Plate Theory as an Exact Consequence of Three-Dimensional Linear Elasticity

Standard presentations of plate theory are generally inconsistent with three-dimensional elasticity: in fact, if one insists on both Kirchhoff's displacements and Lamé's elasticity tensor, consistency is impossible. It is shown here how to resolve the issue of consistency. Plate theory is obtained by thickness integration of the equations for a three-dimensional body occupying a plate-like region, made of a suitably constrained, monoclinic material and subject to general loads. Both single and multilayered plates are considered, the relevant field and boundary operators being derived in terms of both stress resultants and displacements. The special cases of single layered orthotropic plate and mid plane symmetric laminated plate made of orthotropic layers are also discussed.