A $\Gamma$-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 $\Gamma$-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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Jérémy Bleyer, Guillaume Carlier, Vincent Duval, Jean-Marie Mirebeau, Gabriel Peyré. A $\Gamma$-Convergence Result for the Upper Bound Limit Analysis of Plates. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2015, ⟨10.1051/m2an/2015040 ⟩. ⟨hal-01069919v2⟩

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