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Computational Mechanics
Published in: Computational Mechanics 3/2019

25-02-2019 | Original Paper

Rotation vector and its complement parameterization for singularity-free corotational shell element formulations

Authors: Jinsong Yang, Pinqi Xia

Published in: Computational Mechanics | Issue 3/2019

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Abstract

Theoretical and computational aspects of rotation vector and its complement parameterization are examined in detail in this paper. The mutual relationships between the variations of rotation vector and its complement and the spin variable are presented. It shows that the switch of rotation parameter between rotation vector and its complement preserves not only the strains but also the angular velocity and acceleration, and the force vectors and tangent matrices of an element. Two singularity-free corotational shell element formulations are presented. The first formulation is a non-consistent one, in which a simple way only using rotation vector is proposed to modify the exact rotation update approach via the Baker–Campbell–Hausdorff formula, while the second formulation is a consistent one. The novelty is that, following the presented method, the existing singular spatial beam and shell element formulations based on rotation vector parameterization could be modified to be the singularity-free ones with only a few changes. Finally, three numerical examples involving large rotations are analyzed to demonstrate the capability of the presented formulations.
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Metadata
Title
Rotation vector and its complement parameterization for singularity-free corotational shell element formulations
Authors
Jinsong Yang
Pinqi Xia
Publication date
25-02-2019
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 3/2019
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-019-01681-8

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