A generalized formulation for contact between beams

The currently available formulations for contact between beams are based on the identification of the minimal distance points along the beam axes, followed by some tuning in case of non-circular beam cross-sections. Up to now a suitable implementation within the framework of the Finite Element Method is available both for the frictionless and for the frictional case. The procedure requires the explicit computation of the virtual work contribution due to the contacts. In such a context for solving the problem with implicit schemes, the formulation has also to be consistently linearized. With this respect both the frictionless and the frictional formulation present severe problems. To overcome all the cited problems a generalized formulation is proposed, which deals with contact between circular beams. It has to be remarked that the contact problem is treated first in a completely generic framework, and only in a second step the results are particularized to the FE formulation. For such purpose the centroids of the beams in the 3-D space are considered as parametric functions. The framework for the consistent linearization is developed in a very rigorous and systematic way, providing evidence of the symmetry of the operators. The procedure is quite cumbersome, hence here only the most heavy part, related to the computation of all the fundamental geometrical terms involved, is presented.