Numerical integration of the equations of motion of structural systems undergoing large 3D rotations: dynamics of corotational slender beam elements

This paper deals with the numerical simulation of the dynamic response of frame structures undergoing large displacements and 3D rotations.The corotational and the geometrically exact approaches are combined in the formulation of a 3D beam element. Inertia forces are evaluated starting from an exact expression of the element kinetic energy. This last is defined only in terms of nodal variables in the global inertial frame of the mechanical problem, so to avoid cumbersome calculations coming from the corotational decomposition of the motion. The proposed procedure is formally independent from the definition of the corotated frame. The performance of the proposed formulation is discussed with reference to some classic benchmarks involving slender frame structures undergoing large 3D rotations and displacements.