Prestress Design of Tensegrity Structures Using Semidefinite Programming

Abstract

Finding appropriate prestresses which can stabilize the system is a key step in the design of tensegrity structures. A semidefinite programming- (SDP-) based approach is developed in this paper to determine appropriate prestresses for tensegrity structures. Three different stability criteria of tensegrity structures are considered in the proposed approach. Besides, the unilateral property of members and the evenness of internal forces are taken into account. The stiffness of the whole system can also be optimized by maximizing the minimum eigenvalue of the tangent stiffness matrix. Deterministic algorithms are used to solve the semidefinite programming problem in polynomial time. The applicability of the proposed approach is verified by three typical examples. Compared to previous stochastic-based approaches, the global optimality of the solution of the proposed approach is theoretically guaranteed and the solution is exactly reproducible.