation variables are shown. They are based either on elementary rotations or on rotation vectors.

Contrary to continuum elements the linearization of shell or beam elements with rotational degrees of freedom yields an extra contribution to the stiffness matrix.


Rotational Vector Large Rotation Rotation Tensor Fixed Axis Tangent Stiffness Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Büchter, N.: Zusammenführung von Degenerationskonzept und Schalentheorie bei endlichen Rotationen. Dissertation. Bericht Nr. 14, Instituts für Baustatik, Universität Stuttgart, Stuttgart 1992.Google Scholar
  2. 2.
    Büchter, N.; Ramm, E.: Shell Theory versus Degeneration–A Comparison in Large Rotation Finite Element Analysis. International Journal for Numerical Methods in Engineering, Vol. 34 (1992) 39–59.CrossRefzbMATHGoogle Scholar
  3. 3.
    Büchter, N.; Ramm, E.: Comparison of Shell Theory and Degeneration. Nonlinear Analysis of Shells by Finite Elements CISM, Udine, June 24–28, 1991.Google Scholar
  4. 4.
    Cardona, A.; Geradin, M.: A beam finite element non-linear theory with finite rotations. International Journal for Numerical Methods in Engineering, 26, 2403–2438 (1988).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ramm, E.; Matzenmiller, A.: Large deformation shell analyses based on the degeneration concept. State-of-the-Art Texts on ‘Finite Element Methods for Plate and Shells Structures’, Pineridge Press, Swansea, UK (1986).Google Scholar
  6. 6.
    Pietraszkiewicz, W.; Badur, J.: Finite rotations in the description of continuum deformation. Int. J. Engng. Sci. Vol. 21, No. 9, 1097–1115 (1983).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Ramm, E.: Geometrisch nichtlineare Elastostatik und finite Elemente. Habilitation. Bericht Nr. 76–2, Institut für Baustatik, Universität Stuttgart (1976).Google Scholar
  8. 8.
    Ramm, E.: A plate/shell element for large deflections and rotations. US - Germany Symp. on “Formulations and computational algorithms in finite element analysis”, MIT 1976, MIT-Press (1977).Google Scholar
  9. 9.
    Schiehlen, W.: Technische Dynamik. Teubner Studienbücher. Stuttgart (1986).zbMATHGoogle Scholar
  10. 10.
    Simo, J. C.; Vu-Quoc, L.: On the dynamics of 3-d finite-strain rods. Finite element methods for plate and shell structures, 2: Formulations and algorithms. Pineridge Press, Swansea, U.K., 1–30, (1986).Google Scholar
  11. 11.
    Stanley, G.M.; Park, K.C.; Hughes, T.J.R.: Continuum-based resultant shell elements. Finite element methods for plate and shell structures, ed. T.J.R. Hughes et. al., Pineridge Press, Swansea, pp. 1–45 (1986).Google Scholar

Copyright information

© Springer-Verlag Wien 1992

Authors and Affiliations

  • N. Büchter
    • 1
  • E. Ramm
    • 1
  1. 1.University of StuttgartStuttgartGermany

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