Deformation einer elastischen Flexlippe

D. Kröner (), A. Koop (), B. Schupp (), S. Müller, S. Schmitz and B. Schroeter
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D. Kröner: Institut für Angewandte Mathematik
A. Koop: Institut für Angewandte Mathematik
B. Schupp: Institut für Angewandte Mathematik
S. Müller: ETH-Zentrum, Departement Mathematik
S. Schmitz: Reifenhäuser GmbH & Co Maschinenfabrik
B. Schroeter: Reifenhäuser GmbH & Co Maschinenfabrik

A chapter in Mathematik Schlüsseltechnologie für die Zukunft, 1997, pp 177-189 from Springer

Abstract: Abstract The aim of the project deformation of an elastic cylinder under point-wise radial loads in collaboration with the machine factory Reifenhäuser is to determine the deformation of a cylindrical tube clamped radially with a given number of feeding mechanisms. Furthermore a hydrostatic pressure from inside is caused by a flow through the tube. Besides the geometry of the undeformed tube and the pressure only the positions of the control elements are given. The forces at the contact points are unknown and have to be determined as well. The problem arises in the production of tube-shaped plastic foils with a profile extruding machine, the pressure is caused by the flow of the plastic mass. The mathematical formulation of the problem using a linear Kirchhoff-type shell model leads to a minimization problem with one constraint for each control element. The Lagrange multipliers are the constraining forces. Numerically we solve the problem by a conforming finite element method. For the Euler-Lagrange equation of the constrained problem we use an Uzawa-algorithm, the active constraints are determined with a primal active-set-method. The problem has already been treated in [KO] with an 1-D model.

Date: 1997
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DOI: 10.1007/978-3-642-60550-5_16

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