An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids

Liu, G.R.; Nguyen-Thoi, T.; Lam, Kwok‐Yan

doi:10.1016/j.jsv.2008.08.027

Cited by 603 publications

(353 citation statements)

References 17 publications

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“…In the other front of the development of numerical methods, Liu and Nguyen Thoi [39] have integrated the strain smoothing technique [40] into the finite element method (FEM) to create a series of smoothed FEMs (S-FEMs) such as cell/element-based smoothed FEM (CS-FEM) [41][42][43], node-based smoothed FEM (NS-FEM) [44][45][46], edge-based smoothed FEM (ES-FEM) [47,48], face-based smoothed FEM (FS-FEM) [49], and a group of alpha-FEM [50][51][52][53]. Each of these smoothed FEMs has different properties and has been used to produce desired solutions for a wide class of benchmark and practical mechanics problems.…”

mentioning

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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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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“…As shown in [8,11], ES-FEM behaves well in many contexts of analysis. The reason for this good behaviour is that the discontinuity of the approximate strain field is reduced significantly, due to the smoothing effect.…”

Section: Comparison With Other Fe Modelsmentioning

confidence: 84%

“…The usual formulation of the ES-FEM assumes a constant strain on the element [8]. Here the finite element model is constructed by assuming independent interpolations to approximate the displacement and the stress field.…”

Section: The Stress Interpolationmentioning

confidence: 99%

Composite Fem Models for Limit and Shakedown Analysis

Leonetti¹,

Garcea²,

Nguyen‐Xuan³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The paper improved S-FEMs formulations with an enriched displacement field, making use of modified Allman's shape functions. This mixed interpolation is the natural context in performing lower bound strategy for shakedown, limit analysis and elastoplastic analysis. The model takes advantages from the simplicity and few addressed requirements for good performances in nonlinear analysis. The simple assumption made for the stress field regards the convenience of using self-equilibrated stress interpolations in Cartesian coordinates. In the proposed composite elements the stress is discontinuous on the element and across their sides and the mesh of the elements is coincident with the discretization of the geometry. This stress interpolation is able to address the discontinuities in the plastic strain and, in such a way, to define in their description a finer mesh with respect the basic grid.

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“…Based on how the strain smoothing procedure is done, there are three main types of SFEM: 1-Cell based SFEM (CSFEM) [9], 2-Node based SFEM (NSFEM) [10], and 3-Edge based SFEM (ESFEM) [11]. In the CSFEM, strain smoothing is done on domains that are created by dividing the elements of the original FEM mesh into sub-cells; the NSFEM uses nodes to create smoothing domains, and in the ESFEM smoothing domain creation is based on the edges of the elements.…”

Section: Introductionmentioning

confidence: 99%

Application of smoothed finite element method in coupled hydro-mechanical analyses

Karimian

Oliaei

2017

Scientia Iranica

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Smoothed finite element method (SFEM) was introduced by application of the stabilized conforming nodal integration in the conventional finite element method. In this method, integration is performed on "smoothing domains" rather than elements. Smoothing domains are created based on cells, nodes or edges for two dimensional problems. Based on the smoothing domain creation method, different types of SFEM are developed that have different properties. It has been shown that these methods are insensitive to mesh distortion and are generally more computationally efficient than mesh-free and finite element methods for the same accuracy level. Because of their interesting features, they have been used to solve different problems. This paper investigates the performance of these methods in coupled hydro-mechanical (consolidation) analysis, by solution of some problems using a developed SFEM/FEM code. Biot's consolidation theory is reviewed, and after introduction of the idea and formulation of SFEMs, discretized form of equations is given. Requirements for creation of stable coupled hydro-mechanical models are discussed and based on them, two methods for creation of stable SFEM models are introduced. To investigate the effectiveness of the methods, a number of examples are solved and results are compared with the finite element and analytical ones.

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An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids

Cited by 603 publications

References 17 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)

Composite Fem Models for Limit and Shakedown Analysis

Application of smoothed finite element method in coupled hydro-mechanical analyses

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