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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. (Postprint)
In: Computer Methods in Applied Mechanics and Engineering, 316, Elsevier, ISSN 0045-7825,
DOI: 10.26083/tuprints-00019821,
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Item Type: Article
Origin: Secondary publication service
Status: Postprint
Title: Isogeometric collocation methods for Cosserat rods and rod structures
Language: English
Abstract:

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.

Journal or Publication Title: Computer Methods in Applied Mechanics and Engineering
Volume of the journal: 316
Publisher: Elsevier
Collation: 24 Seiten
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 600 Technik
600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 16 Department of Mechanical Engineering > Cyber-Physical Simulation (CPS)
Date Deposited: 04 Jan 2022 14:06
Last Modified: 04 Jan 2022 14:06
DOI: 10.26083/tuprints-00019821
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-198217
Additional Information:

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

URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19821
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