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On annular disks of variable thickness subjected to external pressure

Exact solutions are obtained for the elastic stress distribution in variable thickness annular disks under external pressure. Two different thickness functions both in parabolic form are considered. It is shown that, depending on the geometric parameters describing the shape of the disk profile, the plastic deformation in the variable thickness annular disk commences at the inner or at the outer or simultaneously at both surfaces. The critical values of the geometric parameters which cause the plastic deformation to begin simultaneously at both surfaces are obtained for both of the disk profiles.