A mortar formulation for frictionless line-to-line beam contact

Abstract

Abstract This paper describes the quasi-static formulation of frictionless line contact between flexible beams by employing the mortar finite element approach. Contact constraints are enforced in a weak sense along the contact region using Lagrange multipliers. A simple projection appropriate for thin beams with circular cross-sections is proposed for the computation of contact regions. It is combined with the geometrically exact beam formalism on the Lie group $SE(3)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>)</mml:mo> </mml:math> . Interestingly, this framework leads to a constraint gradient and a tangent stiffness invariant under rigid body transformations. The formulation is tested in some numerical examples.