Isogeometric collocation methods for Cosserat rods and rod structures

By Oliver Weeger, Sai-Kit Yeung, Martin L. Dunn. 2017

115 citations recorded by the source corpus.

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 geometrically exact, nonlinear Cosserat rod theory. The rod centerlines are represented as spatial NURBS curves and 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 with rigid, quasi- G 1 -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 based on 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 rod structure with several hundreds of coupled rods and complex buckling behavior.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/08b92bdf77f7d5d7e361d27703d429b9d3c08af0

How researchers see this paper

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In Computational Mechanics

1. Josef Kiendl
2. Martin L. Dunn
3. Oliver Weeger
4. Laura De Lorenzis
5. Bharath Narayanan
6. Enzo Marino
7. Thomas J. R. Hughes
8. Alessandro Reali

In Computer Graphics and Computer-Aided Design

1. Laura De Lorenzis
2. Josef Kiendl

In Control and Systems Engineering

1. Bharath Narayanan
2. Martin L. Dunn
3. Laura De Lorenzis
4. Josef Kiendl
5. Oliver Weeger

Citations in the corpus

• An isogeometric collocation method for frictionless contact of Cosserat rods (2017, methodology): “This nonlinear system is then solved with Newton’s method, which requires also the evaluation of the stiffness matrix K(~r, ~q) = df/d(~r,~q) for linearization, see [27] for details.”