A triangular finite shell element based on a fully nonlinear shell formulation

verfasst von: E. M.B. Campello, P. M. Pimenta, Peter Wriggers
Abstract: This work presents a fully nonlinear six-parameter (3 displacements and 3 rotations) shell model for finite deformations together with a triangular shell finite element for the solution of the resulting static boundary value problem. Our approach defines energetically conjugated generalized cross-sectional stresses and strains, incorporating first-order shear deformations for an inextensible shell director (no thickness change). Finite rotations are treated by the Euler-Rodrigues formula in a very convenient way, and alternative parameterizations are also discussed herein. Condensation of the three-dimensional finite strain constitutive equations is performed by applying a mathematically consistent plane stress condition, which does not destroy the symmetry of the linearized weak form. The results are general and can be easily extended to inelastic shells once a stress integration scheme within a time step is at hand. A special displacement-based triangular shell element with 6 nodes is furthermore introduced. The element has a nonconforming linear rotation field and a compatible quadratic interpolation scheme for the displacements. Locking is not observed as the performance of the element is assessed by several numerical examples, which also illustrate the robustness of our formulation. We believe that the combination of reliable triangular shell elements with powerful mesh generators is an excellent tool for nonlinear finite element analysis.
Organisationseinheit(en): Institut für Baumechanik und Numerische Mechanik
Externe Organisation(en): Universidade de Sao Paulo
Typ: Artikel
Journal: Computational mechanics
Band: 31
Seiten: 505-518
Anzahl der Seiten: 14
ISSN: 0178-7675
Publikationsdatum: 08.2003
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Numerische Mechanik, Meerestechnik, Maschinenbau, Theoretische Informatik und Mathematik, Computational Mathematics, Angewandte Mathematik
Elektronische Version(en): https://doi.org/10.1007/s00466-003-0458-8 (Zugang: Unbekannt)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{ba3238ff150e4c5091c095e816ae986f,
title = "A triangular finite shell element based on a fully nonlinear shell formulation",
abstract = "This work presents a fully nonlinear six-parameter (3 displacements and 3 rotations) shell model for finite deformations together with a triangular shell finite element for the solution of the resulting static boundary value problem. Our approach defines energetically conjugated generalized cross-sectional stresses and strains, incorporating first-order shear deformations for an inextensible shell director (no thickness change). Finite rotations are treated by the Euler-Rodrigues formula in a very convenient way, and alternative parameterizations are also discussed herein. Condensation of the three-dimensional finite strain constitutive equations is performed by applying a mathematically consistent plane stress condition, which does not destroy the symmetry of the linearized weak form. The results are general and can be easily extended to inelastic shells once a stress integration scheme within a time step is at hand. A special displacement-based triangular shell element with 6 nodes is furthermore introduced. The element has a nonconforming linear rotation field and a compatible quadratic interpolation scheme for the displacements. Locking is not observed as the performance of the element is assessed by several numerical examples, which also illustrate the robustness of our formulation. We believe that the combination of reliable triangular shell elements with powerful mesh generators is an excellent tool for nonlinear finite element analysis.",
keywords = "Finite rotations, Large strains, Nonlinear shell formulation, Triangular shell element",
author = "Campello, {E. M.B.} and Pimenta, {P. M.} and Peter Wriggers",
year = "2003",
month = aug,
doi = "10.1007/s00466-003-0458-8",
language = "English",
volume = "31",
pages = "505--518",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "6",
}