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Linear and non‐linear finite element error estimation based on assumed strain fields
Author(s) -
Gabaldón F.,
Goicolea J. M.
Publication year - 2002
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.507
Subject(s) - finite element method , linear elasticity , elasticity (physics) , von mises yield criterion , mixed finite element method , mathematics , norm (philosophy) , plasticity , galerkin method , work (physics) , strain energy , mathematical analysis , structural engineering , mechanical engineering , engineering , physics , political science , law , thermodynamics
In this work we analyse the use of enhanced strain fields for the purpose of error estimation in finite element solid mechanics applications. The proposed approach evaluates the quality of the solution for standard Galerkin displacement elements, taking into account the enrichment of the solution with enhanced assumed strain mixed elements. The contribution of the enhanced strain modes is measured with an energy norm. The method proposed has two interesting advantages. Firstly, it results in a local formulation which is evaluated element by element. Secondly, it is easily extended to non‐linear problems. In this work, the formulation is developed for linear elasticity, for finite strain elasticity, and von Mises small strain plasticity. Finally, some representative numerical simulations are presented which show in practice the performance of the method. Copyright © 2002 John Wiley & Sons, Ltd.