SUMMARY 8M m,a
The formulation of limit analysis by means of the finite element method leads to an optimization f/G
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problem with a large number of variables and constraints. Here we present a method for obtaining ~ g$Pb[V
strict lower bound solutions using second-order cone programming (SOCP), for which efficient primaldual 7MreBs(M
interior-point algorithms have recently been developed. Following a review of previous work, we L*t n>AO
provide a brief introduction to SOCP and describe how lower bound limit analysis can be formulated in pX
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this way. Some methods for exploiting the data structure of the problem are also described, including ye1kI~LO(
an efficient strategy for detecting and removing linearly dependent constraints at the assembly stage. SS@F:5),
The benefits of employing SOCP are then illustrated with numerical examples. Through the use of an 6y&d\_?Y
effective algorithm/software, very large optimization problems with up to 700 000 variables are solved yu~~"Rq)
in minutes on a desktop machine. The numerical examples concern plane strain conditions and the p{7"a
Mohr–Coulomb criterion, however we show that SOCP can also be applied to any other problem of 7-81,ADv(
lower bound limit analysis involving a yield function with a conic quadratic form (notable examples ^y"Rdv
being the Drucker–Prager criterion in 2D or 3D, and Nielsen’s criterion for plates). Copyright 2005 w~>V2u_-
John Wiley & Sons, Ltd. }?xu/C
KEY WORDS: limit analysis; lower bound; cohesive-frictional; finite element; optimization; conic \?)@
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programming
