Optimizing stiffness properties of tensegrity structures

The design of mechanical systems normally exploits numerical analysis and optimization.We make a plea for symbolic computation and give an example where the desired results are symbolic. Geometrical design parameters enter in this computation. The resulting expressions reveal the values which yield desirable properties for, e.g., stiffness or damping. This is applied to repetitive (fractal) mechanical systems, namely tensegrity structures. A set of equations linear in the degrees-of-freedom, but nonlinear in the design parameters, is solved symbolically. 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 like dimensions, but also by selecting the number of stages used to build up the structure (a discrete design parameter)