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A nonlinear quadrilateral shell element with drilling degrees of freedom

Ein nichtlineares Vier-Knoten-Schalenelement unter Verwendung von Drehfreiheitsgraden in der Schalenmittelfläche

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Summary

A bending theory for thin shells undergoing finite deformations is presented, and its associated finite element model is described. The kinematic assumptions are of Reissner-Mindlin type. The formulation is based on the introduction of a mixed functional with independent in-plane rotation field and skew-symmetric part of membrane forces. The resulting Euler-Lagrangian equations yield the equilibrium of stress resultants and the couple resultant with respect to the surface normal. Furthermore, the equality of the independent rotation field with the displacement dependent rotation field is enforced. Hence, the symmetry of the stress resultants is fulfilled in a weak sence. Naturally, the development of a quadrilateral finite element includes drilling degrees of freedom. The displacement field is approximated using an Allman-type interpolation.

Übersicht

Es wird eine Biegetheorie dünner Schalen bei finiten Deformationen sowie die zugehörige Finite-Element-Formulierung vorgestellt. Die kinematischen Annahmen sind vom Reissner-Mindlin-Typ. Die Darstellung basiert auf der Einführung eines gemischten Funktionals mit unabhängigen Drehfreiheitsgraden in der Schalenmmittelfläche und einem schiefsymmetrischen Anteil der Membrankräfte. Die resultierenden Euler-Lagrange-Gleichungen ergeben das Gleichgewicht und die Symmetrie der Schnittgrößen. Weiterhin ergibt sich die Gleichheit des unabhängigen mit dem verschiebungsabhängigen Rotationsfeld. Die Entwicklung des Vier-Knoten-Schalenelementes enthält somit auch den Drehfreiheitsgrad um die Schalenormale. Für das Verschiebungsfeld wird ein Allman-Ansatz gewählt.

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Authors and Affiliations

  1. Institut für Baumechanik und Numerische Mechanik, Universität Hannover, Appelstr. 9A, D-3000, Hannover 1, Federal Republic of Germany

    F. Gruttmann & W. Wagner

  2. Institut für Mechanik TH Darmstadt, Hochschulstr. 1, D-6100, Darmstadt, Federal Republik of Germany

    P. Wriggers

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  1. F. Gruttmann
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  2. W. Wagner
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  3. P. Wriggers
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Gruttmann, F., Wagner, W. & Wriggers, P. A nonlinear quadrilateral shell element with drilling degrees of freedom. Arch. Appl. Mech. 62, 474–486 (1992). https://doi.org/10.1007/BF00810238

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