Makrodimopoulos, A. and Martin, C.M.
Lower bound limit analysis of cohesive-frictional materials using second-order cone programming.
International Journal for Numerical Methods in Engineering, 66, (4), . (doi:10.1002/nme.1567).
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The formulation of limit analysis by means of the finite element method leads to an optimization
problem with a large number of variables and constraints. Here we present a method for obtaining
strict lower bound solutions using second-order cone programming (SOCP), for which efficient primaldual
interior-point algorithms have recently been developed. Following a review of previous work, we
provide a brief introduction to SOCP and describe how lower bound limit analysis can be formulated in
this way. Some methods for exploiting the data structure of the problem are also described, including
an efficient strategy for detecting and removing linearly dependent constraints at the assembly stage.
The benefits of employing SOCP are then illustrated with numerical examples. Through the use of an
effective algorithm/software, very large optimization problems with up to 700 000 variables are solved
in minutes on a desktop machine. The numerical examples concern plane strain conditions and the
Mohr–Coulomb criterion, however we show that SOCP can also be applied to any other problem of
lower bound limit analysis involving a yield function with a conic quadratic form (notable examples
being the Drucker–Prager criterion in 2D or 3D, and Nielsen’s criterion for plates).
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