Multibody implementation of finite volume C-0 beams

A C-0 beam discretization based on the finite volume concept is described. In the linear case this approach leads to a collocated evaluation of the stiffness matrix of the beam; it proves to be intrinsically free from shear locking. In the nonlinear formulation only a collocated evaluation of the elastic forces is required, which dramatically simplifies the computation of the elastic contribution to the equilibrium equations. The formulation is here developed for the general geometrically nonlinear case and implemented in multibody formulation. The proposed approach proved to be consistent; its major drawback lies in the loss of symmetry of both the linear and the linearized beam matrices. For this reason the method is particularly suitable for dynamic problems like a nonlinear implicit multibody numerical approximation, in which the symmetry of the matrices is not so important, as it is already lost, whereas the ease in the generation of the contributions to the equations can lead to faster and cheaper analyses. Some applications are outlined, and the most relevant results are discussed.