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.
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⟩
