Characterization of the limit load in the case of an unbounded elastic convex

Elyacoubi, Adnene, and Hadhri, Taieb. "Characterization of the limit load in the case of an unbounded elastic convex." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.4 (2005): 637-648. <http://eudml.org/doc/245820>.

@article{Elyacoubi2005,
abstract = {In this work we consider a solid body $\Omega \subset \{\mathbb \{R\}\}^3$ constituted by a nonhomogeneous elastoplastic material, submitted to a density of body forces $\lambda f $ and a density of forces $\lambda g$ acting on the boundary where the real $\lambda $ is the loading parameter. The problem is to determine, in the case of an unbounded convex of elasticity, the Limit load denoted by $\bar\{\lambda \}$ 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 $\Omega $, denoted by K(x), is written in the form of $\mbox\{K\}^D (x) + \{\mathbb \{R\}\}\mbox\{I\}$, I is the identity of $\{\{\mathbb \{R\}\}^9\}_\{sym\}$, and the deviatoric component $\mbox\{K\}^D$ is bounded regardless of x $\in \Omega $, we show under the condition “Rot f $\ne 0$ or g is not colinear to the normal on a part of the boundary of $\Omega $”, that the Limit Load $\bar\{\lambda \}$ 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 $\lambda =1$; moreover we show that this infimum is reached in a suitable function space.},
author = {Elyacoubi, Adnene, Hadhri, Taieb},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {elasticity; limit load},
language = {eng},
number = {4},
pages = {637-648},
publisher = {EDP-Sciences},
title = {Characterization of the limit load in the case of an unbounded elastic convex},
url = {http://eudml.org/doc/245820},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Elyacoubi, Adnene
AU - Hadhri, Taieb
TI - Characterization of the limit load in the case of an unbounded elastic convex
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 4
SP - 637
EP - 648
AB - In this work we consider a solid body $\Omega \subset {\mathbb {R}}^3$ constituted by a nonhomogeneous elastoplastic material, submitted to a density of body forces $\lambda f $ and a density of forces $\lambda g$ acting on the boundary where the real $\lambda $ is the loading parameter. The problem is to determine, in the case of an unbounded convex of elasticity, the Limit load denoted by $\bar{\lambda }$ 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 $\Omega $, denoted by K(x), is written in the form of $\mbox{K}^D (x) + {\mathbb {R}}\mbox{I}$, I is the identity of ${{\mathbb {R}}^9}_{sym}$, and the deviatoric component $\mbox{K}^D$ is bounded regardless of x $\in \Omega $, we show under the condition “Rot f $\ne 0$ or g is not colinear to the normal on a part of the boundary of $\Omega $”, that the Limit Load $\bar{\lambda }$ 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 $\lambda =1$; moreover we show that this infimum is reached in a suitable function space.
LA - eng
KW - elasticity; limit load
UR - http://eudml.org/doc/245820
ER -