An iterative algorithm for limit analysis with nonlinear yield functions

Zouain, Néstor; Herskovits, José; Borges, Lisa; Feijóo, Raúl A.

doi:10.1016/0020-7683(93)90220-2

Cited by 94 publications

(56 citation statements)

References 4 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%

“…For the NLP algorithms, some recently important contributions can be mentioned such as the algorithm based on feasible directions by Zouain et al [10] or by Lyamin and Sloan [19], the algorithm based on the interior-point method by Andersen et al [20] or by Krabbenhoft and Damkilde [21], and the general-purpose NLP codes CONOPT and MINOS by Tin-Loi and Ngo [22]. Recently, one of the most efficient NLP algorithms based on the primal-dual interior-point method was proposed by Andersen et al [23].…”

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confidence: 99%

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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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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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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“…While linear programming involves piecewise linear yield functions, nonlinear programming involves nonlinear yield surfaces. Much progress has been made in developing numerical procedures for limit analysis problems [5][6][7][8][9][10]. Current research is focussing on developing limit analysis tools which are sufficiently efficient and robust to be of use to engineers working in practice.…”

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confidence: 99%

Limit analysis of plates using the EFG method and second‐order cone programming

Gilbert

Askes

2009

Numerical Meth Engineering

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Published paperLe, Canh V., Gilbert, Matthew and Askes, Harm (2009) SUMMARYThe meshless Element-Free Galerkin (EFG) method is extended to allow computation of the limit load of plates. A kinematic formulation which involves approximating the displacement/velocity field using the moving least squares technique is developed. Only one displacement variable is required for each EFG node, ensuring that the total number of variables in the resulting optimization problem is kept to a minimum, with far fewer variables being required compared with finite element formulations. A stabilized conforming nodal integration scheme is extended to plastic plate bending problems. The evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions. Difficulties imposing essential boundary conditions are overcome by enforcing directly displacements at the nodes. The formulation can be expressed as the problem of minimizing a sum of Euclidean norms subject to a set of equality constraints. This non-smooth minimization problem can be transformed into a form suitable for solution using Second-Order Cone Programming (SOCP). The procedure is applied to several benchmark problems and is found in practice to generate good upper bound solutions for benchmark problems.

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“…Various techniques have been proposed in the literature to overcome this singularity problem. These include linearization of the yield condition [32], regularization of the plastic dissipation function [33][34][35][36], and a direct iterative algorithm [37,38]. One of the most robust and efficient algorithms to overcome this difficulty is the primal-dual interior-point method presented in [39,40] and implemented in commercial codes such as the Mosek software package.…”

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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An iterative algorithm for limit analysis with nonlinear yield functions

Cited by 94 publications

References 4 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)

Limit analysis of plates using the EFG method and second‐order cone programming

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

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