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Application of discontinuity layout optimization to plane plasticity problems

Smith, C. and Gilbert, Matthew (2007) Application of discontinuity layout optimization to plane plasticity problems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463 (2086). pp. 2461-2484. ISSN 1364-5021

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Abstract

A new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described. The procedure is used here to determine the critical layout of discontinuities and associated upper-bound limit load for plane plasticity problems. Potential discontinuities, which interlink nodes laid out over the body under consideration, are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient linear programming solvers can be employed when certain popular failure criteria are specified (e. g. Tresca or Mohr Coulomb in plane strain). Stress/velocity singularities are automatically identified and visual interpretation of the output is straightforward. The procedure, coined 'discontinuity layout optimization' (DLO), is related to that used to identify the optimum layout of bars in trusses, with discontinuities (e. g. slip-lines) in a translational failure mechanism corresponding to bars in an optimum truss. Hence, a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here. The procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems. Close agreement with the exact analytical solutions is obtained.

Item Type: Article
Copyright, Publisher and Additional Information: © 2007 Royal Society. This is an author produced version of a paper subsequently published in Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences. Uploaded in accordance with the publisher's self-archiving policy.
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield)
Depositing User: Sherpa Assistant
Date Deposited: 04 Oct 2007 17:41
Last Modified: 08 Feb 2013 16:55
Published Version: http://dx.doi.org/10.1098/rspa.2006.1788
Status: Published
Publisher: Royal Society
Refereed: Yes
Identification Number: 10.1098/rspa.2006.1788
URI: http://eprints.whiterose.ac.uk/id/eprint/3397

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