Large Deformations of Circular Rings Under Nonuniform Normal Pressure

The deformations and static stability of thin elastic circular rings under nonuniform pressures are studied. The investigation takes into account large bending deformations of the ring which is treated as an elastica. The loads considered remain normal to the center line during deformations. Numerical methods are used to solve the ordinary differential equations of equilibrium and of perturbed equilibrium for a particular case of loads which vary as p = p₀(1 + q cos 2θ). The ring is found to deform only in a doubly symmetric fashion. Static buckling into an asymmetric deformation pattern does not occur.