The Infinite Hierarchy of Elastic Shell Models: Some Recent Results and a Conjecture
We summarize some recent results of the authors and their collaborators, regarding the derivation of thin elastic shell models (for shells with mid-surface of arbitrary geometry) from the variational theory of 3d nonlinear elasticity. We also formulate a conjecture on the form and validity of infinitely many limiting 2d models, each corresponding to its proper scaling range of the body forces in terms of the shell thickness.
The first author was partially supported by the NSF grants DMS-0707275 and DMS-0846996, and by the Polish MN grant N N201 547438. The second author was partially supported by the University of Pittsburgh grant CRDF-9003034 and by the NSF grant DMS-0907844.
Received 7/12/2009; Accepted 9/12/2010
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