On the accuracy of Reissner–Mindlin plate model for stress boundary conditions

Sheng Zhang

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

  • Volume: 40, Issue: 2, page 269-294
  • ISSN: 0764-583X

Abstract

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For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the Reissner–Mindlin model is accurate but the Kirchhoff–Love model totally fails. In the intermediate case, while the Kirchhoff–Love model fails, the Reissner–Mindlin solution also has a relative error comparing to the elasticity solution, which does not decrease when the plate thickness tends to zero. We also show that under the conventional definition of the resultant loading functional, the well known shear correction factor 5/6 in the Reissner–Mindlin model should be replaced by 1. Otherwise, the range of applicability of the Reissner–Mindlin model is not wider than that of Kirchhoff–Love's.

How to cite

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Zhang, Sheng. "On the accuracy of Reissner–Mindlin plate model for stress boundary conditions." ESAIM: Mathematical Modelling and Numerical Analysis 40.2 (2006): 269-294. <http://eudml.org/doc/249689>.

@article{Zhang2006,
abstract = { For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the Reissner–Mindlin model is accurate but the Kirchhoff–Love model totally fails. In the intermediate case, while the Kirchhoff–Love model fails, the Reissner–Mindlin solution also has a relative error comparing to the elasticity solution, which does not decrease when the plate thickness tends to zero. We also show that under the conventional definition of the resultant loading functional, the well known shear correction factor 5/6 in the Reissner–Mindlin model should be replaced by 1. Otherwise, the range of applicability of the Reissner–Mindlin model is not wider than that of Kirchhoff–Love's. },
author = {Zhang, Sheng},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Reissner–Mindlin plate; shear correction factor; stress boundary condition.; Reissner-Mindlin plate; stress boundary condition},
language = {eng},
month = {6},
number = {2},
pages = {269-294},
publisher = {EDP Sciences},
title = {On the accuracy of Reissner–Mindlin plate model for stress boundary conditions},
url = {http://eudml.org/doc/249689},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Zhang, Sheng
TI - On the accuracy of Reissner–Mindlin plate model for stress boundary conditions
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/6//
PB - EDP Sciences
VL - 40
IS - 2
SP - 269
EP - 294
AB - For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the Reissner–Mindlin model is accurate but the Kirchhoff–Love model totally fails. In the intermediate case, while the Kirchhoff–Love model fails, the Reissner–Mindlin solution also has a relative error comparing to the elasticity solution, which does not decrease when the plate thickness tends to zero. We also show that under the conventional definition of the resultant loading functional, the well known shear correction factor 5/6 in the Reissner–Mindlin model should be replaced by 1. Otherwise, the range of applicability of the Reissner–Mindlin model is not wider than that of Kirchhoff–Love's.
LA - eng
KW - Reissner–Mindlin plate; shear correction factor; stress boundary condition.; Reissner-Mindlin plate; stress boundary condition
UR - http://eudml.org/doc/249689
ER -

References

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