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A new discontinuous upper bound limit analysis formulation
Author(s) -
Krabbenhoft Kristian,
Lyamin Andrei V.,
Hjiaj Mohammed,
Sloan Scott W.
Publication year - 2005
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.1314
Subject(s) - classification of discontinuities , upper and lower bounds , limit analysis , limit (mathematics) , mathematics , extension (predicate logic) , contrast (vision) , interpretation (philosophy) , duality (order theory) , calculus (dental) , mathematical analysis , computer science , combinatorics , medicine , dentistry , artificial intelligence , programming language
Abstract A new upper bound formulation of limit analysis of two‐ and three‐dimensional solids is presented. In contrast to most discrete upper bound methods the present one is formulated in terms of stresses rather than velocities and plastic multipliers. However, by means of duality theory it is shown that the formulation does indeed result in rigorous upper bound solutions. Also, kinematically admissible discontinuities, which have previously been shown to be very efficient, are given an interpretation in terms of stresses. This allows for a much simpler implementation and, in contrast to existing formulations, extension to arbitrary yield criteria in two and three dimensions is straightforward. Finally, the capabilities of the new method are demonstrated through a number of examples. Copyright © 2005 John Wiley & Sons, Ltd.