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Bisector and zero‐macrospin co‐rotational systems for shell elements
Author(s) -
Izzuddin B. A.,
Liang Y.
Publication year - 2015
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/nme.4978
Subject(s) - quadrilateral , tangent stiffness matrix , invariant (physics) , element (criminal law) , tangent , mathematics , rotational invariance , computation , finite element method , geometry , stiffness matrix , engineering , algorithm , structural engineering , political science , law , mathematical physics
Summary A principal issue in any co‐rotational approach for large displacement analysis of plates and shells is associated with the specific choice of the local reference system in relation to the current deformed element configuration. Previous approaches utilised local co‐rotational systems, which are invariant to nodal ordering, a characteristic that is deemed desirable on several fronts; however, the associated definitions of the local reference system suffered from a range of shortcomings, including undue complexity, dependence on the local element formulation and possibly an asymmetric tangent stiffness matrix. In this paper, new definitions of the local co‐rotational system are proposed for quadrilateral and triangular shell elements, which achieve the invariance characteristic to the nodal ordering in a relatively simple manner and address the aforementioned shortcomings. The proposed definitions utilise only the nodal coordinates in the deformed configuration, where two alternative definitions, namely, bisector and zero‐macrospin definitions, are presented for each of quadrilateral and triangular finite elements. In each case, the co‐rotational transformations linking the local and global element entities are presented, highlighting the simplicity of the proposed approach. Several numerical examples are finally presented to demonstrate the effectiveness and relative accuracy of the alternative definitions proposed for the local co‐rotational system. Copyright © 2015 John Wiley & Sons, Ltd.