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A stabilized 9‐node non‐linear shell element
Author(s) -
Kebari H.,
Cassell A. C.
Publication year - 1992
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.1620350104
Subject(s) - finite element method , polar decomposition , von mises yield criterion , isotropy , linearity , mathematics , node (physics) , mathematical analysis , buckling , shell (structure) , stress (linguistics) , geometry , structural engineering , polar , engineering , physics , mechanical engineering , linguistics , philosophy , electrical engineering , quantum mechanics , astronomy
A non‐linear 9‐node stress resultant shell finite element with six degrees of freedom per node is formulated. The material non‐linearity is based on an implicit integration scheme using the von Mises yield criterion and linear isotropic bardening. The small strain geometric non‐linearity is formulated using the polar decomposition theorem of continuum mechanics via a corotational updated Lagrangian method, which represents finite rotations with accuracy. Reduced integration is used to remove locking and calculate the stresses at their optimal stress accuracy points. A practical procedure is employed to stabilize the troublesome spurious zero energy modes. A number of tests covering the non‐linear material and geometry ranges and buckling show the good performance of the new element.