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Kinematic limit analysis modelling by a regularization approach and finite element method
Author(s) -
Chaaba Ali,
Bousshine Lahbib,
De Saxce Gery
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.710
Subject(s) - finite element method , regularization (linguistics) , singularity , mathematics , dissipation , limit analysis , plane stress , plasticity , norm (philosophy) , mathematical analysis , computer science , physics , structural engineering , engineering , artificial intelligence , law , political science , upper and lower bounds , thermodynamics
Kinematical approach by limit analysis is one of the fundamental methods used to predict the plastic limit state and it is applied successfully to deal with engineering problems in solid mechanics. The kinematical approach consists of minimizing the plastic dissipation power throughout the body, produced by plasticity, which involves functional with norm integrand. Besides, to derive the stress field within the body, one uses the inverse plastic law that is a subdifferential of the dissipation power. The complexity and possible singularity in the derivatives of functionals become a source of many numerical troubles. To overcome these encountered difficulties, we propose a solving algorithm by using a regularization procedure on the basis of the inf‐convolution operation. Some numerical applications by plane strain or axisymmetric finite element method are presented to illustrate the algorithm. Copyright © 2003 John Wiley & Sons, Ltd.