Issue |
ESAIM: M2AN
Volume 39, Number 4, July-August 2005
|
|
---|---|---|
Page(s) | 637 - 648 | |
DOI | https://doi.org/10.1051/m2an:2005028 | |
Published online | 15 August 2005 |
Characterization of the limit load in the case of an unbounded elastic convex
LIM, Polytechnic School of Tunisia. adnene.elyacoubi@ept.rnu.tn; taieb.hadhri@ept.rnu.tn
Received:
6
February
2004
In this work we consider a solid body constituted by a
nonhomogeneous elastoplastic material, submitted to a density of body forces
and a density of forces
acting on the boundary where the real
is the
loading parameter.
The problem is to determine, in the case of an unbounded convex of elasticity, the Limit
load denoted by
beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri, RAIRO: Modél. Math. Anal. Numér. 29 (1995) 391–419].
Then assuming that the convex of elasticity at the point x of Ω, denoted
by K(x), is written in the form of
, I is the identity of
, and the
deviatoric component
is bounded regardless of x
, we show under the condition “Rot f
or g is not colinear to the normal on a part of the boundary of Ω", that the
Limit Load
searched is equal to the inverse of
the infimum of the gauge of the Elastic convex translated by
stress field equilibrating the unitary load corresponding to
; moreover we show that this infimum is reached in a
suitable function space.
Mathematics Subject Classification: 74xx
Key words: Elasticity / limit load.
© EDP Sciences, SMAI, 2005
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