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Mathematics > Analysis of PDEs
Title: A constrained Cosserat shell model up to order $O(h^5)$: Modelling, existence of minimizers, relations to classical shell models and scaling invariance of the bending tensor
(Submitted on 27 Oct 2020 (v1), last revised 28 Oct 2020 (this version, v2))
Abstract: We consider a recently introduced geometrically nonlinear elastic Cosserat shell model incorporating effects up to order $O(h^5)$ in the shell thickness $h$. We develop the corresponding geometrically nonlinear constrained Cosserat shell model, we show the existence of minimizers for the $O(h^5)$ and $O(h^3)$ case and we draw some connections to existing models and classical shell strain measures. Notably, the role of the appearing new bending tensor is highlighted and investigated with respect to an invariance condition of Acharya [Int. J. Solids and Struct., 2000] which will be further strengthened.
Submission history
From: Ionel-Dumitrel Ghiba [view email][v1] Tue, 27 Oct 2020 14:10:48 GMT (710kb,D)
[v2] Wed, 28 Oct 2020 07:53:15 GMT (1417kb,D)
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