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A general non‐linear optimization algorithm for lower bound limit analysis
Author(s) -
Krabbenhoft Kristian,
Damkilde Lars
Publication year - 2002
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.551
Subject(s) - interior point method , linear programming , limit analysis , discretization , limit (mathematics) , mathematics , upper and lower bounds , mathematical optimization , finite element method , limit point , algorithm , point (geometry) , linear fractional programming , branch and bound , yield (engineering) , mathematical analysis , geometry , engineering , structural engineering , materials science , metallurgy
The non‐linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound load optimization problem, and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non‐linear yield criteria. Copyright © 2002 John Wiley & Sons, Ltd.