Elimination of high frequencies in the absolute nodal coordinate formulation

Abstract

The performance of the coordinate partitioning method, the method of Lagrangian multipliers with Baumgarte's stabilization, and the penalty method to account for non-linear constraints of a linear beam element based on the absolute nodal coordinate formulation is studied. Proper non-linear constraints are selected to avoid high-frequency transverse or shear oscillations of the beam. The results show that harmful oscillations can be successfully eliminated from the beam response and efficiency of the numerical solution improves when these constraints are used in the solution procedure. In case of a swinging pendulum, the calculation speed could be improved, when compared to the non-constrained case. It was found that the overall performance of the Lagrange multiplier method with Baumgarte's stabilization and carefully selected stabilization parameters was the best approach.