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Fundamental Equations and Extremum Principles in the Theory of Thin Shells

  • R. De Boer
  • W. Walther
Conference paper
Part of the Lecture Notes in Engineering book series (LNENG, volume 19)

Abstract

The present paper contributes to the non-linear theory of thin elastic shells in the frame of small strains but finite displacements and rotations (see [2], [3]). In describing the kinematic of deformations as well as in deducing the equilibrium conditions from the conservation laws of continuum mechanics the approximation is consequently applied that strains are small in every material point of the shell. The classification of occuring rotations as e.g. in [4] or restrictions in magnitude are not necessary.

Keywords

Unit Normal Vector Thin Shell Middle Surface Extremum Principle Actual Placement 
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References

  1. 1.
    DE BOER, R.: Vektor- und Tensorrechnung für Ingenieure, Springer-Verlag, Berlin-Heidelberg-New York 1982.MATHGoogle Scholar
  2. 2.
    NAGHDI, P.M.: The theory of shells and plates, in: Encyclopedia of Physics, Vol. VI a/2, Mechanics of Solids II, Ed. by S. Flügge, 425–640, Springer-Verlag, Berlin-Heidelberg-New York 1972.Google Scholar
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    STEIN, E., BERG, A., WAGNER, W.: Different levels of nonlinear shell theory in finite element stability analysis, in: Buckling of shells, Ed. by E. Ramm, Springer-Verlag, Berlin-Heidelberg-New York 1982.Google Scholar
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    PIETRASZKIEWICZ, W.: Lagrangian description and incremental formulation in the non-linear theory of thin shells, Int. J. Non-linear Mechanics 19, No.2, 115–140, 1984.CrossRefMATHADSGoogle Scholar
  5. 5.
    VON KÁRMÁN, Th.: Festigkeitsprobleme im Maschinenbau, in: Encyclopädie der Mathematischen Wissenschaften, Vol. 4/4, 311–385, 1910.Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1986

Authors and Affiliations

  • R. De Boer
    • 1
  • W. Walther
    • 1
  1. 1.Institut für MechanikUniversität EssenEssen 1Germany

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