Comptes Rendus
The elastic torus: anomalous stiffness of shells with mixed type
Comptes Rendus. Mécanique, Volume 330 (2002) no. 6, pp. 425-432.

We investigate the deformation of a thin elastic torus under axisymmetric surface loads. The strain concentrates near the top and bottom parallels and the inner and outer halves essentially undergo rigid-body translations in opposite directions. An analysis of the inner boundary layers is presented, which allows one to compute the effective stiffness of the torus for this loading. This stiffness is found anomalous compared to classical shells. These mechanical properties are interpreted using purely geometrical arguments.

Nous étudions la déformation d'un tore élastique mince sous l'effet de forces de surface axisymétriques. La déformation est concentrée au voisinage des parallèles supérieur et inférieur et les moitiés externe et interne subissent essentiellement une translation uniforme l'une par rapport à l'autre. Une analyse de couche limite permet de calculer la rigidité effective du tore, qui suit une loi anormale. Toutes ces propriétés mécaniques sont interprétées par des arguments purement géométriques.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-0721(02)01479-1
Keywords: solids and structures, elastic shells, boundary layers
Mot clés : solides et structures, coques élastiques, couches limite

Basile Audoly 1; Yves Pomeau 2

1 Laboratoire de modélisation en mécanique, UMR 7607 du CNRS Université Pierre et Marie Curie, 4, place Jussieu, 75252 Paris cedex 05, France
2 Laboratoire de physique statistique, UMR 8550 du CNRS, École normale supérieure, 24, rue Lhomond, 75231 Paris cedex 05, France
@article{CRMECA_2002__330_6_425_0,
     author = {Basile Audoly and Yves Pomeau},
     title = {The elastic torus: anomalous stiffness of shells with mixed type},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {425--432},
     publisher = {Elsevier},
     volume = {330},
     number = {6},
     year = {2002},
     doi = {10.1016/S1631-0721(02)01479-1},
     language = {en},
}
TY  - JOUR
AU  - Basile Audoly
AU  - Yves Pomeau
TI  - The elastic torus: anomalous stiffness of shells with mixed type
JO  - Comptes Rendus. Mécanique
PY  - 2002
SP  - 425
EP  - 432
VL  - 330
IS  - 6
PB  - Elsevier
DO  - 10.1016/S1631-0721(02)01479-1
LA  - en
ID  - CRMECA_2002__330_6_425_0
ER  - 
%0 Journal Article
%A Basile Audoly
%A Yves Pomeau
%T The elastic torus: anomalous stiffness of shells with mixed type
%J Comptes Rendus. Mécanique
%D 2002
%P 425-432
%V 330
%N 6
%I Elsevier
%R 10.1016/S1631-0721(02)01479-1
%G en
%F CRMECA_2002__330_6_425_0
Basile Audoly; Yves Pomeau. The elastic torus: anomalous stiffness of shells with mixed type. Comptes Rendus. Mécanique, Volume 330 (2002) no. 6, pp. 425-432. doi : 10.1016/S1631-0721(02)01479-1. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01479-1/

[1] M. Spivak A Comprehensive Introduction to Differential Geometry, Publish or Perish, Houston, 1975

[2] S. Timoshenko; S. Woinowsky-Krieger Theory of Plates and Shells, McGraw-Hill, New York, 1959

[3] A.E. Green; W. Zerna Theoretical Elasticity, Dover, New York, 1992

[4] P. Karamian; J. Sanchez-Hubert; É. Sanchez-Palencia A model problem for boundary layers of thin elastic shells, Math. Modelling Numer. Anal., Volume 34 (2000), pp. 1-30

[5] A.L. Gol'denveizer Theory of Elastic thin Shells, Pergamon Press, New York, 1961 (Published for the American Society of Mechanical Engineers)

[6] W. Flügge Stresses in Shells, Springer-Verlag, Berlin, 1973 (pp. 30 and 94)

[7] B. Audoly Courbes rigidifiant les surfaces, C. R. Acad. Sci. Paris, Série I, Volume 328 (1999), pp. 313-316

[8] B. Audoly, Y. Pomeau, in preparation

Cited by Sources:

Comments - Policy