Bending of Sectorial Plates with Clamped Edges

A solution for the deflection of a uniformly loaded sectorial plate with all edges clamped is presented. Numerical results for both 60 and 90° sectors are given, but the method of solution applies to plates of other sectorial angles. The governing equation for the small deflection theory of thin plates is satisfied. The boundary conditions on the radial edges of the plate are satisfied exactly, while those on the circumferential edge are satisfied to vanishingly small residues. A homogeneous solution is derived to satisfy the boundary conditions along the radial boundaries and then superposed on the known solution for a clamped, uniformly loaded semi-infinite plate to correct for the slope and deflection along the circumferential edge. Carrier and Shaw presented a solution for the 60° sectorial plate using an infinite series of eigenfunctions and an averaging technique on the circumferential edge. This study employs the method of collocations on the same boundary. Carrier and Shaw outlined a solution but presented no numerical results. Numerical results which can be compared with those of this study were generated by Conway and Huang, who used the method of superposition in conjunction with a series of line loads along the radii of the plate defining a particular sector angle. The line loads were adjusted to correct for the boundary conditions along the radial edges. Their results, which do not include results for the 60° sector, compare very closely to the results of this investigation for both the magnitude and location of the maximum deflection for the 90° plate.