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On the accuracy of Reissner–Mindlinplate modelfor stress boundary conditions

Published online by Cambridge University Press:  21 June 2006

Sheng Zhang
Sheng Zhang*
Affiliation:
Department of Mathematics, Wayne State University, Detroit, Michigan 48202, USA. sheng@math.wayne.edu
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Abstract

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

Keywords

Reissner–Mindlin plateshear correction factorstress boundary condition.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 2 , March 2006 , pp. 269 - 294
Copyright
© EDP Sciences, SMAI, 2006

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