Edge layers in thin elastic plates

Monique DAUGE and Isabelle GRUAIS Abstract. This paper deals with the asymptotics of the displacement of a thin elastic 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 in uence of the edges of the plate where boundary conditions of di erent types meet. The singular perturbation analysis uses the thickness | denoted by " | as small parameter tending to zero. Relying on general results of [11, 12] 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. This is unlike the hard supported plate which has weaker boundary and edge layers and even no 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.