A Novel Two-Step Tensegrity Topology-Finding Method Based on Mixed Integer Programming and Nonlinear Programming

A two-step topology-finding method based on mixed integer programming and nonlinear programming is proposed for tensegrity structures. In the first step, feasible and symmetric strut connectivities are obtained through a ground structure method combined with mixed integer programming; in the second step, the cable connectivities are optimized through nonlinear programming to obtain a feasible tensegrity structure. The same ground structure used in the first step is adopted in the second step, which is beneficial to find a more symmetric cable layout. The independent continuous mapping method is used in the second step to convert the 0–1 binary variables of cable connectivities to continuous variables to transform the combinatorial optimization problem into a nonlinear programming problem. The number of strut lengths is adopted as a control parameter and a symmetry objective function is proposed to generate a variety of regular and symmetric tensegrity structures. A multi-stage computation scheme is proposed to improve the computational efficiency. Typical examples are carried out to validate the proposed method. The computational efficiency of the method is benchmarked with existing methods fully based on mixed integer programming. Results demonstrate that the computational efficiency of the proposed method is significantly improved compared to the existing methods.