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A cell‐based smoothed finite element method for kinematic limit analysis
Author(s) -
Le Canh V.,
NguyenXuan H.,
Askes H.,
Bordas Stéphane P. A.,
Rabczuk T.,
NguyenVinh H.
Publication year - 2010
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.2897
Subject(s) - finite element method , mathematics , finite element limit analysis , mathematical optimization , kinematics , von mises yield criterion , smoothing , limit (mathematics) , quadratic programming , second order cone programming , sequential quadratic programming , limit analysis , plane stress , mixed finite element method , displacement (psychology) , mathematical analysis , geometry , upper and lower bounds , convex optimization , structural engineering , engineering , psychology , statistics , physics , classical mechanics , regular polygon , psychotherapist
Abstract This paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell‐based smoothed finite element method with second‐order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non‐smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second‐order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged. Copyright © 2010 John Wiley & Sons, Ltd.