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An exact finite rotation shell theory, its mixed variational formulation and its finite element implementation
Author(s) -
Sansour Carlo,
Bufler Hans
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.1620340107
Subject(s) - finite element method , mixed finite element method , shell (structure) , parametric statistics , finite strain theory , degrees of freedom (physics and chemistry) , mathematics , rotation (mathematics) , mathematical analysis , extended finite element method , shell theory , geometry , physics , structural engineering , engineering , mechanical engineering , statistics , quantum mechanics
A non‐linear shell theory, including transverse shear strains, with exact description of the kinematical fields is developed. The strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor. Thus in‐plane rotations, also called drilling degrees of freedom, are included in a natural way. Various alternatives of the theory are derived. For a special version of the theory, with altogether six kinematical fields, different mixed variational principles are given. A hybrid finite element formulation, which does not exhibit locking phenomena, is developed. Numerical examples of shell deformation at finite rotations, with excellent element performance, are presented. Comparison with results reported in the literature demonstrates the features of the theory as well as the proposed finite element formulation.