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Geometrically non‐linear method of incompatible modes in application to finite elasticity with independent rotations
Author(s) -
Ibrahimbegović Adnan,
Frey Francois
Publication year - 1993
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.1620362406
Subject(s) - elasticity (physics) , linear elasticity , mathematics , finite element method , mathematical analysis , nonlinear system , convergence (economics) , physics , structural engineering , engineering , quantum mechanics , economics , thermodynamics , economic growth
We discuss a geometrically non‐linear method of incompatible modes. The model problem chosen for the discussion is the finite elasticity with independent rotations. The conditions which ensure the convergence of the method and the methodology to construct incompatible modes are presented. A detailed derivation of variational equations and their linearized form is given for a two‐dimensional plane problem. A couple of geometrically non‐linear two‐dimensional elements with independent rotational freedoms are proposed based on the presented methodology. The elements exhibit a very satisfying performance over a set of problems in finite elasticity.