Conserving time-integration of beams under contact constrains using B-Spline interpolation

Abstract

The design of energy-momentum algorithms for geometrically exact beams has been achieved more than 15 years ago. However, many of the desired conserivng propeties do not carry over into constrained systems such as beams subjected to sliding contact conditions. We here model such situation and derive a sliding contact conditions that conserves energy and momenta. Basic ingredients of the resulting formulation is the inteprolation of incremental tangent-scaled rotations and a relaxation of the exact sliding condition. We also combine this formulation with a B-Spline interpolation of the beam centroid axis. In this manner, we achieve to smooth the contact loads thrughout the analysis and consequently increase the stability of the numerical model. We demonstrate these advantages and the conserving properties of the algorithm with a set of two-dimensional numerical examples.