A modified constraint force algorithm for flexible multibody dynamics with loop constraints

This paper presents a modified constraint force algorithm (m-CFA) for the dynamics of flexible multibody systems in arbitrary topologies. The m-CFA can efficiently calculate the constraint forces while solving for the motion of the system. The motion equations are based on recursive formulation, whereas a global equation is generated to obtain the explicit expression of the constraint forces and the motion of the system. For flexible bodies, the modal superposition method is employed under the assumption of a small deformation. The auxiliary generalized velocities or Lagrange multipliers in complex forms are avoided in the constraint equations for structural loops. To improve the efficiency of the m-CFA, a parallel implementation method is utilized to reduce the required arithmetic operations to order-n·logn, where n is the number of bodies in the system. The accuracy and efficiency of m-CFA are validated through numerical examples of a flexible dual-arm space robot. The results show that the m-CFA agrees with the well-developed recursive method and the order of the relative errors of the generalized velocities are smaller than 10 ^{- 10}.