The floating plate-load system: a new stability problem

The interesting problem of a flat elastic plate and a weight which would sink individually but may float as a system is presented. Using beam and plate theories, the two-dimensional strip and the circular disc are solved exactly for the minimum width for which the system would float. Three types of loading are considered: a centered point load, two symmetric point loads or a ring load, and a continuous uniform load. These problems represent a new class of stability problems which illustrate the interaction of load, elasticity, and hydrostatics.