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Derivation and Justification of Plate Models by Variational Methods

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.