Sander, O. (2010) Geodesic finite elements for Cosserat rods. International Journal for Numerical Methods in Engineering, 82 (13). pp. 16451670. ISSN 10970207

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Official URL: https://dx.doi.org/10.1002/nme.2814
Abstract
We introduce geodesic finite elements as a new way to discretize the nonlinear configuration space of a geometrically exact Cosserat rod. These geodesic finite elements naturally generalize standard onedimensional finite elements to spaces of functions with values in a Riemannian manifold. For the special orthogonal group, our approach reproduces the interpolation formulas of Crisfield and Jelenić. Geodesic finite elements are conforming and lead to objective and pathindependent problem formulations. We introduce geodesic finite elements for general Riemannian manifolds, discuss the relationship between geodesic finite elements and coefficient vectors, and estimate the interpolation error. Then we use them to find static equilibria of hyperelastic Cosserat rods. Using the Riemannian trustregion algorithm of Absil et al. we show numerically that the discretization error depends optimally on the mesh size. Copyright © 2009 John Wiley & Sons, Ltd.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  1882 
Deposited By:  Ekaterina Engel 
Deposited On:  13 Apr 2016 10:45 
Last Modified:  03 Mar 2017 14:42 
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