Bending Stress in Symmetrically Loaded Circular Plates

Abstract

As the most fundamental problem in bending of circular plates of variable thickness, here is given a stress analysis of plates, in which thickness is decreased with the increase of distance from the centre, loaded with some hydrostatic pressure. Assuming thin plates and load independent of azimuthal location, the problem is reduced to be one dimentional. Here thickness variation is given in the form of h=h_max(1-ρ^μ)^m/s, which is an equivalent expression to the variation of flexural rigidity D=D_max(1-ρ^μ)^m. General solutions for such cases are shown, and numerical results are given of some examples when plates are clamped at inner radius, free at outer, and bent by hydrostatic pressure. Result for a plate with constant thickness and bent under the corresponding condition is also calculated, and compared with those in case of variable thickness.