Aspects of Contact Problems in Computational Multibody Dynamics

Abstract

This paper, first of all, explains briefly some of the well-known and frequently used methods for contact treatment through finite element methods and multibody systems dynamics and gives a short description of their computational aspects in applications dealing with contact problems. Then, as the core of this paper, a formulation for considering unilateral contact of constrained and non-constrained planar deformable bodies in a multibody system leading to Linear Complementarity Problems (LCPs) is presented. In doing so, kinematic relationships governing the behavior of contact are formulated in a way that they consider the effect of deformations. As a general approach for flexible multibody systems, the moving frame of reference approach and modal coordinates are used to describe deformable bodies. In this formulation the effects of deformation are taken into account starting from the relative velocity of contact points in the normal and tangential direction and then the procedure is followed by introducing the relative acceleration of contact points which includes all the necessary terms needed for considering deformations. Then, the complementarity relations are reformulated following the same procedure as for rigid bodies contact. Therefore, the main difference of this algorithm compared to the rigid body case is in the formulation of the kinematics of contact. This formulation just considers the continual contact case of deformable bodies and for impact calculation this formulation has to be extended.