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Y. Vetyukov, E. Oborin, J. Scheidl, M. Krommer, C. Schmidrathner:
"Flexible belt hanging on two pulleys: Contact problem at non-material kinematic description";
International Journal of Solids and Structures, 168 (2019), 183 - 193.

We propose a non-material finite element scheme for modelling large deformations of a closed flexible rod supported by two rigid pulleys in the field of gravity. The mixed Eulerian-Lagrangian kinematic description of circumferential and transverse displacements is beneficial for simulations of moving belt drives. The necessary C1 inter-element continuity in a compound coordinate system with Cartesian and polar domains requires a nonlinear finite element approximation. The theoretically predicted singular reaction force distribution prevents us from using the technique of Lagrange multipliers for normal contact. A novel semi-analytical solution of the static problem based on the integration of the equations of the nonlinear theory of rods in the free spans as well as in the segments of contact with pulleys is presented for the sake of validation. We demonstrate the mutual convergence of simulation results for a benchmark problem and additionally justify them by comparison against conventional Lagrangian finite element solutions.

Belt drive mechanics; Mixed Eulerian-Lagrangian description; Finite element analysis; Contact problem; Kirchhoff rod theory

http://dx.doi.org/10.1016/j.ijsolstr.2019.03.034

https://doi.org/10.1016/j.ijsolstr.2019.03.034

Project Head Yury Vetyukov:
LaLaBand