On the mathematical foundation of the (1,1,2)-platemode

The plate problem of three!dimensional "2!D#\ linearized elastostatics is considered in the framework of the hierarchical modelling with the help of the energy projection method[ It is shown that the "0\0\1#!bending model is the {simplest| asymptotically correct model in the hierarchical family\ i[e[ the distance between the solution of the 2!D problem and the model!solution in the energy norm tends to zero for vanishing plate thickness h while using unmodi_ed\ 2!D material laws[ The formulation of the "0\0\1#!bending model and the mechanical signi_cance of its ingredients are discussed[ We present error estimates for the deviation of the "0\0\1#!solution from the Kirchho} solution as well as from the 2!D!solution\ by using the "0\0\1#!energy norm and the 2!D!energy norm\ respectively[ The analysis leads to zh as order of convergence[ The results are illustrated by a numerical example