A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

Nguyen‐Xuan, H.; Rabczuk, Timon; Nguyen‐Thanh, Nhon; Nguyen-Thoi, T.; Bordas, Stéphane Pierre Alain

doi:10.1007/s00466-010-0509-x

Cited by 141 publications

(86 citation statements)

References 82 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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)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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“…In the present work the integrals in Equations (13), (14), and (17) are evaluated numerically using Gaussian quadrature rule. The number of integration sampling points to obtain an exact integration result for an element with linear, quadratic, and cubic shape functions are listed in Table 2, assuming q is a linear function.…”

Section: Numerical Integrationmentioning

confidence: 99%

“…The DSG technique was subsequently generalized and applied to remove membrane locking [12]. It also has successfully applied in the context of an alternative finite element formulation called the smoothed FEM [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Study of the Discrete Shear Gap Technique in Timoshenko Beam Elements

Wong¹,

Sugianto²

2017

ced

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A major difficulty in formulating a finite element for shear-deformable beams, plates, and shells is the shear locking phenomenon. A recently proposed general technique to overcome this difficulty is the discrete shear gap (DSG) technique. In this study, the DSG technique was applied to the linear, quadratic, and cubic Timoshenko beam elements. With this technique, the displacement-based shear strain field was replaced with a substitute shear strain field obtained from the derivative of the interpolated shear gap. A series of numerical tests were conducted to assess the elements performance. The results showed that the DSG technique works perfectly to eliminate the shear locking. The resulting deflection, rotation, bending moment, and shear force distributions were very accurate and converged optimally to the corresponding analytical solutions. Thus the beam elements with the DSG technique are better alternatives than those with the classical selective-reduced integration.

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“…The bending stiffness matrix was calculated by a boundary integral along the boundaries of the smoothing elements [23]. Nguyen-Xuan et al [24] provided a four-node quadrilateral shell element with smoothed membranebending, the element is a combination of a plate bending and membrane element, and a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements was formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates [25]. In [26,27], presented an alternative alpha finite element method using triangular meshes for static, free vibration and buckling analyses of Mindlin-Reissner plates and laminated composite plates.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Characteristics and Stability of Axially Moving Viscoelastic Plate with Piezoelectric Layer

Wang

Cao

Tao

et al. 2014

Journal of Low Frequency Noise, Vibration and Active Control

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The dynamic stability of the moving viscoelastic plate with the piezoelectric layer is studied. On the basis of the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of the axially moving viscoelastic rectangular plate with piezoelectric layer in the Laplace domain is formulated, the equation is suitable for various viscoelastic differential models. Then, the differential equation of motion of the viscoelastic plate with elastic dilatation and Kelvin-Voigt distortion in time domain is derived, with the piezoelectric effect. The complex eigenvalue equations of axially moving viscoelastic plate are established by the differential quadrature method. The generalized eigenvalue equations are solved, and the force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force; this force is used to improve the stability of the axially moving viscoelastic plate. Via numerical calculation, the results for the instability type and the corresponding critical moving speed of viscoelastic plate are presented to show the variations in these factors with respect to the dimensionless moving speed, the dimensionless delay time and the applied voltages. The dynamic stability of the axially moving viscoelastic plates can be effectively improved by the determination of the optimal location for the piezoelectric layers and the most favorable voltage assignment.

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A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

Cited by 141 publications

References 82 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)

Study of the Discrete Shear Gap Technique in Timoshenko Beam Elements

Dynamic Characteristics and Stability of Axially Moving Viscoelastic Plate with Piezoelectric Layer

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