SUMMARY ErDL^M- `
The formulation of limit analysis by means of the finite element method leads to an optimization c@(1:,R
problem with a large number of variables and constraints. Here we present a method for obtaining a4&:@ ` =
strict lower bound solutions using second-order cone programming (SOCP), for which efficient primaldual gvyT-XI
interior-point algorithms have recently been developed. Following a review of previous work, we qVBL>9O*.
provide a brief introduction to SOCP and describe how lower bound limit analysis can be formulated in :<GfET Is
this way. Some methods for exploiting the data structure of the problem are also described, including L2fVLK H
an efficient strategy for detecting and removing linearly dependent constraints at the assembly stage. _faJ B@a_
The benefits of employing SOCP are then illustrated with numerical examples. Through the use of an n3 ZAF'
effective algorithm/software, very large optimization problems with up to 700 000 variables are solved hD
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in minutes on a desktop machine. The numerical examples concern plane strain conditions and the [M:S`{SbY
Mohr–Coulomb criterion, however we show that SOCP can also be applied to any other problem of #mLuU
lower bound limit analysis involving a yield function with a conic quadratic form (notable examples b RPO:lAy
being the Drucker–Prager criterion in 2D or 3D, and Nielsen’s criterion for plates). Copyright 2005 #s2B%X
John Wiley & Sons, Ltd. ZJ(rG((!
KEY WORDS: limit analysis; lower bound; cohesive-frictional; finite element; optimization; conic K\&o2lo]
programming
