A robust triangular plate bending element of the Reissner–Mindlin type

Zienkiewicz, O.C.; Lefebvre, D. R.

doi:10.1002/nme.1620260511

Cited by 98 publications

(28 citation statements)

References 20 publications

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“…As a result, various methods have been proposed to overcome shear-locking effect for elastic plate problems, including selective reduced integration scheme [11,12], mixed formulation/hybrid elements [13,14], enhanced assumed strain [15], assumed natural strain [16] and discrete shear gap (DSG) formulation [17]. Shear-locking for limit analysis of Reissner-Mindlin plate has been recently studied by Le [18], where a stabilized strain smoothing technique is used in combination with DSG elements.…”

Section: Introductionmentioning

confidence: 99%

Locking‐free discontinuous finite elements for the upper bound yield design of thick plates

Bleyer

Buhan

2015

Numerical Meth Engineering

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This work investigates the formulation of finite elements dedicated to the upper bound kinematic approach of yield design or limit analysis of Reissner-Mindlin thick plates in shear-bending interaction. The main novelty of this paper is to take full advantage of the fundamental difference between limit analysis and elasticity problems as regards the class of admissible virtual velocity fields. In particular, it has been demonstrated for 2D plane stress, plane strain or 3D limit analysis problems that the use of discontinuous velocity fields presents a lot of advantages when seeking for accurate upper bound estimates. For this reason, discontinuous interpolations of the transverse velocity and the rotation fields for Reissner-Mindlin plates are proposed. The subsequent discrete minimization problem is formulated as a second-order cone programming (SOCP) problem and is solved using the industrial software package Mosek. A comprehensive study of the shear-locking phenomenon is also conducted and it is shown that discontinuous elements avoid such a phenomenon quite naturally, whereas continuous elements cannot without any specific treatment. This particular aspect is confirmed through numerical examples on classical benchmark problems and the so-obtained upper bound estimates are confronted to recently developed lower bound equilibrium finite elements for thick plates.

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Section: Introductionmentioning

confidence: 99%

Locking‐free discontinuous finite elements for the upper bound yield design of thick plates

Bleyer

Buhan

2015

Numerical Meth Engineering

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“…The results for central displacement w C are reported on Figure 12. They are compared with the results obtained by our MiSP elements presented in Reference [21] and by two other Reissner-Mindlin plate elements considered as robust: the T63B3 element [45] and the MITC4 element (Bathe and Dvorkin [23]). These results are given in terms of active dofs, i.e.…”

Section: Accuracy Assessment Of Misp3+ Elementmentioning

confidence: 96%

“…Several elements use this approach now, we mention in particular: Saleeb et al [44] hybrid-mixed elements, the triangular element HMPL3 or HMSH3(plate) is simple to formulate (w; ÿ x ; ÿ y : linear, M x ; M y ; M xy : constant, T x ; T y : linear) but it is unfortunately used in the form of a four-triangle (cross-diagonal mesh). The mixed element with bubble functions T63B3 due to Zienkiewicz and Lefebvre [45] (6-node triangle with fourth-order bubble functions for rotations ÿ x and ÿ y ) have 12 internal variables: 3T x ; 3T y ; 3ÿ x and 3ÿ y which are eliminated using a static condensation at the element level. The element is considered by many researchers as robust.…”

Section: Synthesis Of Triangular ÿNite Elements For Plate Bending=shementioning

confidence: 99%

An improved three‐node hybrid‐mixed element for Mindlin/Reissner plates

Ayad

Rigolot

Talbi

2001

Numerical Meth Engineering

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SUMMARYBased on the mixed shear projected (MiSP) approach [6], an enhanced bending approximation for homogeneous isotropic plates is presented. Some hard benchmark tests, as skew plate (30 • ) problem for instance, have often shown poor convergence when low order elements (3-or 4-node element) are developed using linear approximations for kinematic variables. To put right this weakness, we propose a high-order interpolation for rotational dofs which results in more rich bending curvatures. The mid-side rotational nodes are eliminated using a combination of local discrete kinematic and constitutive Mindlin hypothesises. The derived 3-node triangular element, called MiSP3+, is free of shear locking and passes all patch-tests for thick and thin plates in an arbitrary mesh.

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“…See also the related element of Zienkiewicz-Lefebvre [52]. The element diagram for the lowest order Falk-Tu element (k = 2) is depicted below.…”

Section: The Falk-tu Elements With Discontinuous Shear Stresses [35]mentioning

confidence: 99%

Locking-free finite elements for the Reissner-Mindlin plate

Falk

1999

Math. Comp.

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A robust triangular plate bending element of the Reissner–Mindlin type

Cited by 98 publications

References 20 publications

Locking‐free discontinuous finite elements for the upper bound yield design of thick plates

Locking‐free discontinuous finite elements for the upper bound yield design of thick plates

An improved three‐node hybrid‐mixed element for Mindlin/Reissner plates

Locking-free finite elements for the Reissner-Mindlin plate

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