An improved variable-length beam element with a torsion effect based on the absolute nodal coordinate formulation

This paper proposes an improved variable-length beam element based on absolute nodal coordinate formulation and arbitrary Lagrangian–Eulerian description to build dynamic model of a one-dimensional medium with mass transportation and a non-ignorable torsion effect. The rotational angle of the presented element is interpolated using the same Hermite polynomials as the position vector such that the change rate of the rotational angles of the two nodes are also introduced into generalized coordinates of the element, which ensures the continuity of the nodal torque. Numerical examples demonstrate that the proposed element can precisely describe the dynamic behaviour of a one-dimensional medium. Furthermore, its ability to describe the torsion effect is significantly enhanced compared to earlier element in the literature. In engineering applications, the proposed element can be used in the dynamic analysis of drill stems in the drilling process, slender workpieces of cylinder shafts in turning processes and leading screws in ball screw mechanisms.