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 -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.
Keywords
Cite
@article{arxiv.1410.0326,
title = {A $\Gamma$-Convergence Result for the Upper Bound Limit Analysis of Plates},
author = {Jérémy Bleyer and Guillaume Carlier and Vincent Duval and Jean-Marie Mirebeau and Gabriel Peyré},
journal= {arXiv preprint arXiv:1410.0326},
year = {2014}
}