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 ar e used to compute the tangent iteration matrices used to integrate imp licitly the equations of motion in descriptor form. A total Lagrangian primal corotational method and an updated Lagrangian mixed variationa l method are proposed to compute the tangent stiffness matrix. The tan gent inertia matrices, including the gyroscopic and centrifugal terms, are also obtained by using the tangent maps of rotation. The numerica l examples analyzed in this paper include static (pre- and postbucklin g) and dynamic analysis of flexible beams structures. The new finite e lements show a very good performance, in terms of fewer number of elem ents used and accuracy during the simulation, both for static and dyna mic problems.