The Plate Paradox for Hard and Soft Simple Support

Abstract

This paper studies the plate-bending problem with hard and soft simple support. It shows that in the case of hard support, the plate paradox, which is known to occur in the Kirchhoff model, is also present in the three-dimensional model and the Reissner–Mindlin model. The paradox consists of the fact that, on a sequence of convex polygonal domains converging to a circle, the solutions of the corresponding plate-bending problems with a fixed uniform load do not converge to the solution of the limit problem. The paper also shows that the paradox is not present when soft simple support is assumed. Some practical aspects are briefly discussed.