Analysis of thin beams and cables using the absolute nodal co-ordinate formulation

The purpose of this paper is to present formulations for beam elements based on the absolute nodal co-ordinate formulation that can be effectively and efficiently used in the case of thin structural applications. The numerically stiff behaviour resulting from shear terms in existing absolute nodal co-ordinate formulation beam elements that employ the continuum mechanics approach to formulate the elastic forces and the resulting locking phenomenon make these elements less attractive for slender stiff structures. In this investigation, additional shape functions are introduced for an existing spatial absolute nodal co-ordinate formulation beam element in order to obtain higher accuracy when the continuum mechanics approach is used to formulate the elastic forces. For thin structures where bending stiffness can be important in some applications, a lower order cable element is introduced and the performance of this cable element is evaluated by comparing it with existing formulations using several examples. Cables that experience low tension or catenary systems where bending stiffness has an effect on the wave propagation are examples in which the low order cable element can be used. The cable element, which does not have torsional stiffness, can be effectively used in many problems such as in the formulation of the sliding joints in applications such as the spatial pantograph/catenary systems. The numerical study presented in this paper shows that the use of existing implicit time integration methods enables the simulation of multibody systems with a moderate number of thin and stiff finite elements in reasonable CPU time.