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On the treatment of finite rotations in the discretization of a geometrically exact beam model
Paul Wasmer
2025
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This work examines the discretizations of finite rotations in the Finite Element Method and Isogeometric Analysis for geometrically exact beam theory. As demonstrated, classical discretization does not achieve optimal convergence behavior. Alternatively, projection-based elements and Gauss-Lobatto elements are explored for beam formulations using directors and quaternions. A formulation based on quaternions proves to be better suited due to its simpler discretization approach.
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Keywords
- geometrically exact beam
- Geometrisch exakter Balken
- isogeometric analysis
- Isogeometrische Analysis
- projection-based finite elements
- Projektions-basierte Finite Elemente
- Quaternionen
- Quaternions
- Rotationen
- rotations
- Simo-Reissner Balken
- Simo-Reissner beam
Links
DOI: 10.5445/KSP/1000178526Editions