Mathematical justification of an elastic elliptic membrane obstacle problem

Ángel Rodríguez-Arós

doi:10.1016/j.crme.2016.10.014

Mathematical justification of an elastic elliptic membrane obstacle problem

Ángel Rodríguez-Arós ¹

¹ E.T.S. Náutica e Máquinas, Paseo de Ronda, 51, 15011, Departamento de Métodos Matemáticos e Representación, Universidade da Coruña, Spain

Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 153-157.

Abstract

Starting from the 3D Signorini problem for a family of elastic elliptic shells, we justify that the obstacle problem of an elastic elliptic membrane is the right approximation posed in a 2D domain, when the thickness tends to zero. Specifically, we provide convergence results in the scaled and de-scaled formulations.

Received: 2016-09-14
Accepted: 2016-10-24
Published online: 2016-11-15

DOI: 10.1016/j.crme.2016.10.014

Keywords: Shells, Contact, Asymptotic analysis, Elasticity, Membrane, Rigid foundation, Signorini

Author's affiliations:

Ángel Rodríguez-Arós ¹

¹ E.T.S. Náutica e Máquinas, Paseo de Ronda, 51, 15011, Departamento de Métodos Matemáticos e Representación, Universidade da Coruña, Spain

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     title = {Mathematical justification of an elastic elliptic membrane obstacle problem},
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     pages = {153--157},
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Ángel Rodríguez-Arós. Mathematical justification of an elastic elliptic membrane obstacle problem. Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 153-157. doi : 10.1016/j.crme.2016.10.014. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.10.014/

References
Cited by

[1] A. Léger; B. Miara The obstacle problem for shallow shells in curvilinear coordinates, C. R. Acad. Sci. Paris, Ser. I, Volume 348 (2010), pp. 1235-1239

[2] A. Léger; B. Miara The obstacle problem for shallow shells: curvilinear approach, Int. J. Numer. Anal. Model. Ser. B, Volume 2 (2011) no. 1, pp. 1-26

[3] A. Rodríguez-Arós Models of elastic shells in contact with a rigid foundation: an asymptotic approach, J. Elasticity (2016) (submitted)

[4] P.G. Ciarlet Mathematical Elasticity, vol. III: Theory of Shells, Stud. Math. Appl., vol. 29, North-Holland Publishing Co., Amsterdam, 2000

[5] P.G. Ciarlet Mathematical Elasticity, vol. I: Three-Dimensional Elasticity, Stud. Math. Appl., vol. 20, North-Holland Publishing Co., Amsterdam, 1988

[6] A. Rodríguez-Arós, Mathematical justification of an elastic elliptic membrane obstacle problem: an asymptotic approach, preprint.

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