Stiffness of planar tensegrity truss topologies

This paper proposes and demonstrates a symbolic procedure to compute the stiffness of truss structures built up from simple basic units. Geometrical design parameters enter in this computation. A set of equations linear in the degrees-of-freedom, but nonlinear in the design parameters, is solved symbolically in its entirety. The resulting expressions reveal the values of the design parameters which yield desirable properties for the stiffness or stiffness-to-mass ratio. By enumerating a set of topologies, including the number of basic units, and a set of material distribution models, stiffness properties are optimized over these sets. This procedure is applied to a planar tensegrity truss. The results make it possible to optimize the structure with respect to stiffness properties, not only by appropriately selecting (continuous) design parameters like geometric dimensions, but also by selecting an appropriate topology for the structure, e.g., the number of basic units, and a material distribution model, all of which are discrete design decisions.