Section: New Results

A $\Gamma$-Convergence Result for the Upper Bound Limit Analysis of Plates

Bleyer, Jérémy and Carlier, Guillaume and Duval, Vincent and Mirebeau, Jean-Marie and Peyré, Gabriel

[23]

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.