O.A. Bauchau, C.L. Bottasso, L. Trainelli
Robust
Integration Schemes for Flexible Multibody Systems
Computer Methods in Applied
Mechanics and Engineering, 192 (3/4): 395-420 (2003).
Abstract
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.