  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.
