A cell‐based smoothed finite element method for kinematic limit analysis

Le, Canh V.; Nguyen‐Xuan, H.; Askes, Harm; Bordas, Stéphane; Rabczuk, Timon; Nguyen-Vinh, H.

doi:10.1002/nme.2897

Cited by 89 publications

(33 citation statements)

References 62 publications

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“…Recently, the interest of scientists in numerical limit analysis [9][10][11][12][13][14][15] has been resurged, principally thanks to the rapid development of efficient optimization algorithms and the continuous improvement in computer facilities. Current research is focusing on developing numerical limit analysis tools which are efficient and robust for the practice usage of engineers.…”

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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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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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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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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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“…In recent years efforts have focussed principally on the development of efficient and robust numerical limit analysis tools of potential use to engineers working in practice, which either use continuous (e.g. using finite element [1][2][3][4][5][6][7] or meshless [8][9][10] methods), semi-continuous [11] or truly discontinuous [12] representations of the relevant field variables. However, the accuracy of numerical limit analysis solutions is highly affected by local singularities arising from localized plastic deformations [13].…”

Section: Introductionmentioning

confidence: 99%

Adaptive element-free Galerkin method applied to the limit analysis of plates

Askes

Gilbert

2010

Computer Methods in Applied Mechanics and Engineering

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The implementation of an h-adaptive Element-Free Galerkin (EFG) method in the framework of limit analysis is described. The naturally conforming property of meshfree approximations (with no nodal connectivity required) facilitates the implementation of h-adaptivity. Nodes may be moved, discarded or introduced without the need for complex manipulation of the data structures involved. With the use of the Taylor expansion technique, the error in the computed displacement field and its derivatives can be estimated throughout the problem domain with high accuracy. A stabilized conforming nodal integration scheme is extended to error estimators and results in an efficient and truly meshfree adaptive method. To demonstrate its effectiveness the procedure is then applied to plates with various boundary conditions.

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“…5 . 142 with 200 nodal divisions) improves on existing FELA upper-bound solutions in the literature (Sloan & Kleeman, 1995;da Silva & Antao, 2007;Makrodimopoulos & Martin, 2007), and is also better than the approximate rather than strict upper-bound solution recently obtained by Le et al (2010) using a cell-based, smoothed, finite-element procedure. Furthermore, extrapolated solutions are in both cases very close to the exact solution.…”

Section: S Lcmentioning

confidence: 62%

Identification of rotational failure mechanisms in cohesive media using discontinuity layout optimisation

Smith¹,

Gilbert²

2013

Géotechnique

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Discontinuity layout optimisation (DLO) is a generally applicable numerical limit analysis procedure that can be used to identify critical plastic collapse mechanisms in geotechnical problems. Previous research has focused on using plane-strain DLO to identify mechanisms that are purely translational, or which involve rotations only along predefined boundaries. In this paper a more general formulation, capable of identifying mechanisms that can involve arbitrary rotations and/or translations in cohesive media, is presented. The formulation is then verified through investigation of the yield surface and evolution of the collapse mechanism associated with a footing under combined vertical and moment (V, M) loading, and through study of the well-known anchor uplift problem. It is shown that results of very high accuracy can be obtained, in terms of the collapse load and of the predicted failure mechanism. In the light of the new results, the Bransby design formula for combined vertical and moment loading has been modified to improve its accuracy. Additionally, the more general DLO formulation presented is shown to have several inherent advantages compared with existing numerical limit analysis approaches.

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A cell‐based smoothed finite element method for kinematic limit analysis

Cited by 89 publications

References 62 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)

Adaptive element-free Galerkin method applied to the limit analysis of plates

Identification of rotational failure mechanisms in cohesive media using discontinuity layout optimisation

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