Title: Derivation and justification of plate models by variational methods

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

Source:  In M. Fortin, editor, Plates and shells (Quebec, QC, 1996), 
         volume 21 of CRM Proc. Lecture Notes, pages 1--20. Amer. Math. Soc., 
         Providence, RI, 1999. 

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 

URL: http://www.math.rutgers.edu/~falk/papers/platederiv.pdf