Mechanical Analysis of a Solid Circular Plate Simply Supported Along Two Antipodal Edge Arcs and Loaded by a Central Force

Abstract

A mechanical analysis is presented for a solid circular plate, deflected by a transverse central force, and simply supported along two antipodal periphery arcs, the remaining part of the boundary being free. By exploiting a Green function expressed in analytical form, the original problem is formulated in terms of a Fredholm integral equation of the first kind, where the kernel is particularly complex. This initial formulation is then simplified, and two descriptions of this problem in terms of integral equations are achieved. In the first description, this plate problem is reformulated as an integral equation encountered in wing theory. Then, the same problem is expressed as a Fredholm integral equation of the second kind. Preliminary approximate analytical results and experimental measurements are also reported.