A Γ-Convergence Result for the Upper Bound Limit Analysis of Plates
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 50 (2016) no. 1, pp. 215-235.

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.

Received:
DOI: 10.1051/m2an/2015040
Classification: 73E20, 73K10, 73V05
Mots-clés : 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.
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     title = {A $\Gamma{}${-Convergence} {Result} for the {Upper} {Bound} {Limit} {Analysis} of {Plates}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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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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