Robust integration schemes for flexible multibody systems Original Research Article

A framework for the development of robust time integration schemes for nonlinear, flexible multibody systems is presented. The proposed schemes are designed to meet four specific requirements: nonlinear unconditional stability of the scheme, a rigorous treatment of both geometric and material nonlinearities, exact satisfaction of the constraints, and the presence of high frequency numerical dissipation. Specific algorithms are presented for rigid bodies, cables, beams, shells, and elasto-dynamics. The kinematic nonlinearities are treated in a rigorous manner for all elements, and the material nonlinearities can be handled when the constitutive laws stem from the existence of a strain energy density function. The treatment of the constraint equations associated with the six lower pair joints are presented as well. The efficiency and robustness of the proposed approach is demonstrated with specific numerical examples.