A Finite Element Approach for the Line-to-Line Contact Interaction of   Thin Beams with Arbitrary Orientation
  The objective of this work is the development of a novel finite element formulation describing the contact interaction of slender beams in complex 3D configurations involving arbitrary beam-to-beam orientations. It is shown in a mathematically concise manner that standard beam contact models based on a point-wise contact force fail to describe a considerable range of configurations, which are, however, likely to occur in practical applications. On the contrary, the formulation proposed here models beam-to-beam contact by means of distributed line forces, a procedure that is shown to be applicable for arbitrary geometrical configurations. The proposed formulation is based on a Gauss-point-to-segment type contact discretization and a penalty regularization of the contact constraint. By means of detailed theoretical and numerical investigations, it is shown that this approach is more suitable for beam contact than possible alternatives based on mortar type contact discretizations or constraint enforcement by means of Lagrange multipliers. The proposed formulation is enhanced by a consistently linearized integration interval segmentation avoiding numerical integration across strong discontinuities. In combination with a smoothed contact force law and the employed C1-continuous beam elements, this procedure drastically reduces the numerical integration error, an essential prerequisite for optimal spatial convergence rates. The resulting line-to-line contact algorithm is supplemented by contact contributions of the beam endpoints, which represent boundary minima of the underlying minimal distance problem. Finally, a series of numerical test cases is analyzed in order to investigate the accuracy and consistency of the proposed formulation regarding integration error, spatial convergence behavior and resulting contact force distributions. 
Christoph Meier, Alexander Popp and Wolfgang A. Wall
cs.CE