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A three-dimensional nonlinear finite element for thin beams isproposed within the absolute nodal coordinate formulation (ANCF). Thedeformation of the element is described by means of displacement vector,axial slope and axial rotation parameter per node. The element is based onthe Bernoulli–Euler theory and can undergo coupled axial extension, bendingand torsion in the large deformation case. Singularities – which aretypically caused by such parameterizations – are overcome by a director perelement node. Once the directors are properly defined, a cross sectionalframe is defined at any point of the beam axis. Since the director is updatedduring computation, no singularities occur. The proposed element is athree-dimensional ANCF Bernoulli–Euler beam element free of singularities andwithout transverse slope vectors. Detailed convergence analysis by means ofvarious numerical static and dynamic examples and comparison to analyticalsolutions shows the performance and accuracy of the element

A novel director-based Bernoulli–Euler beam finite element in absolute nodal coordinate formulation free of geometric singularities