Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing

Nguyen‐Xuan, H.; Tran, Loc V.; Thai, Chien H.; Nguyen-Thoi, T.

doi:10.1016/j.tws.2012.01.013

Cited by 128 publications

(56 citation statements)

References 33 publications

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“…Several theoretical aspects of the S-FEM models have been provided in [54,55]. The S-FEM models have also been further investigated and applied to various problems such as plates and shells [56][57][58][59][60][61][62][63][64][65][66][67][68], piezoelectricity [69,70], fracture mechanics [71], visco-elastoplasticity [72][73][74], limit and shakedown analysis for solids [75][76][77], and some other applications [78,79].…”

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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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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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“…Lee et al [15,16] developed the elementfree kp-Ritz method to study behaviour of FGM plate. Also, developed smoothed finite element methods based on triangular meshes were formulated to analyse static, free vibration and elastic stability of FGM plates [17][18][19] and so on.…”

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confidence: 99%

Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates

Tran

Phung‐Van

Lee

et al. 2016

Composite Structures

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“…Developments of new materials such as functionally graded materials (FGMs), however, have necessitated more research in this area. It is observed from the literature that studies involving stability (in terms of buckling) characteristics of FGM plates subjected to thermal [3-25, 46, 47, 52], mechanical loading [26][27][28][29][30][31][32][33][34][35], or combinations of [20,[36][37][38][39][40][41][42] based on deterministic analysis have received greater attention [43][44][45].…”

Section: Introductionmentioning

confidence: 99%

“…The material properties of the FG plate, except Poisson's ratio, were assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Nguyen-Xuan et al [43] analysed the static, free vibration and mechanical/thermal buckling problems of FG plates using the finite element approach in which a node-based strain smoothing is merged into shearlocking-free triangular plate elements. This work is the extension of the earlier works carried out by the same authors [44,45] on an edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap (DSG) technique using triangular meshes (ES-DSG) to enhance the accuracy of the existing finite element methods for analysis of isotropic Reissner/Mindlin plates.…”

Section: Introductionmentioning

confidence: 99%

Thermal stability analysis of functionally graded plates using simple refined plate theory

Bouazza¹,

Boucheta²,

Becheri³

et al. 2017

Int. J. Automot. Mech. Eng.

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The present paper investigates the thermal stability analysis of functionally graded material plates subjected to three types of thermal loadings, namely; uniform temperature rise, linear temperature rise and non-linear temperature rise through the thickness, using a novel simple refined theory. The theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Material properties are varied continuously in the thickness direction according to a simple power law distribution. A buckling analysis of a functionally graded plate under there types of thermal loads is carried out and results in closed-form solutions thermal stability analysis of functionally graded plates using simple refined plate theory. The influence of various factors such as gradient index, temperature loads, thickness and aspect ratios are carefully studied. The results are verified with the known data in the literature. This theory is seen to behave well, and the results of the sample problem show good agreement with the literature values as seen from the validation checks.

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Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing

Cited by 128 publications

References 33 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)

Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates

Thermal stability analysis of functionally graded plates using simple refined plate theory

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