Accuracy of the Reissner-Mindlin and the (1,1,2) Model for the Clamped-in Plate Problem

Li, L.; Babuška, Ivo

doi:10.21236/ada232755

1990

DOI: 10.21236/ada232755

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Accuracy of the Reissner-Mindlin and the (1,1,2) Model for the Clamped-in Plate Problem

L. Li¹,

Ivo Babuška²

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1994

1995

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“…F49620-92-J0100. series of papers [23], [35]. This hierarchy is based on a spectral discretization of the three-dimensional plate equations in the transverse direction and leads to a singularly perturbed elliptic system in the midsurface of the plate which is then in turn solved approximately by the FEM.…”

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Boundary layers of hierarchical beam and plate models

Schwab

Wright

1995

J Elasticity

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The boundary behavior of a family of hierarchical models of linearly elastic, isotropic plates is studied. The hierarchical models are obtained by spectral semidiscretization of the displacement fields in the transverse direction and strain energy projection. The well known Reissner-Mindlin model is contained in the hierarchy as a special case. A decomposition of the boundary layers of any model in the hierarchy into a bending and a torsion layer, both of which are model dependent, is given. It is shown further that the bending and torsion layers arise as Galerkin approximations of certain (nonlinear) eigenvalue problems in the plate cross section with the subspaces used to derive the hierarchical model. It is shown that the bending layers converge, as the order of the plate model tends to infinity, to the so-called Papkovich functions on an elastic strip.The regularity of the solution on polygonal plates is investigated for the whole hierarchy of plate models and shown to equal the regularity of the plane elasticity problem.The mathematical problem of plate modeling in elasticity has a history of more than 150 years, starting with the derivation of the biharmonic equation by Germain [11] and Kirchhoff [19] to explain plate bending phenomena. For a long time, this remained the most widely used model until Reissner [30] and later Mindlin [26] suggested the more sophisticated model which carries their names. Contrary to the Germain-Kirchhoff model, it consists of a singularly perturbed, coupled system of three second order differential equations. The derivations of these models were based upon intuitive mechanical principles and a mathematical justification of the Germain-Kirchhoff model as zero thickness limit of the three-dimensional elasticity problem was done only much later (see [9] and the references there).With the advent of modern digital computers, the Finite Element Method (FEM) and the need for highly accurate and efficient solutions of finite thickness plate problems, the use of a flexible hierarchy of models of variable order and complexity became feasible and was suggested and analyzed in a

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confidence: 99%

Boundary layers of hierarchical beam and plate models

Schwab

Wright

1995

J Elasticity

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Wilson's element for the Reissner-Mindlin plate

Zhang

1994

Computer Methods in Applied Mechanics and Engineering

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Accuracy of the Reissner-Mindlin and the (1,1,2) Model for the Clamped-in Plate Problem

Cited by 2 publications

References 0 publications

Boundary layers of hierarchical beam and plate models

Boundary layers of hierarchical beam and plate models

Wilson's element for the Reissner-Mindlin plate

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