Error Analysis of Mixed-Interpolated Elements for Reissner-Mindlin Plates

Brezzi, Franco; Fortin, Michel; Stenberg, Rolf

doi:10.1142/s0218202591000083

Cited by 187 publications

(200 citation statements)

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“…In these équations t > 0 is the plate thickness and the positive constant X = Ek/2( 1 -f v) with E the Young's modulus, v the Poisson ratio, and k the shear correction factor. For all 2 x 2 symmetrie matrices t, Cx is the 2x2 symmetrie matrix defined by A proof of existence, uniqueness, and a priori estimâtes for this System based on Brezzi's theory of saddle-point problems may be found in [9]. We note that Problem (M), unlike Problem (P), has a sensé when î = 0.…”

Section: Cq(q)mentioning

confidence: 99%

“…Several families of locking-free methods are proposed and analysed in [9]. These methods f all into our framework, but have some additional properties.…”

Section: Finite Element Approximation Schemesmentioning

confidence: 99%

“…Second, the operator R^ extends to a bounded operator from H 1 to T h and its norm in J5? (H\L 2 ) is bounded uniformly with respect to h. Most important are the following five properties, which were formulated in [9] as the basis of the convergence theory.…”

Section: Finite Element Approximation Schemesmentioning

confidence: 99%

“…The discrete Helmholtz décomposition (Hl) is derived from (PI) through (P4) in [9]. Hypothesis (H2) clearly follows from the assumption that R^ is uniformly bounded in «£?…”

Section: Finite Element Approximation Schemesmentioning

confidence: 99%

See 3 more Smart Citations

Preconditioning discrete approximations of the Reissner-Mindlin plate model

Arnold¹,

Falk²,

Winther³

1997

ESAIM: M2AN

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Section: Cq(q)mentioning

confidence: 99%

“…Several families of locking-free methods are proposed and analysed in [9]. These methods f all into our framework, but have some additional properties.…”

Section: Finite Element Approximation Schemesmentioning

confidence: 99%

Section: Finite Element Approximation Schemesmentioning

confidence: 99%

“…The discrete Helmholtz décomposition (Hl) is derived from (PI) through (P4) in [9]. Hypothesis (H2) clearly follows from the assumption that R^ is uniformly bounded in «£?…”

Section: Finite Element Approximation Schemesmentioning

confidence: 99%

See 2 more Smart Citations

Preconditioning discrete approximations of the Reissner-Mindlin plate model

Arnold¹,

Falk²,

Winther³

1997

ESAIM: M2AN

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“…In [22] a simpler variant of this method, allowing the lowest polynomial order, is proposed and analysed. In [8] an interpolation of the test functions into the lowest order Raviart-Thomas space is used within the least-squares term, thus making this method only usable for first order elements. A recent stabilised alternative, using the same unknowns, has been developed in [18].…”

Section: Introductionmentioning

confidence: 99%

Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model

Barrenechea

Barrios

Wachtel

2014

Calcolo

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This version is available at https://strathprints.strath.ac.uk/50948/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model * Gabriel R. Barrenechea † , Tomás P. Barrios ‡ , and Andreas Wachtel § , AbstractThis work presents new stabilised finite element methods for a bending moments formulation of the Reissner-Mindlin plate model. The introduction of the bending moment as an extra unknown leads to a new weak formulation, where the symmetry of this variable is imposed strongly in the space. This weak problem is proved to be well-posed, and stabilised Galerkin schemes for its discretisation are presented and analysed. The finite element methods are such that the bending moment tensor is sought in a finite element space constituted of piecewise linear continuos and symmetric tensors. Optimal error estimates are proved, and these findings are illustrated by representative numerical experiments.Mathematics Subject Classifications (1991):

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On evaluating the inf-sup condition for plate bending elements

Iosilevich

Bathe

Brezzi

1997

Int. J. Numer. Meth. Engng.

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This paper addresses the evaluation of the inf-sup condition for Reissner-Mindlin plate bending elements. This fundamental condition for stability and optimality of a mixed ÿnite element scheme is, in general, very diicult to evaluate analytically, considering for example distorted meshes. Therefore, we develop a numerical test methodology. To demonstrate the test methodology and to obtain speciÿc results, we apply it to standard displacement-based elements and elements of the MITC family. Whereas the displacement-based elements fail to satisfy the inf-sup condition, we ÿnd that the MITC elements pass our numerical test for uniform meshes and a sequence of distorted meshes. ?

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Error Analysis of Mixed-Interpolated Elements for Reissner-Mindlin Plates

Cited by 187 publications

References 0 publications

Preconditioning discrete approximations of the Reissner-Mindlin plate model

Preconditioning discrete approximations of the Reissner-Mindlin plate model

Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model

On evaluating the inf-sup condition for plate bending elements

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