Large static problem in numerical limit analysis: A decomposition approach

Kammoun, Zied; Pastor, Franck; Smaoui, Hichem; Pastor, J.

doi:10.1002/nag.887

Cited by 17 publications

(11 citation statements)

References 21 publications

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“…has so far defied solution, but the latest bounds from largescale FELA (Kammoun et al, 2010;Pastor et al, 2009) are…”

Section: Vertical Cutmentioning

confidence: 99%

The use of adaptive finite-element limit analysis to reveal slip-line fields

Martin

2011

Géotechnique Letters

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The numerical method known as finite-element limit analysis (FELA) is generally employed as a tool for obtaining lower and upper bounds on the exact collapse load of a perfectly plastic structure or continuum. Most applications of FELA in geotechnical engineering have focused on plane strain problems involving the classical Tresca and Mohr-Coulomb yield criteria, and considerable computational effort has been expended on the calculation of lower-and upper-bound solutions for particular problems. This paper discusses and demonstrates an alternative use of FELA -as a tool for ascertaining slip-line fields for plane strain problems. A simple but effective strategy for adaptive mesh refinement is a key feature of the process; it allows the layout of plastic regions, rigid regions and velocity discontinuities to be determined by inspection of the FELA mesh. The corresponding slip-line field can then be constructed numerically in the usual way. The examples presented are restricted to purely cohesive soil, but the same approach is applicable in principle to frictional or cohesive-frictional materials.

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“…has so far defied solution, but the latest bounds from largescale FELA (Kammoun et al, 2010;Pastor et al, 2009) are…”

Section: Vertical Cutmentioning

confidence: 99%

The use of adaptive finite-element limit analysis to reveal slip-line fields

Martin

2011

Géotechnique Letters

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“…While the decomposition techniques for optimisation problems is a relatively recent topic, its application to limit analysis and other plasticity problems has found far less attention [12]. We also refer the reader to [11], where alternative decomposition techniques of the limit analysis problem has been introduced. We here first briefly describe some of the general ideals of decomposition of optimisation problems.…”

Section: Decomposition Techniquesmentioning

confidence: 99%

Computation of Bounds for Anchor Problems in Limit Analysis and Decomposition Techniques

Muñoz

Rabiei

Lyamin

et al. 2014

Direct Methods for Limit States in Structures and Materials

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Numerical techniques for the computation of strict bounds in limit analyses have been developed for more than thirty years. The efficiency of these techniques have been substantially improved in the last ten years, and have been successfully applied to academic problems, foundations and excavations. We here extend the theoretical background to problems with anchors, interface conditions, and joints. Those extensions are relevant for the analysis of retaining and anchored walls, which we study in this work. The analysis of three-dimensional domains remains as yet very scarce. From the computational standpoint, the memory requirements and CPU time are exceedingly prohibitive when mesh adaptivity is employed. For this reason, we also present here the application of decomposition techniques to the optimisation problem of limit analysis. We discuss the performance of different methodologies adopted in the literature for general optimisation problems, such as primal and dual decomposition, and suggest some strategies that are suitable for the parallelisation of large three-dimensional problems. The propo sed decomposition techniques are tested against representative problems.

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“…In the early works, the convex yield criterion was approximated in a piecewise linear form so that the LA problem could be solved using linear [43] or quadratic programming [41]. The subsequent developments in mathematical programming provided solvers (e.g., [44]) that can handle static [45][46][47][48][49] and kinematic [19,46,50] numerical problems of LA involving more complex yield criteria.…”

Section: Introductionmentioning

confidence: 99%