A Weak Formulation of Constraints to Couple Rigid and Elastic Bodies - a Study with FEniCS

Abstract: Many complex mechanical systems are simplified by considering them as multibody systems. In recent years, flexible multibody dynamics has become more and more in demand. In~\cite{simeon2013}, a weakly constrained joint model was presented, which in a well-defined way models the interconnection of an elastic and a rigid body by a massless rigid joint. However, the joint model assumes that the orientation of the joint-elastic body interface is unaffected by the displacement field of the elastic body. The aim of this study is to highlight the limitations of the joint model due to this assumption. In this study, the joint model was applied for two-body system of an elastic and a rigid body, connected by a small rigid joint. During deformation the joint-body interface was expected to rotate due to the displacement field of the elastic body. However, due to the assumption the interface stayed fixed which distorted the displacement field of the elastic body. This assumption could be avoided if the orientation of the interface during deformation was predicted, which would be possible by the use of observer points.