Bending of Curvilinear and Rectilinear Polygonal Plates Symmetrically Loaded Over a Concentric Circle

Abstract

ABSTRACTComplex variable methods are applied to obtain exact solutions for the complex potentials and deflexions of thin isotropic slabs bounded by regular curvilinear polygonal contours withnsides and subject to symmetrical loading distributed over a concentric circle. The supported boundary is either clamped or has equal boundary cross-couples. The plates taken in thez-plane are conformally mapped on the unit circle in the ζ-plane by the mapping function. Polynomial approximations to the Schwarz—Christoffel transformations are then used to discuss the bending of clamped and simply supported rectilinear plates symmetrically loaded over a concentric circle or acted upon by a central point load.