Topology-Finding of Tensegrity Structures Considering Global Stability Condition

Abstract

This study proposes a general framework for topology-finding or topology optimization of tensegrity structures. The existing topology-finding formulation of tensegrity structures based on mixed-integer linear programming (MILP) was improved and transformed into a formulation based on mixed-integer semidefinite programming (MISDP) which considers the global stability condition of tensegrity. We illustrated and analyzed two undesirable phenomena, loss of prestress stability and loss of integrity, caused by the missing global stability condition in previous MILP-based approaches. A branch-and-bound algorithm combined with a primal-dual interior-point algorithm is employed to solve the proposed MISDP model. Some numerical examples illustrated the improvements and effectiveness of the proposed approach. The proposed approach successfully can avoid the two undesirable phenomena and ensure the global stability of the found tensegrity structures. By using different stability conditions in the topology-finding process, the proposed approach can find general stable tensegrity structures and superstable tensegrity structures.