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 -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.
DOI: 10.1051/m2an/2015040
Mots-clés : Bounded Hessian functions, Finite element method, Γ-convergence
@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://archive.numdam.org/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://archive.numdam.org/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://archive.numdam.org/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 , Volume 50 (2016) no. 1, pp. 215-235. doi : 10.1051/m2an/2015040. http://archive.numdam.org/articles/10.1051/m2an/2015040/
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