X International Conference on Computational Plasticity COMPLAS X E. O˜ nate and D.R.J. Owen (Eds) c CIMNE, Barcelona, 2009 ISOGEOMETRICAL APPROACH FOR CURVED BEAMS ALLOWING LARGE SLIDING CONTACT Alexander Konyukhov ∗ , Karl Schweizerhof † ∗ Institute of Mechanics University of Karlsruhe Englesrtrasse 2, 76139, Karlsruhe, Germany e-mail: Konyukhov@ifm.uka.de, web page: http://www.ifm.uni-karlsruhe.de/ † Institute of Mechanics University of Karlsruhe Englesrtrasse 2, 76139, Karlsruhe, Germany e-mail: Schweizerhof@ifm.uni-karlsruhe.de Key words: Covariant approach, Serret-Frenet frame, exact geometry, curve-to-curve, beam- to-beam Summary. In the current contribution, the isogeometrical approach is exploited in order to obtain a finite element for curvilinear cables describing the initial curvilinear geometry exactly. Further, the covariant contact approach is exploited to enhance the corresponding finite elements with the possibility of large sliding contact. 1 Contact kinematics in a local coordinate system Several approaches are known [1], [2] in order to model curvilinear beams possessing various kinematics of deformation. Stable numerical results for cases of large deformation are reported as well. However, there are very few models known describing curvilinear beams allowing contact interaction. The dominant difficulty in modeling is the rather complex kinematics of mutual deformation leading to difficulties in the linearization for iterative solvers. Some applications are known for curvilinear beams e.g. [3] - hereby symbolic algebra programs have been involved into the computation of complex tangent operators. Recent developments in computational con- tact mechanics especially in the case of structures possessing curvilinear geometry have shown a particular robustness of the covariant approach, see [4]. Expanding the geometrical inter- pretation of this approach to the geometry of curves, the contact interaction between curves is considered in a specially defined local coordinate system related to both curves. First, the Serret-Frenet coordinate system defining the differential properties of a curve is introduced, see Fig. 1, Afterwards, the local coordinate system is introduced as: ρ 2 (s 1 , r, ϕ 1 )= ρ 1 (s 1 , r, ϕ 1 )+ re 1 (1) where e 1 = ν 1 cos ϕ 1 + β 1 sin ϕ 1 (2) 1