A new finite element based on the theory of a Cosserat point

Extension to initially distorted elements for 2D plane strain

authored by: E. F.I. Boerner, Stefan Löhnert, Peter Wriggers
Abstract: This paper describes an improvement of the Cosserat point element formulation for initially distorted, non-rectangular shaped elements in 2D. The original finite element formulation for 3D large deformations shows excellent behaviour for sensitive geometries, large deformations, coarse meshes, bending dominated and stability problems without showing undesired effects such as locking or hourglassing, as long as the initial element shape resembles that of a rectangular parallelepiped. In the following, an extension of this element formulation for 2D plane strain is presented which has the same good properties also for the case of non-rectangular initial element shapes. Results of numerical tests are presented, that clearly show the advantages of the improved Cosserat point element compared to the standard displacement elements and the original version of the Cosserat point element.
Organisation(s): Institute of Continuum Mechanics
Institute of Mechanics and Computational Mechanics
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 71
Pages: 454-472
No. of pages: 19
ISSN: 0029-5981
Publication date: 23.07.2007
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, Engineering(all), Applied Mathematics
Electronic version(s): https://doi.org/10.1002/nme.1954 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{6b502be6c3ac40dfb672ab171f06f96d,
title = "A new finite element based on the theory of a Cosserat point: Extension to initially distorted elements for 2D plane strain",
abstract = "This paper describes an improvement of the Cosserat point element formulation for initially distorted, non-rectangular shaped elements in 2D. The original finite element formulation for 3D large deformations shows excellent behaviour for sensitive geometries, large deformations, coarse meshes, bending dominated and stability problems without showing undesired effects such as locking or hourglassing, as long as the initial element shape resembles that of a rectangular parallelepiped. In the following, an extension of this element formulation for 2D plane strain is presented which has the same good properties also for the case of non-rectangular initial element shapes. Results of numerical tests are presented, that clearly show the advantages of the improved Cosserat point element compared to the standard displacement elements and the original version of the Cosserat point element.",
keywords = "Cosserat point theory, Finite elasticity, Finite element technology, Hourglassing, Locking",
author = "Boerner, {E. F.I.} and Stefan L{\"o}hnert and Peter Wriggers",
year = "2007",
month = jul,
day = "23",
doi = "10.1002/nme.1954",
language = "English",
volume = "71",
pages = "454--472",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "4",
}