A form-finding method based on the geometrically exact rod model for bending-active structures

In the field of bending-active structures, the complexity of finding beforehand the equilibrium configuration and the non-linearity of the structural response are main issues during the conceptual phase. The use of tools based on classical form-finding procedures as dynamic relaxation is the main trend today; different mechanical models with 3, 4 or 6 degrees of freedom have been implemented for modelling the bending effect. However, there is a well-established class of mechanical models which has been specifically designed to reproduce the behaviour of very flexible structures and has not been used so far in form-finding of bending-active structures. These are derived from the so-called geometrically exact (or Reissner-Simo) beam theory, and they are able to treat arbitrarily large rotations and displacements. In this paper, we present the development of a form-finding tool based on Reissner-Simo's theory and the dynamic relaxation method, in order to find the static equilibrium of the system. The choice of form-finding parameters as the target curve length and the kinematic constraints at beam ends will determine the shape of the final structure in the 'design-oriented' process. Several numerical examples on a range of structures are tested to validate the formulation.