EDGE LAYERS IN THIN ELASTIC PLATES

This paper deals with the asymptotics of the displacement of a thin el astic 3D plate when it is submitted to various boundary conditions on its lateral face: namely, hard and soft clamped conditions, and hard s upport. Of particular interest is the influence of the edges of the pl ate where boundary conditions of different types meet. Relying on gene ral results of [M. Dauge and I. Gruais, Asymptotics of arbitrary order for a thin elastic clamped plate. I: Optimal error estimates. Asympto tic Anal. 13 (1996) 167-197] and [M. Dauge and I. Gruais, Asymptotics of arbitrary order for a thin elastic clamped plate. II: Analysis of t he boundary layer terms, Asymptotic Anal. (1996) to appear] for the ha rd clamped case, we see that the clamped plate (hard and soft) admit s trong boundary layers, in which are concentrated the edge layers, whil e the hard supported plate has no edge layer and even no boundary laye r at all in certain situations. We conclude with hints about corner la yers, in the case when the mean surface of the plate itself is polygon al. (C) 1998 Elsevier Science S.A.