Mechanics of Axially Moving Structures at Mixed Eulerian-Lagrangian Description

  • Yury VetyukovEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 81)


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.


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The support of the author from the Austrian Science foundation FWF in the framework of the collaboration with the research team of the project “Eulerian Mechanics of Belts” [grant number I2093-N25] is gratefully acknowledged.


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Mechanics and MechatronicsVienna University of TechnologyViennaAustria

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