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3D Derivations of Static Plate Theories

Encyclopedia of Continuum Mechanics
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Dimensional reduction; First-order shear deformation theory; Plate model or theory; Reissner or Hencky or Reissner-Mindlin thick plate theory


  • 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.


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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Lebée, A., Brisard, S. (2018). 3D Derivations of Static Plate Theories. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg.

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  • Print ISBN: 978-3-662-53605-6

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Chapter history

  1. Latest

    Three Dimentional Derivations of Static Plate Theories
    11 October 2019


  2. Original

    3D Derivations of Static Plate Theories
    28 December 2017