Rotational Representation of a Plate Made of Grioli-Toupin Material

Abstract

A solenoidal part of displacement field appearing in a plate made of material with constraints has been determined. The semi-inverse method has been applied to description. The results being obtained together with the already known biharmonic representation (Jemielita, 1992) might be useful in a new micropolar plate theory formulation.

On generalized Cosserat-type theories of plates and shells: a short review and bibliography

“…In [16,17,118,151,259,263] various averaging procedures in the thickness direction together with the approximation of the displacements and rotations or the force and moment stresses in the thickness direction are applied. As a result, one gets different numbers of unknowns and the number of two-dimensional equilibrium equations differs.…”