The minimal mass tensegrity solutions to compressive and tensile loads

This study explores two fundamental problems in engineering mechanics: compression and tension. We introduce lightweight solutions based on the tensegrity paradigm for these challenges. The analysis focuses on two tensegrity configurations: the D-Bar and its counterpart, the D-Bar dual, which swaps bars with strings and vice versa. We provide analytical formulas for minimizing mass under both loading conditions, taking into account bar failure due to yielding and buckling. The design process follows self-similar principles, examining how structure complexity and variations in geometry and material parameters affect mass and stiffness. The results demonstrate that the D-Bar configuration offers significant mass savings compared to a single bar, while the D-Bar dual achieves considerably enhanced stiffness with only a slight increase in mass relative to a single string. These foundational structural configurations pave the way for designing more complex structures and developing high-performance, lightweight materials in engineering.