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Variational principles and membrane finite elements with drilling rotations for geometrically non‐linear elasticity
Author(s) -
Ibrahimbegović Adnan,
Frey François
Publication year - 1995
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.1620381106
Subject(s) - finite element method , linear elasticity , factorization , elasticity (physics) , mathematics , compatibility (geochemistry) , rotation (mathematics) , algebra over a field , mathematical analysis , geometry , pure mathematics , engineering , algorithm , structural engineering , physics , chemical engineering , thermodynamics
Variational principles for geometrically non‐linear continuum with independent rotation field are constructed based on the polar factorization theorem. Their regularized forms are next discussed suitable for the finite element implementation. The considerations are specialized to a two‐dimensional membrane problem, and standard isoparametric interpolations are used in order to construct membrane elements with drilling rotations. The elements are evaluated on a set of problems in geometrically non‐linear elastostatics.