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Stress resultant geometrically non‐linear shell theory with drilling rotations. Part III: Linearized kinematics
Author(s) -
Ibrahimbegović Adnan,
Frey François
Publication year - 1994
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.1620372106
Subject(s) - finite element method , linearization , shell (structure) , kinematics , node (physics) , rotation (mathematics) , mixed finite element method , mathematics , virtual work , linear elasticity , mathematical analysis , geometry , nonlinear system , structural engineering , engineering , classical mechanics , physics , mechanical engineering , quantum mechanics
A consistent formulation of the geometrically linear shell theory with drilling rotations is obtained by the consistent linearization of the geometrically non‐linear shell theory considered in Parts I and II of this work. It was also shown that the same formulation can be recovered by linearizing the governing variational principle for the three‐dimensional geometrically non‐linear continuum with independent rotation field. In the finite element implementation of the presented shell theory, relying on the modified method of incompatible modes, we were able to construct a four‐node shell element which delivers a very high‐level performance. In order to simplify finite element implementation, a shallow reference configuration is assumed over each shell finite element. This approach does not impair the element performance for the present four‐node element. The results obtained herein match those obtained with the state‐of‐the‐art implementations based on the classical shell theory, over the complete set of standard benchmark problems.