Primal and mixed variational principles for dynamics of spatial beams

A general formulation is presented for static and dynamic analysis of spatial elastic beams capable of undergoing finite rotations and small strains. The tangent maps associated to the finite rotation vector are used to compute the tangent iteration matrices used to integrate implicitly the equations of motion in descriptor form. A total Lagrangian primal corotational method and an updated Lagrangian mixed variational method are proposed to compute the tangent stiffness matrix. The tangent inertia matrices, including the gyroscopic and centrifugal terms, are also obtained by using the tangent maps of rotation. The numerical examples analyzed in this paper include static (pre- and postbuckling) and dynamic analysis of flexible beams structures. The new finite elements show a very good performance, in terms of fewer number of elements used and accuracy during the simulation, both for static and dynamic problems.