Justification of the Kirchhoff hypotheses and error estimation for two-dimensional models of anisotropic and inhomogeneous plates, including laminated plates
Oleg V. Motygin · IMA Journal of Applied Mathematics · 2000
Asymptotic analysis of the problem describing deformation of a thin cylindrical plate with clamped lateral side is performed. The problem is considered under the most general statement with the plate being laminated and consisting of an arbitrary number of nonhomogeneous and anisotropic (21 elastic moduli) layers. Explicit integral representations of the differential operators 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 integral representations turn into algebraic ones. The asymptotic procedure is justified with the help of a weighted inequality of Korn'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 intrinsic inconsistency of two of the hypotheses.