A geometrically exact beam element via the gradient-deficient absolute nodal coordinate formulation

Dynamic modeling of beam-like structures undergoing large rotations and deformations within the absolute nodal coordinate formulation (ANCF) often requires a large number of gradient-related degrees of freedom, leading to high computational cost. In this paper, a gradient-deficient geometrically exact ANCF beam element is proposed to achieve a more compact kinematic description while retaining the capability to represent essential deformation modes. The proposed formulation interpolates the axial gradient together with a single transverse gradient to construct a local Cartesian coordinate system for cross-sectional representation, thereby eliminating one redundant transverse gradient. Based on this kinematic framework, the elastic force vector and the generalized external force vectors corresponding to applied moments, concentrated forces, and distributed loads are formulated. Several numerical examples involving large-deflection bending, rolling-up deformation, and pure torsional loading are presented. The results indicate that the proposed element provides accuracy comparable to that of existing fully parameterized ANCF beam elements, while reducing the number of degrees of freedom and the overall computational scale.