Solid circular plate unilaterally supported along two antipodal edge arcs and deflected by a central transverse concentrated force

Abstract

A solid circular plate unilaterally supported along two antipodal edge arcs and deflected by a static central transverse concentrated force is considered. It is clarified that two distinct mechanical responses are possible, depending on the angular extent of the supports; in the first kind of response, valid for small support angular widths, the plate rotates about the support lateral sides, lifting from the supports along their central zone. The second response is valid for high support angular extents, and according to this response the plate additionally beds over the central portion of the support upper faces. Only the first kind of response is examined in this paper. This plate contact problem is classifiable as receding, and the plate deflection is described in terms of a plate Kirchhoff model. The plate deflection is analytically expressed together with the transitional value of the support angular width that describes the passage from the first to the second mechanical response.