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On the simultaneous use of simple geometrically exact shear-rigid rod and shell finite elements

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Abstract

This work addresses simultaneous use of geometrically exact shear-rigid rod and shell finite elements and describes both models within the same framework. Parameterization of the rotation field is performed by Rodrigues rotation vector, which makes the incremental updating of the rotational variables remarkably simple. For the rod element, cubic Hermitian interpolation for the displacements together with quadratic Lagrange interpolation for the incremental torsion angle were employed, while, for the triangular shell element, a complete quadratic Lagrange interpolation was used. The internal incremental torsion angle resulting from the displacement field within the shell element is then made compatible with the boundary incremental torsion angle of the shell element by an internal Lagrange multiplier. The compatibility between contiguous shell elements as well rod elements is mastered in the standard way by simply connecting nodes. This technique is an important contribution of the work, whose performance is illustrated by several numerical examples.

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Acknowledgements

The first author gratefully acknowledges the Federal Institute of Science and Technology Education of São Paulo for financial support. The second and fourth authors gratefully acknowledge support by the Mercator Research Center Ruhr in the Project “Mikromechanische Modellierung der Materialumformung zur Vorhersage der anisotropen Verfestigung” (Pr-2015-0049). In addition to that, the author P. M. Pimenta acknowledges the support by CNPq under the Grant 308142/2018-7 as well as expresses his acknowledgement to the Alexander von Humboldt Foundation for the Georg Forster Award that made possible his stays at the Universities of Duisburg-Essen and Hannover in Germany as well as to the French and Brazilian Governments for the Chair CAPES-Sorbonne that made possible his stay at Sorbonne Universités on a leave from the University of São Paulo.

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Authors and Affiliations

  1. Department of Civil Construction, Federal Institute of Science and Technology Education of São Paulo, São Paulo, Brazil

    Cátia Costa e Silva

  2. Polytechnic School, University of São Paulo, São Paulo, Brazil

    Paulo M. Pimenta

  3. Universität Duisburg-Essen, Duisburg, Germany

    Sascha Florian Maassen & Jörg Schröder

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  1. Cátia Costa e Silva
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  2. Sascha Florian Maassen
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  3. Paulo M. Pimenta
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  4. Jörg Schröder
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Correspondence to Cátia Costa e Silva.

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Costa e Silva, C., Maassen, S.F., Pimenta, P.M. et al. On the simultaneous use of simple geometrically exact shear-rigid rod and shell finite elements. Comput Mech 67, 867–881 (2021). https://doi.org/10.1007/s00466-020-01967-2

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