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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https://hal.inria.fr/hal-01112226
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Submitted on : Monday, February 2, 2015 - 2:35:57 PM
Last modification on : Friday, May 24, 2019 - 5:31:55 PM

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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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