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Keywords
(6)
Equilibrium Problem
Obstacle Problem
sobolev space
Three Dimensional
Unilateral Contact
Shell Model
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Mathematical Justification of the Obstacle Problem in the Case of a Shallow Shell
Mathematical Justification of the Obstacle Problem in the Case of a Shallow Shell,10.1007/s1065900791411,Journal of Elasticity,Alain Léger,Bernadet
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Mathematical Justification of the Obstacle Problem in the Case of a Shallow Shell
(
Citations: 4
)
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Alain Léger
,
Bernadette Miara
This paper deals with the asymptotic formulation and justification of a mechanical model for a shallow shell in frictionless
unilateral contact
with an obstacle. The first three parts of the paper concern the formulation of the equilibrium problem. Special attention is paid to the contact conditions, which are usual within two or
three dimensional
elasticity, but which are not so usual in shell theories. Lastly the limit problem is formulated in the main part of the paper and a convergence result is presented. Two points are worth stressing here. First, we point out that unlike classical bilateral shell models justifications, the functional framework of the present analysis involves cones. Secondly, while the cones result from a positivity condition on the boundary as long as the thickness parameter is finite, leading to a Signorini problem in the
Sobolev space
H 1, the cone results from a positivity condition in the domain, giving rise to a socalled
obstacle problem
in the
Sobolev space
H 2 at the limit.
Journal:
Journal of Elasticity  J ELAST
, vol. 90, no. 3, pp. 241257, 2008
DOI:
10.1007/s1065900791411
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Citation Context
(2)
...In the same way but for the frictionless case, Léger and Miara
2
,
3
extended the study to the elastic shallow shell...
Abdallah Bensayah
,
et al.
Asymptotic modelling of a Signorini problem of generalized Marguerrev...
...Let us mention that in the case of the obstacle problem for a shallow shell in frictionless unilateral contact, similar contact conditions are given in [
13
]...
Christine Bernardi
,
et al.
On the Obstacle Problem for a Naghdi Shell
References
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Journal:
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Citations
(4)
Asymptotic modelling of a Signorini problem of generalized Marguerrevon Kármán shallow shells
Abdallah Bensayah
,
Djamal Ahmed Chacha
,
Abderrezak Ghezal
Journal:
Applicable Analysis
, vol. aheadofp, no. aheadofp, pp. 115, 2012
On the Obstacle Problem for a Naghdi Shell
(
Citations: 1
)
Christine Bernardi
,
Adel Blouza
,
Frekh Taallah
Journal:
Journal of Elasticity  J ELAST
, vol. 103, no. 1, pp. 113, 2011
Asymptotic modeling of a Coulomb frictional Signorini problem for the von Kármán plates
(
Citations: 1
)
Djamal Ahmed Chacha
,
Abdallah Bensayah
Journal:
Comptes Rendus Mecanique  C R MEC
, vol. 336, no. 11, pp. 846850, 2008
ROV competitions for students: developing the next generation of ocean explorers, scientists, technologists, and engineers
J. Zande
,
D. Sullivan
Conference:
OCEANS Conference  OCEANS
, 2003