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A CO‐ROTATIONAL FORMULATION FOR 2‐D CONTINUA INCLUDING INCOMPATIBLE MODES
Author(s) -
CRISFIELD M. A.,
MOITA G. F.
Publication year - 1996
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19960815)39:15<2619::aid-nme969>3.0.co;2-n
Subject(s) - mathematics , geometry , physics , materials science
The co‐rotational finite element method is well known for decomposing the motion of an element into a rigid body motion and a strain‐producing deformation. A key feature is the definition of the rotating frame and, partially for this reason, the method has almost exclusively been applied to beams and shells. A novel feature of the current paper is that the method is applied to continua—in the current case, two‐dimensional. The main motivation is to allow the analyst to quickly introduce the latest and best linear elements into a non‐linear context. To this end, in the current work, a set of ‘incompatible modes’ or ‘enhanced strains’ is added to the conventional four‐noded elements. While the main body of the paper considers small strains, as a further novel aspect, it later applies the co‐rotational method to problems with large strains (here via hyperelasticity) and, to this end, establishes a link between the co‐rotational technique and a Biot stress formulation.