Buckling of tapered circular plates: Allowances for effects of shear and radial deformation

Elastic axisymmetric buckling of tapered circular plates under a compressive radial load is analyzed. The effects of shear and prebuckling radial deformation are considered in the analysis because they are important when plates are thick. No previous buckling data are known to exist for tapered circular plates with allowance for both of these effects. The buckling analysis is performed using the Rayleigh-Ritz method. The shooting method is used in the computation of the varying stress function along the plate radius. Comprehensive generic buckling results for circular plates with linearly or parabolically varying thickness are presented. It is noted that shear deformation tends to reduce the buckling load. However, this reduction in buckling load is somewhat offset by the strength-enhancing effect of prebuckling radial deformation that is smaller but of the same order of magnitude. Optimal taper parameter values for such tapered plates are obtained. It is found that the optimal taper is insensitive to the effects of shear and prebuckling radial deformation. In general, these effects on the buckling load are more significant for plates with optimal tapers.