A Γ-Convergence Result for the Upper Bound Limit Analysis of Plates

Abstract : 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.
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Article dans une revue
ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2016, 50 (1), pp.215-235
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https://hal.inria.fr/hal-01112226
Contributeur : Jean-David Benamou <>
Soumis le : lundi 2 février 2015 - 14:35:57
Dernière modification le : mardi 17 avril 2018 - 11:34:15

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  • HAL Id : hal-01112226, version 1
  • ARXIV : 1410.0326

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Guillaume Carlier, Gabriel Peyré, Jean-Marie Mirebeau, Vincent Duval. A Γ-Convergence Result for the Upper Bound Limit Analysis of Plates. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2016, 50 (1), pp.215-235. 〈hal-01112226〉

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