Step-by-step unbalanced force iteration method for cable-strut structure with irregular shape

In the design process of a cable-strut structure, the desired shape is first defined and the prestress can be obtained if the geometry is feasible; otherwise, the geometry must be modified. Thus, the initial step for prestress calculation is to estimate the feasibility of the geometry. In this paper, a method called Unbalanced Force Iteration (UFI) is proposed to remove the unbalanced forces using the equilibrium and stiffness equations. Feasibility of the geometry can be judged by the convergence property of UFI. Self-stress modes can be directly obtained easily through UFI method, if initial geometry is feasible. For structures with infeasible initial geometry, the Step-by-Step UFI, which combines finite element analysis and UFI, is proposed to gradually move the nodes to feasible locations. Three examples of cable domes with feasible geometry and three examples of cable domes with irregular and infeasible initial geometry are presented to verify the ability of UFI and Step-by-Step UFI for designing new irregular and asymmetric cable-strut structures.