On the form of the contact reaction in a solid circular plate simply supported along two antipodal edge arcs and deflected by a central transverse concentrated force

A static, purely flexural mechanical analysis is presented for a Kirchhoff solid circular plate, deflected by a transverse central force, and bilaterally supported along two antipodal periphery arcs, the remaining part of the boundary being free. Two kinds of contact reactions are considered, namely the case of distributed reaction force alone, and the situation in which the distributed force is added to a distributed couple of properly selected profile. For both cases this plate problem is formulated in terms of an integral equation of the Prandtl type, coupled with two constraint conditions. The existence of solutions in an appropriate scaled weighted Sobolev space is discussed, and the behaviour of the solution at the endpoints of the support is exhibited.