# 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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https://hal.inria.fr/hal-01069919
Contributor : Vincent Duval <>
Submitted on : Tuesday, September 30, 2014 - 11:44:19 PM
Last modification on : Friday, July 17, 2020 - 5:09:09 PM
Document(s) archivé(s) le : Wednesday, December 31, 2014 - 10:36:28 AM

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gamma_cv.pdf
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### Identifiers

• HAL Id : hal-01069919, version 1
• ARXIV : 1410.0326

### Citation

Jérémy Bleyer, Guillaume Carlier, Vincent Duval, Jean-Marie Mirebeau, Gabriel Peyré. A $\Gamma$-Convergence Result for the Upper Bound Limit Analysis of Plates. 2014. ⟨hal-01069919v1⟩

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