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Limit analysis decomposition and finite element mixed method

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2010
auteur(s) Pastor Franck; Loute Etienne
journal (abréviation) Journal of Computational and Applied Mathematics (J Comput Appl Math)
volume (numéro) 234 (7)
  
pages 2213 – 2221
résumé This paper proposes an original decomposition approach to the upper bound method of limit analysis. It is based on a mixed finite element approach and on a convex interior point solver, using linear or quadratic discontinuous velocity fields. Presented in plane strain, this method appears to be rapidly convergent, as verified in the Tresca compressed bar problem in the linear velocity case. Then, using discontinuous quadratic velocity fields, the method is applied to the celebrated problem of the stability factor of a Tresca vertical slope: the upper bound is lowered to 3.7776—value to be compared to the best published lower bound 3.7752—by succeeding in solving a non linear optimization problem with millions of variables and constraints.
mots clés Porous material; Convex optimization; Decomposition; Limit analysis; Finite element method; Mixed approach
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