Mechanical Analysis of a Thin Solid Circular Plate Deflected by Transverse Periphery Forces and by a Central Load

Abstract

A thin, solid, circular plate deflected by a number of transverse, concentrated, periphery forces, not necessarily angularly equispaced or equally oriented, and sustaining a central, transverse, equilibrating load, is mechanically analysed via a purely flexural model. This problem is interpreted as a angularly dephased combination of a relatively simple model. This fundamental scheme consists of a plate loaded by a single periphery force, by a central load of equal intensity and opposite direction, and by a sinusoidal periphery line loading whose wavelength equals the plate border and whose intensity renders the plate loading self-equilibrated. When a sequence of basic schemes, possibly referring to loads of different intensity, is combined, respecting the condition that the resultant of the periphery loads is equilibrated by a central force alone, the sinusoidal load effects vanish and the title problem is recovered. A series solution in terms of plate deflections is obtained for the basic model, whose coefficients are analytically evaluated via a computer algebra package. The series sum is expressed in finite terms involving the dilogarithmic function, valid over the whole plate region. In particular, the series is summed in analytical form for the whole plate periphery, along which the boundary deflections are expressed in closed form.