On the justification of plate theories in linear elasticity theory using exponential decay estimates (Q1898363)

This investigation is based on an (not necessarily homogeneous) infinite isotropic elastic layer. Its aim is the deduction and mathematical justification of two-dimensional plate theories. For the corresponding reduction process, the Fourier transform method in connection with the asymptotic expansion approach is used, the lateral boundaries being pushed away via a rescaling of the length. The solution of the \(F\)- transformed Navier's equations for an infinite, surface- and volume loaded layer is shown to consist of a singular and a holomorphic part, the latter one giving rise to an exponentially decay (boundary layer effect). The relations to laterally bounded domains and to St.-Venant's principle are worked out, and existence and convergence results as well as decay estimates are established. In the limit as the thickness tends to zero, the Kirchhoff's plate equation arises.