Globally stable tensegrity compressive structures for arbitrary complexity

Prior work has derived minimal mass compressive structures subject to the constraint against local buckling. This paper extends that theory to prevent global buckling as well. We show what range of force and geometry constraints will allow the previous theory to avoid global buckling, and we show new designs that guarantee to prevent buckling. For simple complexity q = 1, 2, 3 we provide analytical solutions, and for more complexity we describe the methodology for computing an answer. In addition, we make a comparison with another tensegrity structure, the D-Bar, which is the dual of the T-Bar in the sense that strings are replaced by bars, and bars are replaced by strings. The D-Bar is a tensegrity structure which is not able to develop global instability, as a consequence it could be more efficient than a T-Bar to bear compressive loads. In the results we show the conditions to understand which one, among T-Bar and D-Bar, gives a lighter structure.