Enhanced multiple-point beam-to-beam frictionless contact finite element

In this paper a new contact finite element for beams with circular cross-sections is presented. The element is an enhancement of the previously formulated point-wise beam-to-beam contact finite elements to be used in cases when beams get in contact at very acute angles. In such situation, if beam deformations in the vicinity of the contact zone are taken into account, the contact is not point-wise but it extends to a certain area. To cover such a case in a more realistic way, two additional pairs of contact points are introduced to accompany the original single pair of contact points. The central pair is determined using the orthogonality conditions for the beam axes and the positions of two extra points are defined on one beam axis by a shift of the local co-ordinate. This shift depends on beams geometry and the current angle between tangent vectors at the central contact point. The appropriate kinematic variables for normal contact together with their finite element approximation are derived. Basing on the weak form for normal contact and its linearisation, the tangent stiffness matrix and the residual vector are derived. The new element is tested using author’s computer programs and comparisons with the point-wise contact elements are made.