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The stiffness of prestressed cable structure is provided by self-stress, and the self-stress of the structure is sensitive to external errors due to their high flexibility. Based on the basic theory of the force method (FM) and stochastic search technique, the linear displacement control problem was converted to an optimization question. Genetic algorithm (GA) is used to solve this optimization problem for prestressed structures of linear behavior. And then the dynamic relaxation method (DRM) is introduced to the linear displacement control method to achieve the non-linear displacement control for prestressed structures of non-linear behavior. The non-linear displacement control consists of two phases: (1) use the linear displacement control method as the controller step to determine the selection of actuation members and the variation of these selected members, and (2) use the DRM as the corrector step to calculate the equilibrium state of structures after linear controller deformation. A numerical example is conducted which shows that the non-linear control and the linear control both are in well agreement with the target values in the case of small displacement adjustment, while in the case of large displacement adjustment, the former is superior to the latter.

Force Method for Displacement Adjustment of Prestressed Cable Structures with Dynamic Relaxation Method