On consistent plate theories

Abstract

Applying the uniform-approximation technique, consistent plate theories of different orders are derived from the basic equations of the three-dimensional linear theory of elasticity. The zeroth-order approximation allows only for rigid-body motions of the plate. The first-order approximation is identical to the classical Poisson-Kirchhoff plate theory, whereas the second-order approximation leads to a Reissner-type theory. The proposed analysis does not require any a priori assumptions regarding the distribution of either displacements or stresses in thickness direction.