# Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

# 3D Derivations of Static Plate Theories

• A. Lebée
• S. Brisard
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_132-1

## Definitions

• Thin plate model: A model where the only kinematic d.o.f. is the transverse deflection. It neglects the shear energy.

• Thick plate model: A model including also two in-plane rotation d.o.f. and including shear deflection.

## Introduction

Plates are three-dimensional structures with a small dimension compared to the other two dimensions. Numerous approaches were suggested in order to replace the three-dimensional problem by a two-dimensional problem while guaranteeing the accuracy of the reconstructed three-dimensional fields. Turning the 3D problem into a 2D plate model is known as dimensional reduction.

The approaches for deriving a plate model from 3D elasticity may be separated in two main categories: axiomatic and asymptotic approaches. Axiomatic approaches start with ad hoc assumptions on the 3D field representation of the...

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