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Lower bound limit analysis of cohesive-frictional materials using second-order cone programming.

Makrodimopoulos, A. and Martin, C.M. (2006) Lower bound limit analysis of cohesive-frictional materials using second-order cone programming. International Journal for Numerical Methods in Engineering, 66, (4), pp. 604-634. (doi:10.1002/nme.1567).

Record type: Article

Abstract

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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More information

Published date: 23 April 2006
Keywords: limit analysis, lower bound, cohesive-frictional, finite element, optimization, conic programming

Identifiers

Local EPrints ID: 48048
URI: http://eprints.soton.ac.uk/id/eprint/48048
ISSN: 0029-5981
PURE UUID: 125477ef-aeb7-4164-bc41-29ff81593ae7

Catalogue record

Date deposited: 07 Sep 2007
Last modified: 17 Jul 2017 15:00

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