Interaction of an axisymmetrically loaded plate with the elastic space

Abstract The problem to be examined is that of a circular disk or plate attached to the wall of a cylindrical hole in an infinite solid. The interface boundary stress distribution will be compatible with simple plate theory and the slope and displacements are matched to the wall where the midplane of the plate intersects the solid. The problem is solved for any axisymmetric loading of a plate of uniform thickness and material parameters. This method can be easily extended to any axisymmetric plate solution without midplane forces. The material parameters in the plate and the supporting solid can be specified independently. In the specific examples included, plate deflections for a rigid wall assumption as opposed to a wall and plate of the same material never differ by less than 200%. There is little reason to believe that the trends indicated by the examples would change significantly for other usual loadings and geometries within the scope of the problem.