Improvement of quadratic finite element for Mindlin plate bending

Kim, Sun-Hoon; Choi, Chang Koon

doi:10.1002/nme.1620340112

Cited by 23 publications

(6 citation statements)

References 13 publications

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“…The main drawback of this parametric displacement-based model is that a shear locking phenomenon will occur when the plate becomes thinner. There are several methods to overcome this problem such as reduced or selected integration technique [46,47], assumed shear strain method [48][49][50][51] and nonconforming element method [52][53][54].…”

Section: Introductionmentioning

confidence: 99%

A 3‐node flat triangular shell element with corner drilling freedoms and transverse shear correction

Zhang¹,

Zhou²,

Li³

et al. 2011

Numerical Meth Engineering

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SUMMARYThe formulation, implementation and testing of simple, efficient and robust shell finite elements have challenged investigators over the past four decades. A new 3-node flat triangular shell element is developed by combination of a membrane component and a plate bending component. The ANDES-based membrane component includes rotational degrees of freedom, and the refined nonconforming element methodbased bending component involves a transverse shear correction. Numerical examples are carried out for benchmark tests. The results show that compared with some popular shell elements, the present one is simple but exhibits excellent all-around properties (for both membrane-and bending-dominated situations), such as free of aspect ratio locking, passing the patch test, free of shear locking, good convergence and high suitability for thin to moderately thick plates. The developed element has already been adopted in a warpage simulation package for injection molding.

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Section: Introductionmentioning

confidence: 99%

A 3‐node flat triangular shell element with corner drilling freedoms and transverse shear correction

Zhang¹,

Zhou²,

Li³

et al. 2011

Numerical Meth Engineering

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“…They carried out tests to assess the e ciency of using non-conforming modes for the transverse displacement ÿelds and found that the marked improvement in solution was obtained by the elements tested. The evolution of this concept and the development of a series of new elements has been made by Choi and co-workers [6,7,[10][11][12][13]. Kim and Choi [13] suggested the improved quadratic Mindlin plate-bending element by adding non-conforming modes to two rotational displacement components.…”

Section: Introductionmentioning

confidence: 99%

“…The evolution of this concept and the development of a series of new elements has been made by Choi and co-workers [6,7,[10][11][12][13]. Kim and Choi [13] suggested the improved quadratic Mindlin plate-bending element by adding non-conforming modes to two rotational displacement components. This concept, namely addition of non-conforming modes to rotational displacement components, is successfully used to develop 4-node at shell elements [7].…”

Section: Introductionmentioning

confidence: 99%

“…Among these techniques, the use of nonconforming modes may be one of the most successful approaches to improve the element behaviour in bending situations. The basic concept of this approach can be found in reference papers on this subject [9][10][11][12][13]. The concept of non-conforming modes was originally formulated by Wilson et al [9] in plane stress problems.…”

Section: Introductionmentioning

confidence: 99%

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Direct modification for non‐conforming elements with drilling DOF

Choi

lee

Chung

2002

Numerical Meth Engineering

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SUMMARYA uniÿed approach to eliminate the undesirable lockings in distorted meshes for both non-conforming quadrilateral membrane and hexahedral elements with drilling (or rotational) degrees of freedom is presented. The direct modiÿcation scheme is utilized in the formulation of non-conforming modes to improve the general behaviour of isoparametric-based elements. It is shown that the direct modiÿcation is very e ective in eliminating the locking and this improvement of element behaviour may be doubled if the selective integration scheme is used simultaneously. To verify the validity of elements formulated by the proposed schemes and to evaluate their e ectiveness, several numerical tests are carried out. The combined use of additional non-conforming modes with the direct modiÿcation method and the selective integration technique plays an important role to improve the behaviour of elements, especially for distorted mesh cases. Test results also show that the results for both non-conforming quadrilateral membrane and hexahedral elements obtained by the proposed schemes are equally satisfactory.

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“…However, there exists a shear locking phenomenon in this parametric displacement-based finite element model as the plate becomes thinner [1]. There are several methods to overcome this problem such as reduced or selected integration technique [1,2], assumed shear strain method [3,4], and non-conforming element method [5,6]. Although the technique of reduced or selected integration is an effective method to prevent the occurrence of shear locking, it may exhibit zero-energy deformation modes and gives erroneous results.…”

Section: Introductionmentioning

confidence: 99%

A refined 5‐node plate bending element based on Reissner–Mindlin theory

Sofuoğlu

Gedikli

2006

Commun. Numer. Meth. Engng.

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SUMMARYIn this study, a simple approach was proposed to develop a new 5-node plate bending element, named DRMP. This element formulation is based on the Reissner-Mindlin plate theory and can be used for the analysis of both thin and thick plate. The new element formulation was then coded into FEAP to develop 15-DOF DRMP element for the finite element analysis of plate problems as well as 4-node quadrilateral DRMQ element with 12 DOF. The convergence and usage of DRMP element along with DRMQ element were investigated and the results of the both elements were then compared with the exact solution and the other elements available in the literature. The numerical studies demonstrated that the proposed elements, DRMQ and DRMP, passed the patch test and possessed fast convergence and high accuracy while DRMP element showed the invariability to the fifth node's position. Moreover, they were independent of the shear locking phenomenon for very thin plates. The presented results showed that 5-node DRMP element can be used along with 4-node quadrilateral DRMQ element where mesh refinement is necessary as a transition element.

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Improvement of quadratic finite element for Mindlin plate bending

Cited by 23 publications

References 13 publications

A 3‐node flat triangular shell element with corner drilling freedoms and transverse shear correction

A 3‐node flat triangular shell element with corner drilling freedoms and transverse shear correction

Direct modification for non‐conforming elements with drilling DOF

A refined 5‐node plate bending element based on Reissner–Mindlin theory

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