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Incompressibility in the multimodel Arlequin framework
Author(s) -
Jamond Olivier,
Dhia Hachmi Ben
Publication year - 2013
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.4454
Subject(s) - discretization , compressibility , constraint (computer aided design) , stability (learning theory) , consistency (knowledge bases) , mathematics , mathematical optimization , displacement (psychology) , finite element method , computer science , structural engineering , mathematical analysis , mechanics , engineering , physics , geometry , psychology , machine learning , psychotherapist
SUMMARY In this paper, we show how one can account for the incompressibility constraint within the multimodel Arlequin framework. The main issue is the treatment of a double constraining of the displacement fields in the gluing model zone. An elastic incompressible structure problem is considered. An incompressible Arlequin formulation of this problem is developed and supported by a stability and consistency result. Its discretization by means of mixed finite elements is detailed. The Inf–Sup condition is numerically discussed for different choices of the Arlequin method parameters. Several numerical tests are conducted and practical recommendations for appropriate choices of these parameters are clearly stated. Copyright © 2013 John Wiley & Sons, Ltd.