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.

Résumé

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.

Reçu le : 2016-09-14
Accepté le : 2016-10-24
Publié le : 2016-11-15

DOI : 10.1016/j.crme.2016.10.014

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

Affiliations des auteurs :

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

@article{CRMECA_2017__345_2_153_0,
     author = {\'Angel Rodr{\'\i}guez-Ar\'os},
     title = {Mathematical justification of an elastic elliptic membrane obstacle problem},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {153--157},
     publisher = {Elsevier},
     volume = {345},
     number = {2},
     year = {2017},
     doi = {10.1016/j.crme.2016.10.014},
     language = {en},
}

TY  - JOUR
AU  - Ángel Rodríguez-Arós
TI  - Mathematical justification of an elastic elliptic membrane obstacle problem
JO  - Comptes Rendus. Mécanique
PY  - 2017
SP  - 153
EP  - 157
VL  - 345
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crme.2016.10.014
LA  - en
ID  - CRMECA_2017__345_2_153_0
ER  -

%0 Journal Article
%A Ángel Rodríguez-Arós
%T Mathematical justification of an elastic elliptic membrane obstacle problem
%J Comptes Rendus. Mécanique
%D 2017
%P 153-157
%V 345
%N 2
%I Elsevier
%R 10.1016/j.crme.2016.10.014
%G en
%F CRMECA_2017__345_2_153_0

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/

Bibliographie
Cité par

[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.

G. Castiñeira; Á. Rodríguez-Arós On the justification of viscoelastic flexural shell equations, Computers Mathematics with Applications, Volume 77 (2019) no. 11, p. 2933 | DOI:10.1016/j.camwa.2018.08.062
M.T. Cao-Rial; Á. Rodríguez-Arós Asymptotic analysis of unilateral contact problems for linearly elastic shells: Error estimates in the membrane case, Nonlinear Analysis: Real World Applications, Volume 48 (2019), p. 40 | DOI:10.1016/j.nonrwa.2019.01.009
Á. Rodríguez-Arós Mathematical justification of the obstacle problem for elastic elliptic membrane shells, Applicable Analysis, Volume 97 (2018) no. 8, p. 1261 | DOI:10.1080/00036811.2017.1337894
Ángel Rodríguez-Arós Models of Elastic Shells in Contact with a Rigid Foundation: An Asymptotic Approach, Journal of Elasticity, Volume 130 (2018) no. 2, p. 211 | DOI:10.1007/s10659-017-9638-1

Cité par 4 documents. Sources : Crossref

Commentaires - Politique

Il n'y a aucun commentaire pour cet article. Soyez le premier à écrire un commentaire !

Publier un nouveau commentaire:

Publier une nouvelle réponse: