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Limit analysis and convex programming: A decomposition approach of the kinematic mixed method

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2009
auteur(s) Pastor Franck; Loute Etienne; Pastor Joseph
journal (abréviation) International Journal for Numerical Methods in Engineering (Int J Numer Meth Eng)
volume (numéro) 78 (3)
  
pages 254 – 274
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 with the best published lower bound 3.772 - by succeeding in solving non-linear optimization problems with millions of variables and constraints.
mots clés limit analysis • kinematic method • decomposition approach • convex optimization
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