Justification of the Kirchhoff hypotheses and error estimation for two-dimensional models of anisotropic and inhomogeneous plates, including laminated plates

Asymptotic analysis of the problem describing deformation of a thin cylindr ical plate with clamped lateral side is performed. The problem is considere d under the most general statement with the plate being laminated and consi sting of an arbitrary number of nonhomogeneous and anisotropic (21 elastic moduli) layers. Explicit integral representations of the differential opera tors which form the two-dimensional model of the plate are derived. In the case when the elastic moduli of each of the layers are constant, these inte gral representations turn into algebraic ones. The asymptotic procedure is justified with the help of a weighted inequality of Kern's type. The error estimates obtained give a rigorous mathematical proof of both of Kirchhoff' s hypotheses (kinematic and static) and shed light on the well-known intrin sic inconsistency of two of the hypotheses.