Bending behaviors of simply supported rectangular plates with an internal line sagged and unsagged supports

Abstract

This research work deals with the application of dual series equations to the problems of simply supported rectangular plate with an internal line support under uniformly distributed load. Two different types of problem are considered depending on the nature of singularities that allowed in the fields, The first is the plate having an internal line unsagged support that the moment singularity is assumed at the tip of internal line support. The second involves the advancing contact problem between the plate and the internal line sagged support in which the shear singularity exhibits at the tip of contact. However, both types of singularity are in the order of an inverse square root. By choosing the proper finite Hankel transform, the dual series can be converted to the inhomogeneous Fredholm integral equation. This equation, with a numerical technique, is then reduced to a set of simultaneous equations suitable for numerical solution. The physical quan-tities of the plates and the extent of contact related to the level of loading in the case of free contact are provided in the present work.

Keywords

• plate bending
• advancing contact
• singularity
• dual series equations
• Fredholm integral equation