Engineering Transactions, 63, 4, pp. 439-462, 2015

Contact with Friction Between 3D Beams with Deformable Circular Cross Sections

Olga Kawa
Poznan University of Technology Institute of Structural Engineering

Przemyslaw Litewka
Poznan University of Technology Institute of Structural Engineering

In this paper, contact with friction between three-dimensional elastic beams with deformations at the contact zone is analysed. It is assumed that the analysed beams undergo large displacements, although the strains remain small and the cross sections of the beams are deformed. To include the deformation effect the classical analytical result from Hertzian contact between two elastic cylinders is used [3]. The penalty method is applied to enforce normal contact and friction constraints and the appropriate kinematic variables are defined, linearised and discretised for the finite element method implementation.
Keywords: contact; beams; finite element method; friction; linearization; deformed cross-section
Full Text: PDF


Crisfield M.A., A consistent co-rotational formulation for non-linear, three-dimensional beam-elements, Computer Methods in Applied Mechanics and Engineering, 81(2), 131–150, 1990.

Durville D., Numerical simulation of entangled materials mechanical properties, Journal of Materials Science, 40(22), 5941–5948, 2005.

Durville D., Contact-friction modeling within elastic beam assemblies: an application to knot tightening, Computational Mechanics, 49(6), 687–707, 2012.

Johnson K.L., Contact Mechanics, 81–104, Cambridge University Press, Cambridge, 1985.

Kawa O., Litewka P., Contact between 3-D beams with deformable circular cross sections, in: Recent Advances in Computational Mechanics, T. Łodygowski, J. Rakowski, P. Litewka, Eds., 183–190, CRC Press/Balkema, Taylor & Francis Group, London, 2014.

Konyukhov A., Schweizerhof K., Geometrically exact covariant approach for contact between curves. Computer Methods in Applied Mechanics and Engineering, 199(37–40), 2510–2531, 2010.

Konyukhov A., Schweizerhof K., Computational contact mechanics. Geometrically exact theory for arbitrary shaped bodies. Lecture Notes in Applied and Computational Mechanics, 67, Springer, Heidelberg, New York, Dordrecht, London, 2013.

Litewka P., Finite Element Analysis of Beam to Beam Contact, Springer, Berlin, Heidelberg, 2010.

Litewka P., Enhanced multiple-point beam-to-beam frictionless contact finite element, Computational Mechanics, 52(6), 1365–1380, 2013.

Michałowski R., Mróz Z., Associated and non-associated sliding rules in contact friction problems, Archives of Mechanics, 30(3), 259–276, 1978.

Paczelt I., Beleznai R., Nonlinear contact-theory for analysis of wire rope strand using high-order approximation in the FEM, Computers and Structures, 89(11–12), 1004–1025, 2011.

Popov V.L., Contact Mechanics and Friction, 55–64, Springer, Berlin, Heidelberg, 2010.

Wriggers P., Zavarise G., On contact between three-dimensional beams undergoing large deflections. Communications in Numerical Methods in Engineering, 13(6), 429–438, 1997.

Zavarise G., Wriggers P., Contact with friction between beams in 3-D space, International Journal for Numerical Methods in Engineering, 49(8), 977–1006, 2000.

Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland