Configurational forces in variable-length beams for flexible multibody dynamics

This paper addresses the problem of sliding beams or beams with sliding appendages, with special emphasis on situations where the axial motion of the beam or appendage is not prescribed a priori. Hamilton’s variational principle is used to derive the weak and strong forms of governing equations based on the systematic use of Reynolds’ transport theorem. The strong form of the governing equations involve the mechanical and configurational momentum equations, together with the proper boundary conditions. It is shown that the configurational momentum equations are linear combinations of their mechanical counterparts and hence, are redundant. A weak form of the same equations is also developed; the configurational and mechanical momentum equations become independent because they combine in an integral form the strong mechanical and configurational momentum equations with their respective natural boundary conditions. The domain- and boundary-based formulations, stemming from these two forms of the governing equations, respectively, are proposed, and numerical examples are presented to contrast their relative performances. The predictions of both formulations are found to be in good agreement with those obtained from an ABAQUS model using contact pairs. The domain-based formulation presents a higher convergence rate than the boundary-based formulation. Clearly, the proper treatment of the configurational forces impacts the accuracy of the model significantly.