Edge layers in thin elastic plates Original Research Article

This paper deals with the asymptotics of the displacement of a thin elastic 3D plate when it is submitted to various boundary conditions on its lateral face: namely, hard and soft clamped conditions, and hard support. Of particular interest is the influence of the edges of the plate where boundary conditions of different types meet. Relying on general results of [M. Dauge and I. Gruais, Asymptotics of arbitrary order for a thin elastic clamped plate. I: Optimal error estimates. Asymptotic Anal. 13 (1996) 167–197] and [M. Dauge and I. Gruais, Asymptotics of arbitrary order for a thin elastic clamped plate. II: Analysis of the boundary layer terms, Asymptotic Anal. (1996) to appear] for the hard clamped case, we see that the clamped plate (hard and soft) admit strong boundary layers, in which are concentrated the edge layers, while the hard supported plate has no edge layer and even no boundary layer at all in certain situations. We conclude with hints about corner layers, in the case when the mean surface of the plate itself is polygonal.