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A note on upper bound formulations in limit analysis
Author(s) -
Muñoz J.J.,
Huerta A.,
Bonet J.,
Peraire J.
Publication year - 2012
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.4303
Subject(s) - upper and lower bounds , limit analysis , limit (mathematics) , mathematics , computation , dissipation , field (mathematics) , normality , power (physics) , mathematical optimization , mathematical analysis , algorithm , statistics , physics , pure mathematics , quantum mechanics , thermodynamics
SUMMARY In this paper, we study some recent formulations for the computation of upper bounds in limit analysis. We show that a previous formulation presented by the authors does not guarantee the strictness of the upper bound, nor does it provide a velocity field that satisfies the normality rule everywhere. We show that these deficiencies are related to the quadrature employed for the evaluation of the dissipation power. We derive a formulation that furnishes a strict upper bound of the load factor, which in fact coincides with a formulation reported in the literature. From the analysis of these formulations, we propose a post‐process, which consists in computing exactly the dissipation power for the optimum upper bound velocity field. This post‐process may further reduce the strict upper bound of the load factor in particular situations. Finally, we also determine the quadratures that must be used in the elemental and edge gap contributions, so that they are always positive and their addition equals the global bound gap. Copyright © 2012 John Wiley & Sons, Ltd.