A new locking-free beam element based on absolute nodal coordinates

In this paper, a novel locking-free finite beam element is proposed utilizing the absolute nodal coordinate formulation. By incorporating a gradient vector along the transverse direction at the boundary points, the linear interpolation of the gradient vector field within this element is achieved. Consequently, the problem of constant transverse strain distribution, which is observed in the Omar-Shabana beam element, is effectively addressed. Building upon this concept, this study further extends the proposed element from two dimensions to three dimensions. Additionally, it analyzes and compares the locking alleviation mechanism of the newly developed element and Patel-Shabana beam element. The analysis aims to provide insights into the factors contributing to the locking alleviation of different absolute nodal coordinate formulation (ANCF) elements. Furthermore, to demonstrate the effectiveness of the new element, six numerical simulation examples are designed, comprising three and three dynamic examples. These examples encompass small deformation statics, large deformation statics, small-scale motion, large-scale motion, and rotational motion problems. Finally, the results indicate that the proposed ANCF beam element can effectively alleviate the locking problem. The element exhibits robust adaptability, rationality, and effectiveness when subjected to complex mechanical characteristics by comparing the numerical results of this element with the classical Omar-Shabana, high-order Shen, and Patel-Shabana elements.