Mechanics of Axially Moving Structures at Mixed Eulerian-Lagrangian Description

We discuss a series of methods of the mathematical modelling of large deformations of axially moving strings, beams and plates. Both uni-axial and looped trajectories of motion are considered, which allows the application of these methods to such practically important problems as rolling mills or belt drives. Based on the principles of Lagrangian mechanics, we transform the variational formulations of structural mechanics to problem-oriented exact kinematic descriptions with mixed spatial and material coordinates. The discretization of an intermediate domain results in a consistent non-material finite element formulation with particles of continuum flowing across the mesh. This allows avoiding numerically induced oscillations in the solution, while keeping the discretization fine where necessary, e.g. in the regions of contact.