Post-buckling of a non-uniform ring subjected to uniform external pressure

Rigid plastic analysis is used to find the post-buckling response of a non-uniform circular ring subjected to uniform external pressure. The non-uniform ring has a section of reduced thickness over part of its circumference. A five plastic hinge model is used to describe the non-axisymmetric post-buckling collapse. The principle of virtual work and upper bound theorem are applied to find the collapse pressure and mode of collapse. Depending on the non-uniformity, two modes of collapse can occur: global and snap-through buckling. Global buckling occurs when the angular extent is greater than 90 degrees. When the angular extent is less than 90 degrees and the thickness reduction is large, snap-through buckling takes place. Closed-form expressions for the variation of the collapse load with respect to non-uniformity of the ring are derived.