On the Existence of a Solution for a Solid Circular Plate Bilaterally Supported Along Two Antipodal Boundary Arcs and Loaded by a Central Transverse Concentrated Force

A purely flexural mechanical analysis is presented for a thin, solid, circular plate, deflected by a central transverse concentrated force, and bilaterally supported along two antipodal periphery arcs, the remaining part of the boundary being free. This problem is modeled in terms of a singular integral equation of the Prandtl type, which possesses a unique solution expressed in terms of a reaction force containing a factor exhibiting square root endpoint singularities. This solution is then shown not to respect the requested boundary constraints. It is therefore concluded that, within the framework of the purely flexural plate theory, the title problem cannot admit the weighted $L2$ solution here examined. It cannot, however, be excluded that a solution to the title problem exists, which possesses stronger endpoint singularities than those examined in this paper, or is of a more general form than the one considered here.