Solid Circular Plate Clamped along Two Antipodal Edge Arcs and Deflected by a Central Transverse Concentrated Force

A static, purely flexural mechanical analysis is presented for a Kirchhoff solidcircular plate, deflected by a transverse central force, and clamped along two antipodal arcs,the remaining part of the boundary being free. By adopting an integral formulation, the contactreaction is assumed to be formed by four equal concentrated forces acting at the supportextremities, accompanied by two distributed moments with radial and circumferential axis,respectively. This plate problem is rephrased in terms of a complex-valued Hilbert singularintegral equation of the second kind, whose solution is obtained in analytical, integralform. A design chart is presented that reports the plate central deflection as a function of theangular width of the plate supports.