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A Projection Approach to the Numerical Analysis of Limit Load Problems

Peyré, Gabriel; Ionescu, Ioan; Comte, Myriam; Carlier, Guillaume (2011), A Projection Approach to the Numerical Analysis of Limit Load Problems, Mathematical Models and Methods in Applied Sciences, 21, 6, p. 1291-1316. http://dx.doi.org/10.1142/S0218202511005325

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00450000/fr/
Date
2011
Journal name
Mathematical Models and Methods in Applied Sciences
Volume
21
Number
6
Publisher
World Scientific
Pages
1291-1316
Publication identifier
Metadata
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Author(s)
Peyré, Gabriel
Ionescu, Ioan
Comte, Myriam
Carlier, Guillaume
Abstract (EN)
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.
Subjects / Keywords
functions of bounded deformation; penalizations; Nesterov algorithm; Limit load analysis