Numerical treatment of a geometrically nonlinear planar Cosserat shell model

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...

Full description

Saved in:
Bibliographic Details
Published in:Computational mechanics 2016-05, Vol.57 (5), p.817-841
Main Authors: Sander, Oliver, Neff, Patrizio, Bîrsan, Mircea
Format: Article
Language:English
Subjects:
Algebra
Classical and Continuum Physics
Computational Science and Engineering
Discretization
Engineering
Geodesy
Mathematical analysis
Mathematical models
Minimization
Nonlinearity
Original Paper
Shear
Theoretical and Applied Mechanics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-016-1263-5