A Projection Approach to the Numerical Analysis of Limit Load Problems

Guillaume Carlier (1) , Myriam Comte (2) , Ioan R. Ionescu (3) , Gabriel Peyré (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LJLL - Laboratoire Jacques-Louis Lions
3 PMTM - Propriétés mécaniques et thermodynamiques des matériaux

This paper proposes a numerical scheme to approximate the solution of (vectorial) limit load problems. The method makes use of a strictly convex perturbation of the problem, which corresponds to a projection of the deformation field under bounded deformation and incompressibility constraints. The discretized formulation of this perturbation converges to the solution of the original landslide problem when the amplitude of the perturbation tends to zero. The projection is computed numerically with a multi-steps gradient descent on the dual formation of the problem.

Keywords: Limit load analysis; functions of bounded deformation; penalizations; Nesterov algorithm

Domains: Analysis of PDEs [math.AP]

Guillaume Carlier, Myriam Comte, Ioan R. Ionescu, Gabriel Peyré. A Projection Approach to the Numerical Analysis of Limit Load Problems. Mathematical Models and Methods in Applied Sciences, 2011, 21 (6), pp.1291-1316. ⟨hal-00450000⟩