A spatial shear deformable beam finite element based on the absolute nodal coordinate formulation

In the present paper a three-dimensional beam finite element undergoing large deformations is proposed. Since the definition of the proposed finite element is based on the absolute nodal coordinate formulation (ANCF), no rotational coordinates occur in the formulation. In the current approach, the orientation of the cross section is parameterized by means of slope vectors. Since those are no unit vectors, the cross-section can deform, similar to existing thick beam and shell elements. The nodal displacements and the directional derivatives of the displacements are chosen as nodal coordinates, but in contrast to standard ANCF elements, the proposed formulation is based on the two transversal slope vectors per node only. Different approaches for the virtual work of elastic forces are presented: a continuum mechanics based formulation, as well as a structural mechanics based formulation, which is in accordance with classical nonlinear beam finite elements. Since different interpolation functions as in standard ANCF elements are used, a much better convergence rate (up to order four) can be obtained. Therefore, the present element has high potential for application in geometrically nonlinear problems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)