SUMMARY um/2.S n>
The formulation of limit analysis by means of the finite element method leads to an optimization wUU Dq?!k\
problem with a large number of variables and constraints. Here we present a method for obtaining 2oY.MQD7iW
strict lower bound solutions using second-order cone programming (SOCP), for which efficient primaldual 4<`Qyul-
interior-point algorithms have recently been developed. Following a review of previous work, we QU` M5{#
provide a brief introduction to SOCP and describe how lower bound limit analysis can be formulated in R$[nYw
this way. Some methods for exploiting the data structure of the problem are also described, including q.
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an efficient strategy for detecting and removing linearly dependent constraints at the assembly stage. \BIa:}9O
The benefits of employing SOCP are then illustrated with numerical examples. Through the use of an aQ@9(j>
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effective algorithm/software, very large optimization problems with up to 700 000 variables are solved FG-v71!h#
in minutes on a desktop machine. The numerical examples concern plane strain conditions and the q?R)9E$h
Mohr–Coulomb criterion, however we show that SOCP can also be applied to any other problem of
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lower bound limit analysis involving a yield function with a conic quadratic form (notable examples +ZuT\P&kR5
being the Drucker–Prager criterion in 2D or 3D, and Nielsen’s criterion for plates). Copyright 2005 f W /G_
John Wiley & Sons, Ltd. YIP / N
KEY WORDS: limit analysis; lower bound; cohesive-frictional; finite element; optimization; conic gmCW__oR
programming
