# Locking free matching of different three dimensional models in structural mechanics

Patrick Le Tallec; Saloua Mani Aouadi

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 1, page 129-145
- ISSN: 0764-583X

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topLe Tallec, Patrick, and Mani Aouadi, Saloua. "Locking free matching of different three dimensional models in structural mechanics." ESAIM: Mathematical Modelling and Numerical Analysis 41.1 (2007): 129-145. <http://eudml.org/doc/249943>.

@article{LeTallec2007,

abstract = {
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.
},

author = {Le Tallec, Patrick, Mani Aouadi, Saloua},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {3D coupling; mixed formulations; shells; incompressible elasticity; mortar elements; delinquent modes; inf-sup condition; locking free approximations.; locking free approximations},

language = {eng},

month = {4},

number = {1},

pages = {129-145},

publisher = {EDP Sciences},

title = {Locking free matching of different three dimensional models in structural mechanics},

url = {http://eudml.org/doc/249943},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Le Tallec, Patrick

AU - Mani Aouadi, Saloua

TI - Locking free matching of different three dimensional models in structural mechanics

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/4//

PB - EDP Sciences

VL - 41

IS - 1

SP - 129

EP - 145

AB -
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.

LA - eng

KW - 3D coupling; mixed formulations; shells; incompressible elasticity; mortar elements; delinquent modes; inf-sup condition; locking free approximations.; locking free approximations

UR - http://eudml.org/doc/249943

ER -

## References

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- M.A. Puso, A 3D mortar method for solid mechanic. Int. J. Num. Meth. Engr.59 (2004) 315–336. Zbl1047.74065
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