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Hierarchical modeling of heterogeneous plates
Author(s) -
Carius Ana C.,
Madureira Alexandre L.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3291
Subject(s) - a priori and a posteriori , mathematics , mathematical optimization , calculus (dental) , algorithm , epistemology , medicine , philosophy , dentistry
The use of asymptotic limits to model heterogeneous plates can be troublesome, because it requires a priori knowledge on the ratio between characteristic lengths of heterogeneities and thickness. Moreover, it also relies on some assumption on the inclusions, like periodicity. We propose and analyze here hierarchical modeling techniques and show that such approach not only avoids such pitfalls, but it is actually simpler to obtain, and it provably converges to the correct asymptotic limits. Its derivation does not requires any restrictive assumptions on the heterogeneities. Copyright © 2014 John Wiley & Sons, Ltd.