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

Le, Canh V.; Askes, Harm; Gilbert, Matthew

doi:10.1016/j.cma.2010.04.004

Cited by 41 publications

(21 citation statements)

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“…For the Kirchhoff plates, we can list the works by Christiansen and Larsen [28], Turco and Caracciolo [29], Corradi and Vena [30], Corradi and Panzeri [31], Tran et al [32], Le et al [33][34][35], and Zhou et al [36]. For the Mindlin plates, we can list the works by Capsoni and Corradi [37] and Capsoni and Vicente da Silva [38].…”

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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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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 which˙ e C is determined by Equation (16). In the following, we will show that when triangular elements are used (linear shape functions), CS-FEM and FEM are equivalent, D SF EM ≡ D F EM , regardless the number of SCs.…”

Section: Cs-fem Discretization Of Kinematic Formulationmentioning

confidence: 92%

“…It is known as the stabilized conforming nodal integration (SCNI) scheme. The SCNI scheme has been applied successfully to various problems, for instance, elastic analysis [12][13][14], plastic limit analysis [15], error estimation [16] and a stabilized mesh-free equilibrium model for limit analysis [17]. It is shown that, when the SCNI scheme is applied, the solutions obtained are accurate and stable, and locking problems can also be prevented.…”

Section: Introductionmentioning

confidence: 99%

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

Nguyen‐Xuan

Askes

et al. 2010

Numerical Meth Engineering

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Published paperLe, Canh V., Nguyen-Xuan, H., Askes, H., Bordas , Stéphane P. A., Rabczuk, T. and Nguyen-Vinh, H. (2010) SUMMARYThis paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method (CS-FEM) with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged.

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“…In the regions where error exceeds the pre-de ned tolerance, new nodes are added at the vertices of the cell. It is noteworthy that based on the numerical tests performed by Le et al [16], the optimum value of pre-de ned local error tolerance is selected as 0.001. The restructuring process continues until the error tolerance is satis ed at all nodes.…”

Section: Example (1): Smooth Strip Footing Resting On Purely Cohesivementioning

confidence: 99%

“…This adaptive procedure has been proposed for the nite-element limit analysis [10][11][12][13][14][15] as well as the mesh-free limit analysis [16] approaches. The main policy in these methods is de ning a posteriori error estimator and establishing an adaptive re nement strategy based on the reduction of this error.…”

Section: Introductionmentioning

confidence: 99%

Adaptive mesh-free lower bound limit analysis using non-linear programming

Binesh

Rasekh

2017

Scientia Iranica

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Abstract. An adaptive mesh-free approach is developed to compute the lower bounds of limit loads in plane strain soil mechanics problems. There is no pre-de ned connectivity between nodes in the mesh-free techniques, and this property facilitates the implementation of h-adaptivity. Nodes may be added, moved, or discarded without complex changes in the data structures involved. In this regard, the Shepard mesh-free method is used in conjunction with the nodal stress rate smoothing technique and the lower bound limit analysis theory to establish a non-linear optimization problem. This problem is solved by the second-order cone programming technique, and the result is a stress eld that satis es the lower bound requirements in a non-rigorous manner. The lack of rigorousness arises from relaxation during nodal stress rate smoothing process. An error estimator is introduced by the application of Taylor series expansion, and by controlling the local error via a user-de ned tolerance, the adaptive re nement strategy is established. To demonstrate the e ectiveness of the proposed method, the procedure is applied to the examples of purely cohesive and cohesive-frictional soils.

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

Cited by 41 publications

References 41 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)

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

Adaptive mesh-free lower bound limit analysis using non-linear programming

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