The present paper proposes and analyzes a general locking free mixed strategy for computing the deformation of incompressible three dimensional structures placed inside flexible membranes. The model involves as in Chapelle and Ferent [Math. Models Methods Appl. Sci. 13 (2003) 573-595] a bending dominated shell envelope and a quasi incompressible elastic body. The present work extends an earlier work of Arnold and Brezzi [Math Comp. 66 (1997) 1-14] treating the shell part and proposes a global stable finite element approximation by coupling optimal mixed finite element formulations of the different subproblems by mortar techniques. Examples of adequate finite elements are proposed. Convergence results are derived in two steps. First a global inf-sup condition is proved, deduced from the local conditions to be satisfied by the finite elements used for the external shell problem, the internal incompressible 3D problem, and the mortar coupling, respectively. Second, the analysis of Arnold and Brezzi [Math. Comp. 66 (1997) 1-14] is extended to the present problem and least to convergence results for the full coupled problem, with constants independent of the problem's small parameters.
Mots-clés : 3D coupling, mixed formulations, shells, incompressible elasticity, mortar elements, delinquent modes, inf-sup condition, locking free approximations
@article{M2AN_2007__41_1_129_0,
author = {Le Tallec, Patrick and Aouadi, Saloua Mani},
title = {Locking free matching of different three dimensional models in structural mechanics},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {129--145},
publisher = {EDP-Sciences},
volume = {41},
number = {1},
year = {2007},
doi = {10.1051/m2an:2007013},
mrnumber = {2323694},
zbl = {1223.74018},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2007013/}
}
TY - JOUR AU - Le Tallec, Patrick AU - Aouadi, Saloua Mani TI - Locking free matching of different three dimensional models in structural mechanics JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 129 EP - 145 VL - 41 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2007013/ DO - 10.1051/m2an:2007013 LA - en ID - M2AN_2007__41_1_129_0 ER -
%0 Journal Article %A Le Tallec, Patrick %A Aouadi, Saloua Mani %T Locking free matching of different three dimensional models in structural mechanics %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 129-145 %V 41 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2007013/ %R 10.1051/m2an:2007013 %G en %F M2AN_2007__41_1_129_0
Le Tallec, Patrick ; Aouadi, Saloua Mani. Locking free matching of different three dimensional models in structural mechanics. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 1, pp. 129-145. doi : 10.1051/m2an:2007013. http://www.numdam.org/articles/10.1051/m2an:2007013/
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