Stiffness of Planar Tensegrity Beam Topologies

摘要

This paper demonstrates a symbolic procedure to compute the stiffness of structures. 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. The resulting expressions reveal the values of these parameters which yield desirable properties for the stiffness or stiffness-to-mass ratio. By enumerating a set of topologies, stiffness properties are optimized over this set of topologies. This procedure is applied to a planar tensegrity beam. The results make it possible to optimize the structure with respect to stiffness properties, not only by appropriately selecting (continuous) design parameters like dimensions, but also by selecting an appropriate topology for the structure (a discrete design decision).