Geodesic
A Γ-Convergence Result for the Upper Bound Limit Analysis of Plates
Bleyer, Jérémy1 ; Carlier, Guillaume2  ; Duval, Vincent3  ; Mirebeau, Jean-Marie2  ; Peyré, Gabriel2 
1 UniversitéParis-Est, Laboratoire Navier, École des Ponts ParisTech-IFSTTAR-CNRS (UMR 8205), France.
2 CNRS, CEREMADE, Université Paris-Dauphine, France.
3 INRIA, Domaine de Voluceau, Rocquencourt, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 1, pp. 215-235

Voir la notice de l'article provenant de la source Numdam

Upper bound limit analysis allows one to evaluate directly the ultimate load of structures without performing a cumbersome incremental analysis. In order to numerically apply this method to thin plates in bending, several authors have proposed to use various finite elements discretizations. We provide in this paper a mathematical analysis which ensures the convergence of the finite element method, even with finite elements with discontinuous derivatives such as the quadratic 6 node Lagrange triangles and the cubic Hermite triangles. More precisely, we prove the Γ-convergence of the discretized problems towards the continuous limit analysis problem. Numerical results illustrate the relevance of this analysis for the yield design of both homogeneous and non-homogeneous materials.

Reçu le :
DOI : 10.1051/m2an/2015040
Classification : 73E20, 73K10, 73V05
Keywords: Bounded Hessian functions, Finite element method, Γ-convergence

Bleyer, Jérémy 1 ; Carlier, Guillaume 2 ; Duval, Vincent 3 ; Mirebeau, Jean-Marie 2 ; Peyré, Gabriel 2

1 UniversitéParis-Est, Laboratoire Navier, École des Ponts ParisTech-IFSTTAR-CNRS (UMR 8205), France.
2 CNRS, CEREMADE, Université Paris-Dauphine, France.
3 INRIA, Domaine de Voluceau, Rocquencourt, France. 
@article{M2AN_2016__50_1_215_0,
     author = {Bleyer, J\'er\'emy and Carlier, Guillaume and Duval, Vincent and Mirebeau, Jean-Marie and Peyr\'e, Gabriel},
     title = {A $\Gamma{}${-Convergence} {Result} for the {Upper} {Bound} {Limit} {Analysis} of {Plates}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {215--235},
     publisher = {EDP-Sciences},
     volume = {50},
     number = {1},
     year = {2016},
     doi = {10.1051/m2an/2015040},
     zbl = {1353.74068},
     mrnumber = {3460107},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015040/}
}
TY  - JOUR
AU  - Bleyer, Jérémy
AU  - Carlier, Guillaume
AU  - Duval, Vincent
AU  - Mirebeau, Jean-Marie
AU  - Peyré, Gabriel
TI  - A $\Gamma{}$-Convergence Result for the Upper Bound Limit Analysis of Plates
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2016
SP  - 215
EP  - 235
VL  - 50
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015040/
DO  - 10.1051/m2an/2015040
LA  - en
ID  - M2AN_2016__50_1_215_0
ER  - 
%0 Journal Article
%A Bleyer, Jérémy
%A Carlier, Guillaume
%A Duval, Vincent
%A Mirebeau, Jean-Marie
%A Peyré, Gabriel
%T A $\Gamma{}$-Convergence Result for the Upper Bound Limit Analysis of Plates
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2016
%P 215-235
%V 50
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015040/
%R 10.1051/m2an/2015040
%G en
%F M2AN_2016__50_1_215_0
Bleyer, Jérémy; Carlier, Guillaume; Duval, Vincent; Mirebeau, Jean-Marie; Peyré, Gabriel. A $\Gamma{}$-Convergence Result for the Upper Bound Limit Analysis of Plates. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 1, pp. 215-235. doi: 10.1051/m2an/2015040

Cité par Sources :