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Computational Mechanics of Nonlinear Response of Shells pp 237–257Cite as

An Assumed Strain Mixed Formulation for Nonlinear Shells

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Part of the book series: Springer Series in Computational Mechanics ((SSCMECH))

Summary

A mixed finite element formulation with stabilization matrix is presented for geometrically nonlinear thin shells. This formulation is based on the degenerate solid shell element concept and the Hellinger-Reissner principle with independent strain field. The independent strain field is divided into a lower order part and a higher order part. Using the equivalence between displacement formulation and mixed formulation, the lower order part is replaced by the displacement-dependent strain at reduced integration points. The higher order independent strain terms are selected to stabilize the spurious kinematic modes which exist in the element stiffness matrix obtained by using reduced integration. One set of the higher order assumed independent strain components is presented for a four-node degenerate solid shell element. For a nine-node degenerate solid shell element, two versions of the higher order assumed independent strain field are proposed. Numerical results demonstrate that the nine-node shell element based on the present formulation produces very accurate and reliable solutions even for very thin shells undergoing large rotations.

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Authors and Affiliations

  1. Department of Aerospace Engineering, The University of Maryland, College Park, MD, 20742, USA

    J. J. Rhiu & S. W. Lee

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  1. J. J. Rhiu
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  2. S. W. Lee
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Editors and Affiliations

  1. Institut für Statik und Dynamik, Ruhr-Universität Bochum, Universitätsstraße 150, 4630, Bochum, Germany

    Wilfried B. Krätzig

  2. Escola Tècnica Superior d’Enginyers de Caminos Canales y Puertos, Universidad Politècnica de Catalunya, Jordi Girona Salgado, 31, 08034, Barcelona, Spain

    Eugenio Oñate

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© 1990 Springer-Verlag Berlin Heidelberg

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Rhiu, J.J., Lee, S.W. (1990). An Assumed Strain Mixed Formulation for Nonlinear Shells. In: Krätzig, W.B., Oñate, E. (eds) Computational Mechanics of Nonlinear Response of Shells. Springer Series in Computational Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84045-6_12

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  • DOI: https://doi.org/10.1007/978-3-642-84045-6_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-84047-0

  • Online ISBN: 978-3-642-84045-6

  • eBook Packages: Springer Book Archive

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