Procedure for non-smooth contact for planar flexible beams with cone complementarity problem

Xinxin Yu, Marko K. Matikainen, Ajay B. Harish, Aki Mikkola

Research output: Contribution to journalArticlepeer-review


Contact description plays an important role in modeling of applications involving flexible multibody dynamics. Example of such applications include contact between a belt and pulley, crash-worthiness analysis in aerospace and automotive engineering. Approaches such as the linear complementarity problem (LCP), nonlinear complementarity problem (NCP) and penalty method have been proposed for contact detection and imposition of contact constraints. Contact description within multibody dynamics, however, continues to be a challenging topic, particularly in the case of flexible bodies. This paper describes and compares the use of two contact descriptions in the framework of flexible multibody dynamics; (1) the use of nonlinear cone complementarity approach (CCP) and (2) the penalty method. Both contact models are presented together with a master-slave detection algorithm. The modified form of node-to-node approach presented facilitates creation of pseudo-nodes where gap function can be calculated. This reduces the cumbersome effort of contact search. Since large deformations can be an important phenomenon in flexible multibody applications, beam elements based on the absolute nodal coordinate formulation (ANCF) are implemented in this study. To make a comparison of two approaches, the damping component is included in the penalty method by using the continuous contact model introduced by Hunt and Crossley. Numerical results are based on the simulation of ANCF beam contact with rigid ground, rigid body with an arbitrary shape and pendulum contact. Although kinematic results show a good agreement between both approaches when the coefficient of restitution is zero, the unphysical interpenetration appears in the penalty method. Nonlinear minimization problem solved by CCP approach helps to prevent the penetration during contact event. Furthermore, the proposed contact detection algorithm is proved to be capable of being used for multiple contact between beam and arbitrary shape rigid body; different contact types, such as side-by-side and corner-by-side, can be performed without prediction.

Original languageEnglish
Pages (from-to)179-196
Number of pages18
Journal Institution of Mechanical Engineers. Proceedings. Part K: Journal of Multi-Body Dynamics
Issue number2
Early online date21 Sept 2020
Publication statusPublished - Jun 2021


  • ANCF
  • cone complementarity problem
  • contact mechanics
  • penalty method


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