Locking alleviation in fully parameterized ANCF beam elements: addressing curvature-thickness, shear, and membrane locking via strain field refinement, numerical validation, and locking interdependency insights

This paper addresses locking issues in fully parameterized Absolute Nodal Coordinate Formulation (ANCF) beam elements, focusing on curvature thickness locking, shear locking, and membrane locking—among which membrane locking has rarely been explored in such elements. The primary objective is to unravel the fundamental mechanisms underlying these locking phenomena and develop an effective alleviation approach without sacrificing the inherent advantages of fully parameterized ANCF beam elements. First, a systematic and in-depth analysis of the transverse, shear, and axial strain distributions along the beam axis is conducted. This analysis reveals the fundamental causes of all three locking effects for the first time. Subsequently, the transverse, shear, and axial strains are enhanced by selective re-interpolation of the transverse and axial gradients, leading to improved formulations of generalized elastic forces, which effectively alleviates curvature thickness locking, shear locking, and membrane locking. A key improvement of this approach lies in its ability to directly target the essential factors inducing locking without compromising element continuity, adding extra degrees of freedom, or requiring reduced integration. Finally, static and dynamic numerical simulations validate the effectiveness of the proposed approach, evaluating critical performance metrics such as convergence of beam configuration and strain energy, strain distribution, curvature continuity, system energy variation, and convergence insensitivity to cross-sectional dimension variations. The numerical examples not only clarify the causes of each locking type but also enable a comparative analysis of the three locking phenomena and reveal their previously unreported interdependencies, providing new insights into the nature of locking effects in ANCF beam elements.