Buckling of polar and rectilinearly orthotropic annuli under uniform internal or external pressure loading

The problem of the out of plane buckling of polar orthotropic annuli under uniform internal or external pressure loading has been investigated with the assumption of axisymmetry by numerous researchers. In this paper, the buckling of polar and rectilinearly orthotropic annuli subjected to internal or external pressure loading is examined without restriction to axisymmetric buckling modes. The buckling analyses are performed in both the polar orthotropic and rectilinearly orthotropic cases by the Rayleigh-Ritz method. In the rectilinearly orthotropic cases, the pre-buckling solution is obtained via Galerkin's method as no known exact solution exists, while in the polar orthotropic case the pre-buckling stress distributions used are exact. It is found in both the polar orthotropic and the rectilinearly orthotropic annuli that restriction to axisymmetric buckling modes in the externally pressurized case does not produce the lowest buckling load over a significant range of annuli aspect rations. Example results for commercially used fiber/matrix systems are presented and discussed, and it is concluded that the unwarranted assumption of axisymmetry actually produces nonminimum buckling loads.