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On the range of applicability of the ReissnerMindlin and KirchhoffLove plate bending models

Summary: On the range of applicability of the Reissner­Mindlin
and Kirchhoff­Love plate bending models
Douglas N. Arnold (arnold@ima.umn.edu)
IMA, University of Minnesota, Minneapolis, Minnesota
Alexandre L. Madureira (alm@lncc.br)
LNCC, DMA, Avenida Getulio Vargas, 333 Quitandinha 25651-070 Petropolis, RJ Brasil
Sheng Zhang (sheng@math.wayne.edu)
Department of Mathematics, Wayne State University, Detroit, Michigan
Abstract. We show that the Reissner­Mindlin plate bending model has a wider range of applicability than
the Kirchhoff­Love model for the approximation of clamped linearly elastic plates. Under the assumption
that the body force density is constant in the transverse direction, the Reissner­Mindlin model solution
converges to the three-dimensional linear elasticity solution in the relative energy norm for the full range of
surface loads. However, for loads with a significant transverse shear effect, the Kirchhoff­Love model fails.
Keywords: plate, Kirchhoff­Love, Reissner­Mindlin
Subj. class.: 73K10, 73C02
1. Introduction
The Kirchhoff­Love and Reissner­Mindlin models are the two most common dimensionally
reduced models of a thin linearly elastic plate. It is often remarked in the engineering
literature, based mostly on computational evidence, that the Reissner­Mindlin model is
more accurate, particularly for moderately thin plates and when transverse shear plays a


Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota


Collections: Mathematics