A Variable-Length Beam Element Incorporating the Effect of Spinning

Abstract

This paper proposes a novel variable-length beam element that takes into account the effect of beam spinning. This is the first such beam element of variable length based on the absolute nodal coordinate formulation. In addition to the position and slope vectors, the angles of rotation around the element axis of cross sections that contain two nodes are introduced into the element coordinates to describe the spinning of an assumed Euler-Bernoulli beam with circular cross section. The material coordinates of the two nodes are also included in the arbitrary Lagrangian-Eulerian description used for previous element to describe the varying element length caused by mass transportation at the boundaries. The proposed element facilitates convenient and effective numerical modeling of the dynamics of a circular-cross-section beam with transportation boundaries and that is spinning. Numerical examples demonstrate that the proposed element can describe the dynamic behavior of a circular-cross-section beam effectively. In the field of engineering, this novel element could be used in the dynamic analysis of drill stems, the slender workpiece of a cylindrical shaft during the turning process, and the lead screw in a ball screw mechanism.

Proceedings of The American Modelica Conference 2018, October 9-10, Somberg Conference Center, Cambridge MA, USA

“…It can be argued that this assumption is valid for the vast majority of deployable structures, in particular spacebased structures, as the deployment process often occurs over the course of several minutes to keep structural loads low. The VariableLengthBeam model, however, should be used with care and could potentially be extended to more general cases through implementation of missing terms via derivations such as those provided in Yang et al (2017).…”

Axially variable-length solid element of absolute nodal coordinate formulation

“…For example, Tang et al [9] developed an ANCF-based variable-length cable element by combining Lagrangian and Eulerian descriptions and simulated the deployment process of tethered satellite systems. This cable element, however, is only suitable for simple boundary conditions as the boundary elements must be defined in advance [17]. Hong and Ren [15] and Hong et al [18] developed a variable-length beam element of ALE-ANCF by introducing two material coordinates of the two nodes as the generalized coordinates.…”

“…Hence, the two cable elements by Du et al [11] and Escalona [10] are not the finite elements of ANCF according to the definition by Shabana [19]. Yang et al [17] generalized these variable-length beam elements of ANCF aforementioned and proposed a novel variable-length beam element that uses positions and slopes of two nodes, two material coordinates and two rotation angles of the cross-section as the generalized coordinates. This beam element, therefore, enables one to model flexible variable-length beam structures, for which the torsional effect is not negligible.…”