An extended force density method for form finding of constrained cable nets

The force density method (FDM) is a classical method used in linear and nonlinear form. The linear approach presents a quick tool for finding cable net new shapes by solving a set of linear equilibrium equations for certain topology, boundary conditions and assumed cables force density. The nonlinear approach was introduced to solve cable nets under constraints (assigned certain distance between nodes, limit force or unstressed length in some elements). Any type of constraint introduces nonlinearity.

This paper studied the prestressed cable nets and the loaded cable nets. For prestressed cable nets, coordinate constraints to all nodes of the cable net are introduced to modify the shape after graphically examining the preliminary shape. This preliminary shape resulted from linear analysis of assumed distribution of cable force densities. For analyzing cable nets under different load cases, the first load case is analyzed to achieve the coordinate constraints assigned to nodes. Analysis results are node coordinates, cable forces and lengths. Young’s modulus and areas of cables are used to calculate the unstressed length of all cables using materialization equations, those lengths are used as constraint in the analysis of other load cases. Forces in all cables under different load cases/combinations are calculated. By using this approach, design of cable net under static load is simplified.