Buckling of circular, annular plates of non-uniform thickness

This paper deals with the solution of the title problem in the case where the outer boundary is subjected to uniform, hydrostatic pressure while the inner edge of the plate is free. It is assumed that the plate thickness varies (a) in a discontinuous fashion and (b) linearly.An approximate approach is proposed using polynomial coordinate functions which identically satisfy the boundary conditions at the outer edge, only. The eigenvalues are determined using the optimized Rayleigh-Ritz method and good engineering agreement is shown to exist with buckling parameters obtained by means of a finite element code.