Upper bound limit analysis using discontinuous quadratic displacement fields

Makrodimopoulos, Athanasios; Martin, Constance

doi:10.1002/cnm.998

Cited by 75 publications

(63 citation statements)

References 21 publications

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“…However, for the C0-continuous elements, it can be violated due to the appearance of plastic hinge lines on boundaries of elements. In order to overcome this violation, the internal work dissipated in resulting hinge lines on boundaries of elements should be taken into account as done by Hodge and Belytschko [7] and Makrodimopoulos and Martin [82]. In this paper, the CS-MIN3 uses only three-node triangular plate elements and hence belongs to the C0-continuous elements.…”

Section: Figurementioning

confidence: 99%

RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

Nguyen-Thoi

Phung‐Van

Canh

2014

Asia Pac. J. Comput. Engin.

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Background: The paper presents a numerical procedure for kinematic limit analysis of Mindlin plate governed by von Mises criterion. Methods: The cell-based smoothed three-node Mindlin plate element (CS-MIN3) is combined with a second-order cone optimization programming (SOCP) to determine the upper bound limit load of the Mindlin plates. In the CS-MIN3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the gradient matrices of MIN3 is used to compute the strain rates. Then the gradient smoothing technique on whole the triangular element is used to smooth the strain rates on these three sub-triangles. The limit analysis problem of Mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work. For Mindlin plates, the dissipation power is computed on both the middle plane and thickness of the plate. This minimization problem then can be transformed into a form suitable for the optimum solution using the SOCP. Results and Conclusions: The numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for both thick and thin plates.

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Section: Figurementioning

confidence: 99%

RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

Nguyen-Thoi

Phung‐Van

Canh

2014

Asia Pac. J. Comput. Engin.

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“…Considering the advantage of both continuous and discontinuities-only methods, discontinuous elements have also been developed in parallel [7][8][9]. Such elements allow for velocity discontinuities across all edges shared by adjacent triangles, and consequently dissipation may occur not only inside the triangular elements but also along these discontinuities.…”

Section: Introductionmentioning

confidence: 99%

Locking‐free discontinuous finite elements for the upper bound yield design of thick plates

Bleyer

Buhan

2015

Numerical Meth Engineering

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This work investigates the formulation of finite elements dedicated to the upper bound kinematic approach of yield design or limit analysis of Reissner-Mindlin thick plates in shear-bending interaction. The main novelty of this paper is to take full advantage of the fundamental difference between limit analysis and elasticity problems as regards the class of admissible virtual velocity fields. In particular, it has been demonstrated for 2D plane stress, plane strain or 3D limit analysis problems that the use of discontinuous velocity fields presents a lot of advantages when seeking for accurate upper bound estimates. For this reason, discontinuous interpolations of the transverse velocity and the rotation fields for Reissner-Mindlin plates are proposed. The subsequent discrete minimization problem is formulated as a second-order cone programming (SOCP) problem and is solved using the industrial software package Mosek. A comprehensive study of the shear-locking phenomenon is also conducted and it is shown that discontinuous elements avoid such a phenomenon quite naturally, whereas continuous elements cannot without any specific treatment. This particular aspect is confirmed through numerical examples on classical benchmark problems and the so-obtained upper bound estimates are confronted to recently developed lower bound equilibrium finite elements for thick plates.

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“…The first involves FELA using the author's program OxLim, which combines the lower-and upper-bound methods of Makrodimopoulos & Martin (2006, 2007, 2008) with a simple strategy for adaptive mesh refinement. Essentially, this strategy attempts to equalise the quantity Ð : c max dA (integral of the maximum shear strain rate) over all elements of the mesh, subject to the proviso that no element be 'de-refined' from its initial size.…”

Section: Introductionmentioning

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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Upper bound limit analysis using discontinuous quadratic displacement fields

Cited by 75 publications

References 21 publications

RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

Locking‐free discontinuous finite elements for the upper bound yield design of thick plates

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

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