Form-finding : Force Density

Force density form-finding is a method of form-finding cable networks which originated over 20 years ago in Germany. The tension in each link of the network is made proportional to its length. The resulting stiffness matrix is valid for any displacements and so the method enables linear structural analysis programmes to form-find. The form that is found is that giving the minimum strain energy i.e. the form which minimises the sum of the squares of the lengths of the links multiplied by the stiffnesses of the links.

1D elements – the force density form finding properties set the value of force/length for succeeding bars.

2D elements – force density form finding properties can be used to set the values of (force per width)/area for triangles or for the triangles into which succeeding quads are split. This allows fabric surfaces with different warp and weft tensions to be form-found but the shapes of the elements are generally very irregular.