Existence theorem for a first-order Koiter nonlinear shell model

Sylvia Anicic

doi:10.3934/dcdss.2019106

Article Contents

2019, Volume 12, Issue 6: 1535-1545. Doi: 10.3934/dcdss.2019106

This issue Previous Article Preface Next Article Formal asymptotic analysis of elastic beams and thin-walled beams: A derivation of the Vlassov equations and their generalization to the anisotropic heterogeneous case

Existence theorem for a first-order Koiter nonlinear shell model

Sylvia Anicic

Département de Mathématiques, IRIMAS, Université de Haute-Alsace, 6 rue des Frères Lumière, 68093 Mulhouse Cedex, France

Received: December 31, 2017

Revised: April 30, 2018

Published: April 2019

Abstract Full Text(HTML) Related Papers Cited by

Abstract

We prove the existence of a minimizer for a nonlinearly elastic shell model which coincides to within the first order with respect to small thickness and change of metric and curvature energies with the Koiter nonlinear shell model.

Keywords:

Mathematics Subject Classification: Primary: 74K25, 74B20, 74G65, 74G25; Secondary: 49J20, 35A01, 35Q74.

Citation:

Full Text(HTML)

Related Papers

Cited by

References

	S. Anicic , Polyconvexity and existence theorem for nonlinearly elastic shells, J. Elasticity, 132 (2018) , 161-173. doi: 10.1007/s10659-017-9664-z.
	S. Anicic, A shell model allowing folds, in Numerical Mathematics and Advanced Applications, Springer Italia, (2003), 317-326.
	S. Anicic, From the Exact Kirchhoff-Love Shell Model to a Thin Shell Model and a Folded Shell Model, Ph.D thesis, Joseph Fourier University, France, 2001.
	R. Bunoiu , Ph.-G. Ciarlet and C. Mardare , Existence theorem for a nonlinear elliptic shell model, J. Elliptic Parabol. Equ., 1 (2015) , 31-48. doi: 10.1007/BF03377366.
	Ph.-G. Ciarlet and C. Mardare , A nonlinear shell model of Koiter's type, C. R. Math. Acad. Sci. Paris, 356 (2018) , 227-234. doi: 10.1016/j.crma.2017.12.005.
	Ph.-G. Ciarlet and C. Mardare , A mathematical model of Koiter's type for a nonlinearly elastic "almost spherical" shell, C. R. Math. Acad. Sci. Paris, 354 (2016) , 1241-1247. doi: 10.1016/j.crma.2016.10.011.
	W. T. Koiter On the nonlinear theory of thin elastic shells. Ⅰ, Ⅱ, Ⅲ, Nederl. Akad. Wetensch. Proc. Ser. B, 69 (1966), 1-17, 18-32, 33-54.