A Constructive Proof of Korn’s Scaled Inequalities for Shells
Year: 2025
Author: Cristinel Mardare, Thai Ha Nguyen
Communications in Mathematical Analysis and Applications, Vol. 4 (2025), Iss. 1 : pp. 87–111
Abstract
One of Korn’s scaled inequalities for shells asserts that the H1-norm of a displacement field of a shell with thickness 2ε clamped on a portion of its lateral boundary, once scaled to a domain independent of ε, is bounded above by the L^2-norm of the corresponding scaled infinitesimal strain tensor field multiplied by a constant of order ε^{−1}. We give a constructive proof to this inequality, and to other two inequalities of this type, which is thus different from the original proof of Ciarlet et al. [Arch. Rational Mech. Anal. 136 (1996), 163–190].
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmaa.2024-0007
Communications in Mathematical Analysis and Applications, Vol. 4 (2025), Iss. 1 : pp. 87–111
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Korn inequalities shells asymptotic analysis.
Author Details
Cristinel Mardare Email
Thai Ha Nguyen Email