A Corotational Approach for 3D Absolute Nodal Coordinate Elements

Abstract

The present paper deals with the modeling of three dimensional (3D), nonlinear beam finite elements which do not employ rotational parameters. The beam elements are based on the so-called absolute nodal coordinate formulation (ANCF), which has been introduced in the late 1990’s. Early implementations of 3D ANCF beam finite elements incorporated problems regarding Poisson, thickness and shear locking. In the present paper, two alternative models for the work of elastic forces are presented. The first approach, which is intended to provide reference solutions, is close to the original approach. However, the effect of Poisson and thickness locking is eliminated by proper integration of the contributing terms in the virtual work of elastic forces. In the second approach, a corotationally linearized model is developed, which is based on a simple formulation for the elastic forces. The latter model only takes into account small deformations with respect to a corotating reference frame, but it is different from the conventional floating frame of reference formulation, because it has a constant mass matrix. The second approach is intended to be advantageous in practical applications where only small deformations with respect to large rigid body motions need to be taken into account, such as in robotics or machine dynamics. Numerical results are presented, which show that the new approaches agree with the solution of static and dynamic problems using classical finite elements or analytical methods.