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Computational Mechanics
Erschienen in: Computational Mechanics 5/2016

01.05.2016 | Original Paper

Numerical treatment of a geometrically nonlinear planar Cosserat shell model

verfasst von: Oliver Sander, Patrizio Neff, Mircea Bîrsan

Erschienen in: Computational Mechanics | Ausgabe 5/2016

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Abstract

We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general six-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite elements (GFEs), which leads to an objective discrete model which naturally allows arbitrarily large rotations. GFEs of any approximation order can be constructed. The resulting algebraic problem is a minimization problem posed on a nonlinear finite-dimensional Riemannian manifold. We solve this problem using a Riemannian trust-region method, which is a generalization of Newton’s method that converges globally without intermediate loading steps. We present the continuous model and the discretization, discuss the properties of the discrete model, and show several numerical examples, including wrinkling of thin elastic sheets in shear.
Vorheriger Artikel Assessment and improvement of mapping algorithms for non-matching meshes and geometries in computational FSI
Nächster Artikel A peridynamic model for the nonlinear static analysis of truss and tensegrity structures

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Fußnoten
1
Here we deliberately differ from [54], where a point load is used.
 
2
Note that this radius bounds both corrections to m and to \(\overline{R},\) so it cannot be assigned a unit.
 
3
In [40] it was proposed to use a Riemannian trust-region method instead of the simpler Newton method. Such a choice guarantees convergence of the solver. However, in practice we never observed convergence issues even for the simpler Newton method.
 
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Metadaten
Titel
Numerical treatment of a geometrically nonlinear planar Cosserat shell model
verfasst von
Oliver Sander
Patrizio Neff
Mircea Bîrsan
Publikationsdatum
01.05.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 5/2016
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-016-1263-5

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