Sign in
Author

Conference

Journal

Organization

Year

DOI
Look for results that meet for the following criteria:
since
equal to
before
between
and
Search in all fields of study
Limit my searches in the following fields of study
Agriculture Science
Arts & Humanities
Biology
Chemistry
Computer Science
Economics & Business
Engineering
Environmental Sciences
Geosciences
Material Science
Mathematics
Medicine
Physics
Social Science
Multidisciplinary
Keywords
(7)
Error Estimate
Finite Element
Nite Element Method
Numerical Calculation
reissnermindlin plate
Variational Principle
Shear Stress
Related Publications
(4)
A Posteriori Error Estimation for Hierarchic Models of Elliptic Boundary Value Problems on Thin Domains
Aposteriori modeling error estimation for hierarchic plate models
On the justification of plate theories in linear elasticity theory using exponential decay estimates
A Uniformly Accu...
Subscribe
Academic
Publications
ANALYSIS OF A LINEAR{LINEAR FINITE ELEMENT FOR THE REISSNER{MINDLIN PLATE MODEL
ANALYSIS OF A LINEAR{LINEAR FINITE ELEMENT FOR THE REISSNER{MINDLIN PLATE MODEL,DOUGLAS N. ARNOLD,RICHARD S. FALK
Edit
ANALYSIS OF A LINEAR{LINEAR FINITE ELEMENT FOR THE REISSNER{MINDLIN PLATE MODEL
(
Citations: 11
)
BibTex

RIS

RefWorks
Download
DOUGLAS N. ARNOLD
,
RICHARD S. FALK
An analysis is presented for a recently proposed
nite element method
for the Reissner{ Mindlin plate problem. The method is based on the standard variational principle, uses nonconforming linear elements to approximate the rotations and conforming linear elements to approximate the transverse displacements, and avoids the usual \locking problem" by interpolating the
shear stress
into a rotated space of lowest order Raviart Thomas elements. When the plate thickness t = O(h), it is proved that the method gives optimal order error estimates uniform in t. However, the analysis suggests and numerical calculations conrm that the method can produce poor approximations for moderate sized values of the plate thickness. Indeed, for t xed, the method does not converge as the mesh size h tends to zero.
Published in 1997.
Cumulative
Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
(
www.ima.umn.edu
)
Citation Context
(4)
...Arnold and Falk [
5
] analyzed this element and proved that the method gives optimal order error estimates uniform in t when t h, but that the method does not converge as h goes to zero for t xed...
Richard S. Falk
,
et al.
Lockingfree finite elements for the ReissnerMindlin plate
...(Arnold and Falk [1], Duran and Liberman [13], Onate, Zarate and Flores [15], Brezzi, Fortin and Stenberg [12], :::.) Each of them used the same framework, a pair of subspaces and a reduction operator [
2
]...
...The simplest pair of subspaces is the one given by Onate, Zarate and Flores [15], but Arnold and Falk [
2
] showed that this method does not converge in the classical sense...
James H. Bramble
,
et al.
A negativenorm least squares method for ReissnerMindlin plates
...To partially compensate for this fact, one can use the following result, established in [
14
]...
Richard S. Falk
.
Finite Elements for the Reissner–Mindlin Plate
...In the last decade, through the work of numerous authors (see [9],[10], [11] [
2
], [1], [3], [25], [18] for a small sampling of this literature), a number of results have been established that justify using these model equations as approximations in problems of static elastic behavior ‐ that is to say, when the beam or plate is at rest...
R. E. Lee DeVille
,
et al.
Reduced equations for models of laminated materials in thin domains. I
References
(11)
Innovative nite element methods for plates
(
Citations: 10
)
D. N. Arnold
Published in 1991.
A Uniformly Accurate Finite Element Method for the Reissner–Mindlin Plate
(
Citations: 125
)
Douglas N. Arnold
,
Richard S. Falk
Journal:
Siam Journal on Numerical Analysis  SIAM J NUMER ANAL
, vol. 26, no. 6, 1989
Mixedinterpolated elements for ReissnerMindlin plates
(
Citations: 105
)
Franco Brezzi
,
KlausJürgen Bathe
,
Michel Fortin
Journal:
International Journal for Numerical Methods in Engineering  INT J NUMER METHOD ENG
, vol. 28, no. 8, pp. 17871801, 1989
Error analysis of mixedinterpolated elements for ReissnerMindlin plates
(
Citations: 51
)
F. Brezzi
,
M. Fortin
,
R. Stenberg
Published in 1991.
A nite element method for MindlinReissner plate model
(
Citations: 6
)
R. Duran
,
A. Ghioldi
,
N. Wolanski
Published in 1991.
Sort by:
Citations
(11)
A Stabilized Mixed Finite Element Method for Thin Plate Splines Based on Biorthogonal Systems
Bishnu P. Lamichhane
,
Markus Hegland
Published in 2009.
A Loworder Nonconforming Finite Element for ReissnerMindlin Plates
(
Citations: 18
)
Carlo Lovadina
Journal:
Siam Journal on Numerical Analysis  SIAM J NUMER ANAL
, vol. 42, no. 6, pp. 26882705, 2005
A priori error estimation of a fournode Reissner–Mindlin plate element for elastodynamics
Shen R. Wu
Journal:
Computer Methods in Applied Mechanics and Engineering  COMPUT METHOD APPL MECH ENG
, vol. 194, no. 18, pp. 22572281, 2005
A nonconforming element for the Reissner–Mindlin plate
(
Citations: 24
)
F. Brezzi
,
L. D. Marini
Journal:
Computers & Structures  COMPUT STRUCT
, vol. 81, no. 8, pp. 515522, 2003
A stabilized MITC element for accurate wave response in Reissner–Mindlin plates
(
Citations: 11
)
Lonny L. Thompson
,
Sri Ramkumar Thangavelu
Journal:
Computers & Structures  COMPUT STRUCT
, vol. 80, no. 9, pp. 769789, 2002