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In this paper, foldable structures with scissor-like elements are investigated and then based on constraints geometric design of these structures is formulated for any curved shape. Method of geometric design of foldable structures with any curvature is investigated. Using given connections to these systems in this paper, two models with fixed geometry and variable geometry is designed and constructed on real scale, based on this formulation. Correct behavior of these models is a sample to proof the applicability of formulation and connections. To find the optimal geometry of barrel vaults that structure has minimum displacement, based on formulation, some Macro files are programmed to model barrels with any curvature with ANSYS. Many of barrels are analyzed as linear and geometrically nonlinear, and graph of displacements are illustrated. The results display that there is a special height for any span with two characteristics; the displacement of structure is minimum and the difference of linear and geometrically nonlinear analysis is minimum.