Singularities in bending behavior of plates with free corner supports

The objective of this paper is to examine the order of singularity at the points ofdiscontinuity between simple support and free edge for a square plate case. The plate,without anchoring the corners, is partially simply supported along the central portion onfour edges and subjected to a uniformly distributed load. It is well known that when auniform load is applied to a square plate resting on the unilateral supports, parts of theplate in the vicinity of the corners will separate from the supports and the length of thesupports becomes unspecified. At the points of transition from the unilateral support tofree edge, the shear singularity is of the inverse-square-root type. In the case of a squareplate supported by the simple supports with specified lengths, it is expected that theproper singularity should be in the order of an inverse square root in the moments atthe points of transition from a simple support to a free edge. However, the results showthat the singularity in the moments cannot be allowed, while the singularity in the shearsis proper and still found to be the same order similar to that of the plate resting on theunilateral supports. In addition, there are nonzero corner forces applied at the cornersof partially simply supported plate, while the corner forces vanish for the case of aplate unilaterally supported.