Two generalized conforming quadrilateral Mindlin–Reissner plate elements based on the displacement function

Shang, Yan; Cen, Song; Li, Chenfeng; Fu, Xiang‐Rong

doi:10.1016/j.finel.2015.01.012

Cited by 15 publications

(9 citation statements)

References 46 publications

(84 reference statements)

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“…where l * x and l * y denote the direction cosines of the outer normal of the SS1 edge 12. Similarly, substitution of Equations (38) and (39) into equations in previous sections yields the final formulations of the element IHDF-P4-SS1. This element will be employed to simulate the behaviors in boundary layers near SS1 edges.…”

Section: Related Constraints On the Resultant Fields Of New Elementsmentioning

confidence: 99%

“…Tables IX and X give the normalized central deflections and bending moments calculated by different element models [26,29,34,35,37]. It can be seen that the results obtained by the presented IHDF scheme and the conventional HDF plate element HDF-P4-11 [2] both converge rapidly into the reference solutions [38,39]. [35] 0.988 0.997 -ARS-Q12 [34] 0.988 0.997 0.999 1.000 * CHRM [37] 0.970 0.993 0.998 AC-MQ4 [29] 0.996 0.998 1.000 HDF-P4-11 [2] 1.005 1.001 1.000 IHDF-P4-SS1+HDF-P4- 11 1.005 1.001 1.000 Normalized central moment MITC4 [34] 0.987 0.997 -DKMQ [35] 1.014 1.005 -ARS-Q12 [26] 1.015 1.004 1.001 1.000 ** CHRM [37] 0.993 0.998 1.000 AC-MQ4 [29] 1.025 1.007 1.002 HDF-P4-11 [2] 1.003 1.001 1.000 IHDF-P4-SS1+HDF-P4- 11 1.003 1.001 1.000…”

Section: The Circular Platementioning

confidence: 88%

“…Tables and give the normalized central deflections and bending moments calculated by different element models . It can be seen that the results obtained by the presented IHDF scheme and the conventional HDF plate element HDF‐P4‐11 β both converge rapidly into the reference solutions .…”

Section: Numerical Testsmentioning

confidence: 91%

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Improved hybrid displacement function (IHDF) element scheme for analysis of Mindlin–Reissner plate with edge effect

Shang

Cen

et al. 2017

Numerical Meth Engineering

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Summary For a Mindlin–Reissner plate subjected to transverse loadings, the distributions of the rotations and some resultant forces may vary very sharply within a narrow district near certain boundaries. This edge effect is indeed a great challenge for conventional finite element analysis. Recently, an effective hybrid displacement function (HDF) finite element method was successfully developed for solving such difficulty . Although good performances can be obtained in most cases, the distribution continuity of some resulting resultants is destroyed when coarse meshes are employed. Moreover, an additional local coordinate system must be used for avoiding a singular problem in matrix inversion, which makes the derivations more complicated. Based on a modified complementary energy functional containing Lagrangian multipliers, an improved HDF (IHDF) element scheme is proposed in this work. And two new special IHDF elements, named by IHDF‐P4‐Free and IHDF‐P4‐SS1, are constructed for modeling plate behaviors near free and soft simply supported boundaries, respectively. The present modeling scheme not only greatly improves the precision of the numerical results but also avoids usage of the additional local Coordinate system. The numerical tests demonstrate that the new IHDF element scheme is an effective way for solving the challenging edge effect problem in Mindlin–Reissner plates. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Related Constraints On the Resultant Fields Of New Elementsmentioning

confidence: 99%

Section: The Circular Platementioning

confidence: 88%

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Improved hybrid displacement function (IHDF) element scheme for analysis of Mindlin–Reissner plate with edge effect

Shang

Cen

et al. 2017

Numerical Meth Engineering

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“…Hence, this HDF method can be treated as a kind of "shapefree" finite element method for Mindlin-Reissner plate. In addition, the HDF method can also be applied to construct special elements for dealing with the edge effect problems of the Mindlin-Reissner plate [196], and the displacement function can also be used for developing displacementbased element models [197].…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Developments of Mindlin-Reissner Plate Elements

Cen

Shang

2015

Mathematical Problems in Engineering

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Since 1960s, how to develop high-performance plate bending finite elements based on different plate theories has attracted a great deal of attention from finite element researchers, and numerous models have been successfully constructed. Among these elements, the most popular models are usually formulated by two theoretical bases: the Kirchhoff plate theory and the Mindlin-Reissener plate theory. Due to the advantages that onlyC0continuity is required and the effect of transverse shear strain can be included, the latter one seems more rational and has obtained more attention. Through abundant works, different types of Mindlin-Reissener plate models emerged in many literatures and have been applied to solve various engineering problems. However, it also brings FEM users a puzzle of how to choose a “right” one. The main purpose of this paper is to present an overview of the development history of the Mindlin-Reissner plate elements, exhibiting the state-of-art in this research field. At the end of the paper, a promising method for developing “shape-free” plate elements is recommended.

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“…The smoothed finite element methods (S‐FEM) based on strain smoothing technique , including the cell‐based S‐FEM (CS‐FEM) , the node‐based S‐FEM (NS‐FEM) , the edge‐based S‐FEM (ES‐FEM) , were first introduced by Liu et al into the analysis of plate and shell structures . Cen et al proposed a hybrid displacement function method based on Reissner–Mindlin plate theory, in which the displacement function satisfying all governing equations are used to derive displacement components. Numerical examples had proved that the element models presented in their works perform well even when a severely distorted mesh is employed and can effectively handle the edge effect caused by certain boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Assumed stress quasi-conforming technique for static and free vibration analysis of Reissner-Mindlin plates

Wang

Zhang

et al. 2017

Int. J. Numer. Meth. Engng

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This paper presents a novel formulation based on Hellinger-Reissner variational principle in the framework of quasi-conforming method for static and free vibration analysis of Reissner-Mindlin plates. The formulation starts from polynomial approximation of stresses, which satisfy the equilibrium equations of Reissner-Mindlin plate theory. Then the stress matrix is treated as the weighted function to weaken the straindisplacement equations after the strains are derived by using the constitutive equations. Finally, the string-net functions are introduced to calculate strain integration. As examples, two new plate bending elements, a 4-node quadrilateral element QC-P4-11 and a 3-node triangular element QC-P3-7 , are proposed. Several benchmark examples are demonstrated to show the performance of the elements, and the results obtained are compared with other available ones. Numerical results have proved that both elements possess excellent precision. In particular, the quadrilateral element performs well even when the element shape degenerates into a triangle or concave quadrangle. integration [19,20] and selective integration techniques [21,22]. Unfortunately, these elements are still subjected to some other drawbacks, such as instability for rank deficiency, zero energy modes, or severe accuracy loss on the occasion of mesh distortions. To yield a much higher accuracy and stability of numerical methods, many new formulations, such as the assumed natural strain (ANS) method [23][24][25], the mixed shear projected approach [26,27], and the discrete shear gap (DSG) method [28] have been developed. Other models, including the improved shear strain interpolations approaches derived from Timoshenko's beam function [29,30], the enhanced assumed strain methods [31,32], the mixed interpolated tensorial components (MITC) technique [33][34][35][36] and its extension [37,38] have also been introduced for the linear and nonlinear analysis of plates and shells.To further advance finite element technologies, Chen and Cheung [39-41] developed a series of triangular and quadrilateral plate/shell elements based on the refined non-conforming element method. In their work, the exact displacement function of the Timoshenko's beam is used to derive the element displacements. Numerical examples demonstrated the proposed model is not only free from shear locking but also indeed possesses higher accuracy for both thin and thick plates. The smoothed finite element methods (S-FEM) based on strain smoothing technique [42], including the cell-based S-FEM (CS-FEM) [43], the node-based S-FEM (NS-FEM) [44], the edge-based S-FEM (ES-FEM) [45], were first introduced by Liu et al. [46] into the analysis of plate and shell structures [47]. Cen et al. [48-50] proposed a hybrid displacement function method based on Reissner -Mindlin plate theory, in which the displacement function [51] satisfying all governing equations are used to derive displacement components.Numerical examples had proved that the element models presented in their works perform well...

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Two generalized conforming quadrilateral Mindlin–Reissner plate elements based on the displacement function

Cited by 15 publications

References 46 publications

Improved hybrid displacement function (IHDF) element scheme for analysis of Mindlin–Reissner plate with edge effect

Improved hybrid displacement function (IHDF) element scheme for analysis of Mindlin–Reissner plate with edge effect

Developments of Mindlin-Reissner Plate Elements

Assumed stress quasi-conforming technique for static and free vibration analysis of Reissner-Mindlin plates

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