Dynamic analysis of multi-flexible body systems with spatial beams and finite rotations

A general formulation is presented for static and dynamic analysis of spatial elastic beams capable of undergoing finite rotations and small strains. Primal and mixed variational formulations are introduced to model spatial beams envisioned for multi-flexible body dynamics applications. 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 Lagrangean primal corotational method and an Updated Lagrangean 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 kinematic constraints are appended to the equations by means of Lagrange multipliers and a penalty term, leading to tangent constraint matrices. The numerical examples analyzed in this thesis include: static pre and post-buckling analysis of flexible frames; dynamic analysis of the tumbling motion of highly flexible beam structures, and examples from the multibody literature such as flexible manipulator arms and closed loop kinematic chains. The new finite elements show a very good performance, in terms of less number of elements used and accuracy during the simulation, both for static and dynamic problems, and in multi-flexible body cases.