Title:         Derivation and justification of plate models by
variational methods

Authors:       Stephen M. Alessandrini, Douglas N. Arnold, Richard S. Falk, and
Alexandre L. Madureira

Source:        in: "Plates and Shells (Quebec 1996)", M. Fortin, editor, CRM Proceeding
and Lecture Notes, vol. 21, American Mathematical Society, Providence, RI, 1999,
pp. 1-20

Status:        Published

Abstract:  We consider the derivation of two-dimensional models for the
bending and stretching of a thin three-dimensional linearly elastic
plate using 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 transverse 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.

Keywords:      plate, dimensional reduction, Reissner-Mindlin

Subj. class.:  73K10, 73C02

URL:           http://ima.umn.edu/~arnold/papers/platederiv.pdf