An Extended Force Density Method for the form finding of cable systems with new forms

The Force Density Method (FDM) is an extremely versatile tool in form finding problems concerning nets of cables. In this paper an Extended Force Density Method (EFDM), suitable to deal both with nets of cables only and with cable-strut assemblies, is presented. A usual tool to study these type of cable structures as well as to find the form of tensegrity structures, is the Singular Value Decomposition (SVD) of the equilibrium matrix. This technique, however, has some limitations. First of all, the searching for the eigenvalues, in some cases, must be forced, setting to zero the lower ones, secondly, the SVD may lead to sets of eigenvectors, not physically consistent with the mechanic of the mixed structures, having tensioned cables and compressed struts. Moreover, the geometry of the structure must be given a priori. The EFDM is proposed here as an alternative approach to the SVD. The efficiency and the robustness of method is assessed through comparisons with other form finding techniques in dealing with characteristic applications to the prestress design of cable systems. As a further extension, the EFDM is applied to structures having some parts not yet geometrically defined, as can happen in designing new creative forms.