Simple formulations of imposing moments and evaluating joint reaction forces for rigid-flexible multibody systems

The Absolute-Coordinate-Based (ACB) method that combines the Natural Coordinate Formulation (NCF) describing rigid bodies and the Absolute Nodal Coordinate Formulation (ANCF) describing flexible bodies has been widely used to study the dynamics of rigid-flexible multibody system since it exhibits many good features, such as the constancy of the mass matrix of the derived dynamic equation, and the easy description and great simplification of the constraint conditions. In order to achieve these good features, both NCF and ANCF take the vectors, rather than rotational coordinates, to describe the rotation and deformation of the rigid-flexible bodies. In this study, the physical meaning of the components of the generalized force vector corresponding to the vector coordinates is revealed on the basis of both ANCF and NCF. Some new and simple formulations of imposing moments and evaluating joint reaction forces for rigid-flexible multibody system are proposed by making full use of the physical meaning of vector coordinates and Lagrange multipliers. All the proposed formulations are defined in the global frame so as to avoid the coordinate transformation. Hence, it can be directly applicable to various types of finite elements of ANCF, including the slope deficient elements. Finally, several typical and practical examples are used to verify the effectiveness of the proposed formulations.