Frictional contact analysis of sliding joints with clearances between flexible beams and rigid holes in flexible multibody systems

Joints with clearances in flexible multibody systems have been investigated for many years. However, the previous work is mainly concerned with the lower pair joints with small clearances. The aim of this paper is to present a formulation for the sliding joint with clearance between a flexible beam and a rigid hole, with special focus on the frictional contact. We thoroughly discuss a contact detection method for a flexible beam with circular cross-section and a rigid hole with rectangular cross-section. We employ the layer-wise contact detection concept and propose an efficient and robust approach to address the two-dimensional ellipse–rectangle contact detection problem within the rigid hole cross-section. After the potential contact points on the beam surface and on the hole cross-section are determined, a beam–rigid hole frictional contact element is proposed. The measure of tangential interaction is defined in the current configuration, and the changes of both contact points are taken into consideration. The constitutive relationship for the tangential contact is modeled by the Coulomb friction law with a penalty regularization, and the real tangential force vector in the current step is determined via a trial step and a subsequent return-mapping scheme. In addition, the discontinuity problem across the beam element boundaries in the case of large sliding is circumvented by a simple and effective transformation. Finally, two numerical examples are presented to verify the proposed contact detection method and the beam–rigid hole frictional contact element, and to demonstrate the influence of the frictional contact on the dynamic performance of flexible multibody systems.