Upper bound limit analysis of plates utilizing the C1 natural element method

Zhou, Shuqin; Liu, Yinghua; Chen, Shenshen

doi:10.1007/s00466-012-0688-8

Cited by 21 publications

(12 citation statements)

References 31 publications

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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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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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“…Next, let us consider the rectangular plate (length-to-width ratio a/b = 2) with various boundary conditions. We compare the present results with other published ones such as the EFG method [7], the rectangular non-deforming plate element (ACM) [42] and the C 1 natural element method [9]. Table 5 summarizes the limit load multipliers of a rectangular plate with various boundary conditions such as simply supported (SSSS), fully clamped (CCCC), three-clamped and one-short free sides (CCCsF), three-clamped and one-long free sides (CCClF), and two-clamped and two-short free sides (CCsFF).…”

Section: Rectangular Platesmentioning

confidence: 59%

“…The present solutions fall between lower and upper bound published ones. Table 4 compares the present results with the upper bound solutions [1,2,4,6,9], the quasi-upper bound [7] and the (quasi-) lower bound [4,16]. As seen, the limit load factor using the rotation-free IGA approach is more accurate than that of several published solutions.…”

Section: Rectangular Platesmentioning

confidence: 73%

“…The results of the collapse limit factor with varying skewness angle are listed in Table 6. The obtained result is compared with the analytical solution given by Mansfield [43], the Mindlin plate finite element (N4B0) proposed by Capsoni and Silva [44] and C 1 natural element method (C 1 -NEM) based on Kirchhoff plate model by Zhou et al [9]. For this problem, an analytical approach into lower bound (LB) and upper bound solutions using the square yield criterion were proposed by Mansfield [43].…”

Section: Rhombic Platementioning

confidence: 99%

“…Nowadays, limit analysis has become a well-known tool for assessing the safety load factor of engineering structures as an efficient direct method. Due to limitation of analytical methods, various numerical approaches such as finite element methods (FEM) [1][2][3][4][5][6], meshfree methods [7,8], and natural element method [9], just to mention a few, have therefore been developed.…”

Section: Introductionmentioning

confidence: 99%

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Upper bound limit analysis of plates using a rotation-free isogeometric approach

Nguyen‐Xuan

Thai

Bleyer

et al. 2014

Asia Pac. J. Comput. Engin.

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Background: This paper presents a simple and effective formulation based on a rotation-free isogeometric approach for the assessment of collapse limit loads of plastic thin plates in bending. Methods:The formulation relies on the kinematic (or upper bound) theorem and namely B-splines or non-uniform rational B-splines (NURBS), resulting in both exactly geometric representation and high-order approximations. Only one deflection variable (without rotational degrees of freedom) is used for each control point. This allows us to design the resulting optimization problem with a minimum size that is very useful to solve large-scale plate problems. The optimization formulation of limit analysis is transformed into the form of a second-order cone programming problem so that it can be solved using highly efficient interior-point solvers. Results and conclusions: Several numerical examples are given to demonstrate reliability and effectiveness of the present method in comparison with other published methods.

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On the performance of non‐conforming finite elements for the upper bound limit analysis of plates

Bleyer

Buhan

2013

Numerical Meth Engineering

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This is a preprint version of an article accepted for publication in International Journal for Numerical Methods in Engineering Copyright © 2012 John Wiley & Sons, Ltd.International audienceIn this paper, the upper bound limit analysis of thin plates in bending is addressed using various types of triangular finite elements for the generation of velocity fields and second order cone programming (SOCP) for the minimization problem. Three different C1-discontinuous finite elements are considered : the quadratic 6 node Lagrange triangle (T6), an enhanced T6 element with a cubic bubble function at centroid (T6b) and the cubic Hermite triangle (H3). Through numerical examples involving Johansen and von Mises yield criteria, it is shown that cubic elements (H3) give far better results in terms of convergence rate and precision than fully conforming elements found in the literature, especially for problems involving clamped boundaries

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Upper bound limit analysis of plates utilizing the C1 natural element method

Cited by 21 publications

References 31 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)

Upper bound limit analysis of plates using a rotation-free isogeometric approach

On the performance of non‐conforming finite elements for the upper bound limit analysis of plates

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