Dynamics of a flexible body: a two-field formulation

A two-field formulation of the nonlinear dynamics of an elastic body is presented in which positions/orientations and the resulting velocity field are treated as independent. Combining a nonclassical description of elastic velocity that includes the convection velocity due to elastic deformation with floating reference axes minimizing the relative kinetic energy due to elastic deformation provides a fully uncoupled expression of kinetic energy. A transformation inspired by the classical Legendre transformation concept is introduced to develop the motion equations in canonical form. Finite element discretization is achieved using the same shape function sets for elastic displacements and velocities. Specific attention is brought to the discretization of the gyroscopic forces induced by elastic deformation. A model reduction strategy to construct superelement models suitable for flexible multibody dynamics applications is proposed, which fulfills the essential condition of orthogonality between a rigid body and elastic motions. The problem of expressing kinematic connections at superelement boundaries is briefly addressed. Two academic examples have been developed to illustrate some of the concepts presented.

Rotational self-friction problem of elastic rods

The aim of this paper is to extend the modeling of a hyperelastic rod undergoing large displacements with tangential self-friction to their modeling with rotational self-friction. As well as the discontinuity of contact force into a contact region not known in advance, taking into account the effects of friction in this problem type underlies more serious modeling, mathematical and numerical analysis difficulties. In this paper, we present an accurate modeling of rotational and tangential self-friction with Coulomb's law and also describe an augmented Lagrangian method to present a weak variational formulation approach of this problem. We then use the minimization method of the total energy to present an existence result of solution for the nonlinear penalized formulation. Finally, we give the linearization and the finite-element discretization of the weak variational formulation that can be useful for a numerical implementation.