A Γ-Convergence Result for the Upper Bound Limit Analysis of Plates∗
1 UniversitéParis-Est, Laboratoire
Navier, École des Ponts ParisTech-IFSTTAR-CNRS (UMR 8205),
2 CNRS, CEREMADE, Université Paris-Dauphine, France.
3 INRIA, Domaine de Voluceau, Rocquencourt, France.
Revised: 13 February 2015
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.
Mathematics Subject Classification: 73E20 / 73K10 / 73V05
Key words: Bounded Hessian functions / Finite element method / Γ-convergence
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