The multi-layered ring under parabolic distribution of radial stresses combined with uniform internal and external pressure

Abstract

A recently introduced solution for the stress- and displacement-fields, developed in a multi-layered circular ring, composed of a finite number of linearly elastic concentric layers, subjected to a parabolic distribution of ra-dial stresses, is here extended to encompass a more general loading scheme, closer to actual conditions. The loading scheme includes, besides the para¬-bolic radial stresses, a combination of uniform pressures acting along the outer- and inner- most boundaries of the layered ring. The analytic solution of the problem is achieved by adopting Savin’s pioneering approach for an infinite plate with a hole strengthened by rings. Taking advantage of the results provided by the ana¬lytic solution, a numerical model, simulating the configuration of a three-layered ring (quite commonly encountered in practic¬al applications) is validated. The numerical model is then used for a parametric analysis enlightening some crucial aspects of the overall response of the ring.

Keywords

• Multi-layered ring
• Parabolic pressure
• Stress and displacement fields
• Uniform pressure
• Complex potentials