Flexural problems of circular ring plates and sectorial plates. II

Abstract

ABSTRACTIn a previous paper solutions have been derived for the deflexion of a circular annular plate under various combinations of boundary conditions and subject to certain line loadings spread along the circumference of a concentric circle. These solutions, which were used in the analysis of circular ring plates and sectorial plates acted upon by a concentrated load or a concentrated couple at any point, are utilized in this paper to obtain solutions appropriate to lateral loadings of the typedistributed over the entire circular ring plate. Solutions corresponding to the case φ(r) =rmare then explicitly found, and the principle of superposition can be applied to get the solution when the load on the annulus can be expanded into a Laurent-Fourierseries in the polar coordinatesr, θ. The method of images is used to deduce solutions for an isotropic plate bounded by two arcs of concentric circles and two radii, and loaded by the normal pressurep=p0rmwhen the plate is simply supported along the straight edges and is subject to various conditions along the circular edges.