Constraints in structural and rigid body mechanics: a frictional contact problem

Abstract

In this work, we propose some basic approaches towards a unification of the theories for deformable and rigid bodies. This unification process is based on two fundamental mechanical concepts, which are the principle of virtual work and the principle of d’Alembert–Lagrange. The basic idea is to initially look upon structural elements as general continua, and to endow them later with specific properties like rigidity, imposed by perfect bilateral constraints. It is shown by the example of a simple flexible multibody system how this unifying and systematic approach has to be carried out. The system under consideration consists of a rigid disk and a nonlinear elastic string, which may come into contact with each other. The contact is modeled as a hard unilateral geometric constraint combined with a one-dimensional Coulomb friction element. The contact interactions are formulated as set-valued force laws and impact laws, and the system is consequently treated within the framework of nonsmooth dynamics. The model of the string allows for large deformations in time and for a nonlinear elastic material response. By constraining the kinematics of the string to finite dimensions, a nonlinear finite element formulation is achieved in a very natural way.