Frictional contact between 3D beams

Abstract

 The paper deals with frictional contact between 3D beams with rectangular cross-sections. In the analysis large displacements and small strains are allowed. Hence the cross-section behaves like a rigid body undergoing displacement and rotations. Contact between the beams is assumed to be point-wise between their edges. For the friction the simple non-associated Coulomb law is adopted. The analogy to rigid plasticity is used where stick and slip conditions are considered and backward Euler scheme is applied whenever the yield condition is violated. Contact constraints for normal and tangential part are introduced using the active set strategy and the penalty method. A consistent linearisation of both contact contributions is derived and expressed in suitable matrix form, easy to use in FEM approximations. Several numerical examples including the comparison to the full 3D-solid analysis depict the efficiency of the presented approach.