Singularity-Free Spatial Beam Element via ANCF and the Bishop Frame (ANCF14)
A low-order, two-noded three-dimensional beam finite element (ANCF14) for flexible multibody dynamics that captures longitudinal, bending and torsional deformation with 7 degrees of freedom per node. It is built on the absolute nodal coordinate formulation and replaces the Serret-Frenet frame with the Bishop (rotation-minimizing) frame, which is well-defined even at zero-curvature inflection points and straight segments, yielding a singularity-free formulation while preserving ANCF's constant mass matrix.
2501.00267
This paper develops ANCF14, a new low-order, singularity-free three-dimensional beam finite element for flexible multibody dynamics, built on the absolute nodal coordinate formulation (ANCF) combined…