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Four‐node semi‐EAS element in six‐field nonlinear theory of shells
Author(s) -
Chróścielewski J.,
Witkowski W.
Publication year - 2006
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.1740
Subject(s) - nonlinear system , shell (structure) , field (mathematics) , finite element method , mathematics , rotation (mathematics) , element (criminal law) , matrix (chemical analysis) , transformation (genetics) , node (physics) , kinematics , rotation matrix , geometry , tensor (intrinsic definition) , classical mechanics , structural engineering , engineering , physics , pure mathematics , mechanical engineering , law , biochemistry , chemistry , materials science , quantum mechanics , political science , composite material , gene
We propose a new four‐node C 0 finite element for shell structures undergoing unlimited translations and rotations. The considerations concern the general six‐field theory of shells with asymmetric strain measures in geometrically nonlinear static problems. The shell kinematics is of the two‐dimensional Cosserat continuum type and is described by two independent fields: the vector field for translations and the proper orthogonal tensor field for rotations. All three rotational parameters are treated here as independent. Hence, as a consequence of the shell theory, the proposed element has naturally six engineering degrees of freedom at each node, with the so‐called drilling rotation. This property makes the element suitable for analysis of shell structures containing folds, branches or intersections. To avoid locking phenomena we use the enhanced assumed strain (EAS) concept. We derive and linearize the modified Hu–Washizu principle for six‐field theory of shells. What makes the present approach original is the combination of EAS method with asymmetric membrane strain measures. Based on literature, we propose new enhancing field and specify the transformation matrix that accounts for the lack of symmetry. To gain knowledge about the suitability of this field for asymmetric strain measures and to assess the performance of the element, we solve typical benchmark examples with smooth geometry and examples involving orthogonal intersections of shell branches. Copyright © 2006 John Wiley & Sons, Ltd.