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An enhanced co‐rotational approach for large displacement analysis of plates
Author(s) -
Izzuddin B. A.
Publication year - 2005
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.1415
Subject(s) - quadrilateral , tangent stiffness matrix , rotational symmetry , displacement (psychology) , tangent , mathematics , stiffness , jerk , rotation (mathematics) , rotational invariance , stiffness matrix , mathematical analysis , finite element method , geometry , algorithm , structural engineering , classical mechanics , physics , engineering , psychology , acceleration , psychotherapist
This paper presents a new co‐rotational approach for the large displacement analysis of plates employing 4‐noded quadrilateral flat shell elements. The proposed approach benefits from (i) a simple local co‐rotational system invariant to the element nodal ordering, (ii) the choice of the two smallest components of the nodal normal vector as global rotational degrees of freedom, and (iii) the use of hierarchic freedoms, that are unaffected by the co‐rotational transformations, for higher‐order accuracy. Important additional benefits that arise from the aforementioned features include symmetry of the tangent stiffness matrix and complete insensitivity of the large displacement transformations to the size of the incremental step. The applicability of the new approach to moderately thick as well as thin plates is illustrated by considering two alternative local formulations based on the Reissner–Mindlin and discrete Kirchhoff hypotheses. Several examples are finally presented which demonstrate the accuracy, step‐insensitivity and computational benefits of the proposed co‐rotational approach for large displacement analysis of plate structures. Copyright © 2005 John Wiley & Sons, Ltd.