A Variable-Length Beam Element Incorporating the Effect of Spinning

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.