Symbolic Stiffness Optimization of Planar Tensegrity Structures

During the design of mechanical systems one normally exploits numerical analysis and optimization tools. We make a plea for symbolic computation and give an example where structural displacements under load are computed symbolically. Geometrical design parameters enter in this computation. The set of equilibrium conditions, linear in the displacements, but nonlinear in the design parameters, is solved symbolically. The resulting expressions reveal the geometry which yield optimal properties for stiffness or stiffnessto-mass. This technique is applied to a class of repetitive mechanical systems, namely tensegrity structures. A large scale example with 1533 degrees-of-freedom is computed successfully. The results make it possible to optimize the structure with respect to stiffness properties, not only by appropriately selecting (continuous) design parameters, influencing geometry, but also by selecting the number of stages used to build up the structure (a discrete design parameter), influencing topology.