Interpolation schemes for geometrically exact beams: A motion approach

Abstract

SummaryThis paper focuses on the interpolation of the kinematic fields describing the configuration of geometrically exact beams, namely, the position and rotation fields. Two kinematic representations are investigated: the classical approach that treats the displacement and rotation fields separately and the motion approach that treats those two fields as a unit. The latter approach is found to be more consistent with the kinematic description of beams. Then, two finite element interpolation strategies are presented and contrasted. The first interpolates the displacement and rotation fields separately, whereas the second interpolates both fields as a unit, in a manner consistent with the motion approach. The performance of both strategies is evaluated in light of the fundamental requirements for the convergence of the finite element method: the ability to represent rigid‐body motions and constant strain states. It is shown that the traditional uncoupled interpolation scheme for the position field approximates that based on the motion approach and that the coupling induced by the interpolation of motion yields superior convergence rates for the representation of constant strain states. This property is known to lead to finite elements that are less prone to the locking phenomenon. Copyright © 2017 John Wiley & Sons, Ltd.