A Multi-Body Implementation of Finite Volumes C Beams

The paper describes an unusual C beam discretization based on the nite volumes concept. In the linear case this approach leads to a collocated evaluation of the sti ness matrix of the beam and it proves to be intrinsically free from shear locking. In the non-linear formulation, only a collocated evaluation of the elastic forces is required, that dramatically simpli es the computation of the elastic contribution to the equilibrium equations. The formulation is here developed for the general geometrically non-linear case and implemented in Multi-Body formulation. The proposed approach proved to be consistent; its major drawback lies in the loss of symmetry of both the linear and the linearised beam matrices. For this reason the method happens to be particularly suitable for dynamic problems like a non-linear implicit multi-body numerical approximation, in which the symmetry of the matrices is not so important, as it is already lost, while the ease in the generation of the contributions to the equations may lead to faster and cheaper analyses. Some applications are outlined and the most relevant results are discussed.