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, circu lar plate, deflected by a central transverse concentrated force, and bilate rally supported along two antipodal periphery arcs, the remaining part of t he boundary being free. This problem is modeled in terms of a singular inte gral equation of the Prandtl type, which possesses a unique solution expres sed in terms of a reaction force containing a factor exhibiting square root endpoint singularities. This solution is then shown not to respect the req uested boundary constraints. It is therefore concluded that, within the fra mework of the purely flexural plate theory, the title problem cannot admit the weighted L-2 solution here examined. It, cannot, however, be excluded t hat a solution to the title problem exists, which possesses stronger endpoi nt singularities than those examined in this paper or is of a more general form than the one considered here.