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Isogeometric collocation methods for Cosserat rods and rod structures

Weeger, Oliver ; Yeung, Sai-Kit ; Dunn, Martin L. (2022)
Isogeometric collocation methods for Cosserat rods and rod structures.
In: Computer Methods in Applied Mechanics and Engineering, 2016, 316
doi: 10.26083/tuprints-00019821
Article, Secondary publication, Postprint

Copyright Information: CC BY-NC-ND 4.0 International - Creative Commons, Attribution NonCommercial, NoDerivs.

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Item Type: Article
Type of entry: Secondary publication
Title: Isogeometric collocation methods for Cosserat rods and rod structures
Language: English
Date: 2022
Place of Publication: Darmstadt
Year of primary publication: 2016
Publisher: Elsevier
Journal or Publication Title: Computer Methods in Applied Mechanics and Engineering
Volume of the journal: 316
Collation: 24 Seiten
DOI: 10.26083/tuprints-00019821
Corresponding Links:
Origin: Secondary publication service

We present a novel method for the mechanical simulation of slender, elastic, spatial rods and rod structures subject to large deformation and rotation. We develop an isogeometric collocation method for the geomet-rically exact, nonlinear Cosserat rod theory. The rod centerlines are represented as spatial NURBS curvesand cross-section orientations are parameterized in terms of unit quaternions as 4-dimensional NURBS curves. Within the isogeometric framework, the strong forms of the equilibrium equations of forces and moments of the discretized Cosserat model are collocated, leading to an efficient method for higher-order discretizations. For rod structures consisting of multiple, connected rods we introduce a formulation withrigid, quasi-G1-coupling. It is based on the strong enforcement of continuity of displacement and change of cross-section orientation at interfaces. We also develop a mixed isogeometric formulation, which is basedon an independent discretization of internal forces and moments and alleviates shear locking for thin rods. The novel rod simulation methods are verified by numerical convergence studies. Further computational examples include realistic applications with large deformations and rotations, as well as a large-scale rodstructure with several hundreds of coupled rods and complex buckling behavior.

Status: Postprint
URN: urn:nbn:de:tuda-tuprints-198217
Additional Information:

Isogeometric analysis, Collocation method, NURBS basis functions, Cosserat rod model, Rod structures, Locking-free methods

Classification DDC: 600 Technology, medicine, applied sciences > 600 Technology
600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 16 Department of Mechanical Engineering > Cyber-Physical Simulation (CPS)
Date Deposited: 04 Jan 2022 14:06
Last Modified: 16 Mar 2023 14:09
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19821
PPN: 506022293
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