Engineering Transactions, 66, 3, pp. 281–299, 2018
10.24423/EngTrans.903.20180928

Contact Between 3D Beams with Deformable Circular Cross-Sections – Numerical Verification

Olga KAWA
http://www.zmb.put.poznan.pl/
Poznan University of Technology
Poland

Przemyslaw LITEWKA
http://www.zmb.put.poznan.pl/
Poznan University of Technology
Poland

Robert STUDZIŃSKI
Poznan University of Technology
Poland

In this paper a numerical analysis of contact between three-dimensional elastic beams with deformations at the contact zone is carried out. The authors propose a new model of beam-to-beam contact which is the continuation of ideas presented in [6, 7, 10]. The results of beam-to-beam contact analysis are compared with the ones for full 3D problem solved in the abaqus/enviroment. The aim of the conducted numerical simulations was to select the most appropriate 3D model and to use it as a reference to verify the accuracy of the proposed beam-to-beam contact definition. The verifications were carried out for contact between beams with circular cross-sections. The obtained contact forces and the displacements of beams tips for different beams arrangements and boundary conditions showed a satisfactory correlation.
Keywords: contact; beams; finite element method; linearization; deformed cross-section; numerical analysis
Full Text: PDF

References

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.

Curnier A., Alart P., A generalized Newton method for contact problem with friction, Journal de M´ecanique Th´eorique et Appliqu´ee, 7: 67–82, 1988.

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

Gay Neto A., Pimenta P.M., Wriggers P., Self-contact modeling on beams experiencing loop formation, Computational Mechanics, 55(1): 193–208, 2015.

Johnson K.L., Contact mechanics, pp: 81–104, Cambridge University Press, 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.), pp. 183–190, CRC Press/Balkema, Taylor & Francis Group, London, 2014.

Kawa O., Litewka P., Contact with friction between 3D beams with deformable circular cross sections, Engineering Transactions, 63(4): 439–462, 2015.

Konyukhov A., Schweizerhof K., Geometrically exact theory for arbitrary shaped bodies, Lecture Notes in Applied and Computational Mechanics, Vol. 67, Springer, 2013.

Laursen T.A., Computational contact and impact mechanics, Springer, Heidelberg, 2002.

Litewka P., Finite element analysis of beam to beam contact, Springer, Berlin–Heidelberg, 2010.

Meier C., Wall W., Popp A., A unified approach for beam-to-beam contact, Computer Methods in Applied Mechanics and Engineering, 315: 972–1010, 2017.

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

Simo J.C., Laursen T.A., An augmented Lagrangian treatment of contact problems involving friction, Computers and Structures, 42(1): 97–116, 1992.

Wriggers P., Miehe C., On the treatment of contact contraints within coupled thermomechanical analysis, [in:] Proceedings of EUROMECH, Finite Inelastic Deformations, Desdo B., Stein E. (Eds.), Springer, Berlin 1992.

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

Wriggers P., Computational contact mechanics, 1st Ed., pp. 339–354, Wiley, 2002.

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.

DOI: 10.24423/EngTrans.903.20180928