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The objective of this paper is to examine the order of singularity at the points of discontinuity 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 on four edges and subjected to a uniformly distributed load. It is well known that when a uniform load is applied to a square plate resting on the unilateral supports, parts of the plate in the vicinity of the corners will separate from the supports and the length of the supports becomes unspecified. At the points of transition from the unilateral support to free edge, the shear singularity is of the inverse-square-root type. In the case of a square plate supported by the simple supports with specified lengths, it is expected that the proper singularity should be in the order of an inverse square root in the moments at the points of transition from a simple support to a free edge. However, the results show that the singularity in the moments cannot be allowed, while the singularity in the shears is proper and still found to be the same order similar to that of the plate resting on the unilateral supports. In addition, there are nonzero corner forces applied at the corners of partially simply supported plate, while the corner forces vanish for the case of a plate unilaterally supported. |
