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Y. Vetyukov, P.G. Gruber, M. Krommer:
"Modeling finite deformations of an axially moving elastic plate with a mixed Eulerian-Lagrangian kinematic description";
Talk: 3rd Polish Congress of Mechanics & 21st Computer Methods in Mechanics, Gdansk, Poland; 2015-09; in: "Proceedings of the PCM-CMM-2015 - 3rd Polish Congress of Mechanics & 21st Computer Methods in Mechanics", M. Kleiber et al. (ed.); (2015), 67 - 68.

We consider the motion of a flexible plate across a domain, bounded by two parallel lines. Kinematically prescribed velocities of the plate, entering the domain and leaving it, may vary in space and time. The corresponding deformation of the plate is quasistatically analyzed using the geometrically nonlinear model of a Kirchhoff shell with a mixed Eulerian-Lagrangian kinematic description. In contrast to the formulations, available in the literature, both the in-plane and the out-of-plane deformations are unknown a priori and may be arbitrarily large. The particles of the plate travel across a finite element mesh, which remains fixed in the axial direction. The evident advantage of the approach is that the boundary conditions need to be applied at fixed edges of the finite elements. In the paper, we present the mathematical formulation and demonstrate its consistency by comparing the solution of a benchmark problem against results, obtained with conventional Lagrangian finite elements.

Axially moving plates, nonlinear theory of shells, multiplicative decomposition, Eulerian-Lagrangian description, finite element method

https://publik.tuwien.ac.at/files/publik_246973.pdf