A feasible symmetric state of initial force design for cable-strut structures

For a structure with given shape, to acquire feasible pre-stress states without changing its predefined shape is the main purpose of force finding as a crucial step in structural designs, since mechanical behaviors of cable-strut structures are highly sensitive to their pre-tensioning levels. One of practical ways to initial force designs is double singular value decomposition (DSVD), the essence of which is visual inspections of symmetry properties that could be arbitrary and time consuming due to its manual grouping. To reduce the iteration times of finding a proper group division, a grouping scheme was developed by utilizing the distributed static indeterminacy as a symmetry indicator that represents both geometric and stiffness symmetry. The existing DSVD method was subsequently modified using the proposed scheme that could provide an initial group classification being helpful to decrease the undesirable numbers of pre-stress states. Finally, two examples were investigated to verify the validity and accuracy of the modified method, and then it was applied in an enormous stadium with saddle-shaped roof structure showing good agreement with results obtained by a conventional approach.