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Centre de Recherches Mathematiques CRM Proceedings and Lecture Notes
 

Summary: Centre de Recherches Math´ematiques
CRM Proceedings and Lecture Notes
Volume 00, 0000
Derivation and Justification of Plate
Models by Variational Methods
Stephen M. Alessandrini, Douglas N. Arnold,
Richard S. Falk, and Alexandre L. Madureira
Abstract. We consider the derivation of two-dimensional models for the
bending and stretching of a thin three-dimensional linearly elastic plate us-
ing variational methods. Specifically we consider restriction of the trial space
in two different forms of the Hellinger-Reissner variational principle for 3-D
elasticity to functions with a specified polynomial dependence in the trans-
verse direction. Using this approach many different plate models are possible
and we classify and investigate the most important. We study in detail a
method which leads naturally not only to familiar plate models, but also to
error bounds between the plate solution and the full 3-D solution.
1. Introduction
Let be a smoothly bounded domain in R2
and t (0, 1]. We consider
an isotropic, homogeneous, linearly elastic plate occupying the region Pt = ×

  

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

 

Collections: Mathematics