A general nonlinear order-reduction method based on the referenced nodal coordinate formulation for a flexible multibody system

An accurate and efficient formulation is favorable for dynamic analysis and control in the field of the flexible multibody system. This paper proposes a general nonlinear order-reduction method that can tackle overall motions and large deformations with a significant decrease in degrees of freedom, by incorporating the modal derivative techniques into the referenced nodal coordinate formulation (RNCF) developed earlier. To compute the modal derivatives straightforwardly, the closed-form expression of the tangent stiffness matrix's derivative is obtained. The elastic forces are expressed as cubic polynomials of modal coordinates, such that the geometric nonlinear deformations are explicitly expressed. The effectiveness of the proposed method is validated by several numerical examples. The presented geometrically nonlinear order-reduction method can achieve a great accuracy with a much fewer number of generalized coordinates, and it also inherits the large time step-sizes of the RNCF in dealing with large deformations and high-speed rotations.