Form-finding of complex tensegrity structures using constrained optimization method

摘要

This paper presents a versatile form-finding method for tensegrity structures that is based on solving a constrained optimization problem. A general constrained optimization model simulating the forming process of tensegrity structures is established firstly. Then it has been proved that the optimality conditions of this model are equivalent to the self-equilibrium equations of tensegrity structures. The dynamic relaxation technique with kinetic damping is incorporated into a so-called three-term method to solve this optimization problem, guaranteeing a stable and rapid convergent process. Besides the topology of the structure as well as the initial configuration given randomly, the input parameters of this method also include the power exponent of cable lengths-k, the weight coefficients of cables and the target lengths of struts in the objective function. The reasonable value of 'k', to some extent dominating the effectiveness of this algorithm, is investigated qualitatively, combining with a set of illustrative examples of prismatic tensegrity structures. For cable-strut system with external supports, a twofold scheme to consider the corresponding boundary constraints is presented without increasing the number of constraint equations. Numerical examples show that the proposed method has a huge capacity of searching for free-form tensegrity structures with large members and complicated topology.