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Large static problem in numerical limit analysis: A decomposition approach
Author(s) -
Kammoun Zied,
Pastor Franck,
Smaoui Hichem,
Pastor Joseph
Publication year - 2010
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.887
Subject(s) - limit analysis , interior point method , von mises yield criterion , mathematics , mathematical optimization , upper and lower bounds , finite element method , plane stress , piecewise , piecewise linear function , limit (mathematics) , nonlinear programming , stability (learning theory) , nonlinear system , linear programming , mathematical analysis , computer science , structural engineering , engineering , physics , quantum mechanics , machine learning
A general decomposition approach for the static method of limit analysis is proposed. It is based on piecewise linear stress fields, on a partition into finite element sub‐problems and on a specific coordination of the subproblem stress fields through auxiliary interface problems. The final convex optimization problems are solved using nonlinear interior point programming methods. As validated for the compressed bar with Tresca/von Mises materials in plane strain, this method appears rapidly convergent, so that very large problems with millions of constraints and variables can be solved. Then the method is applied to the classical problem of the stability of a Tresca vertical cut: the static bound to the stability factor is improved to 3.7752, a value to be compared with the recent best upper bound 3.7776. Copyright © 2010 John Wiley & Sons, Ltd.