KINETIC ENERGY AND INTEGRATION OF THE EQUATIONS OF MOTION OF COROTATIONAL BEAM ELEMENTS

In the last years the research group has worked to the development of a numerical procedure devoted to investigate the dynamics of suspended cables under turbulent wind loading and subjected to large displacements and rotations [1],[2],[3]. Within this context, starting from the formulation proposed by Oran in [4] and by Meek and Tan in [5], a corotational shallow beam element was developed for modeling the mechanical behavior of cable elements [2], [3]. As part of the description of the kinematics of the corotational element, when applied to modeling very flexible structures, and in procedures for the definition and updating of the corotated reference frame, a key point is the treatment of large three-dimensional rotations. Due to the presence of large nodal rotations, in fact, the space of configuration of the structure is a non-linear differentiable manifold [6]. Particular care should then be paid to the parameterization of rotations and to the interpolation schemes adopted to numerically solve the dynamic problem. Several parameterization and update strategies of rotations were compared in a companion paper [7], where the issue of the evaluation of the internal forces and the static tangent stiffness matrix was discussed. This paper concerns the description of the dynamics of the beam element. In particular, the focus is concentrated on a new procedure for the evaluation of the inertial forces and the numerical integration of the equations of motion.