Buckling of square and hexagonal semi-rigid rings by concentrated loads

This paper studies rings with rigid segments and rotationally flexible joints under compressive forces. Using geometry and symmetry, exact closed-form expressions for the buckling forces are found. Depending on how the forces are applied, the ring may not buckle at all, or may buckle with a regular pitchfork bifurcation, or may have nonlinear snap-through and hysteresis characteristics. The latter defines a global buckling load below which the ring is stable under any finite disturbances. The buckling properties of the square and hexagonal rings are important since they serve as unit cells for larger structures such as honeycomb, graphene and tensegrity structures.

Automated summary

This paper explores rings with rigid segments and rotationally flexible joints under compressive forces, finding exact closed-form expressions for the buckling forces through geometry and symmetry. Depending on the force application, the ring may exhibit different buckling behaviors, including regular pitchfork bifurcation, nonlinear snap-through, and hysteresis. The buckling properties of square and hexagonal rings are significant as they serve as unit cells for larger structures like honeycomb, graphene, and tensegrity structures.