In this paper, we present a discrete formulation of nonlinear shear- and torsion-free rods introduced by Gebhardt and Romero in [20] that uses isogeometric discretization and robust time integration. Omitting the director as an independent variable field, we reduce the number of degrees of freedom and obtain discrete solutions in multiple copies of the Euclidean space (R^3), which is larger than the corresponding multiple copies of the manifold (R^3 x S^2) obtained with standard Hermite finite elements. For implicit time integration, we choose the same integration scheme as Gebhardt and Romero in [20] that is a hybrid form of the midpoint and the trapezoidal rules. In addition, we apply a recently introduced approach for outlier removal by Hiemstra et al. [26] that reduces high-frequency content in the response without affecting the accuracy, ensuring robustness of our nonlinear discrete formulation. We illustrate the efficiency of our nonlinear discrete formulation for static and transient rods under different loading conditions, demonstrating good accuracy in space, time and the frequency domain. Our numerical example coincides with a relevant application case, the simulation of mooring lines.

翻译：本文提出了一种基于等几何离散化与鲁棒时间积分的非线性无剪切无扭转杆离散化公式，该杆模型由Gebhardt与Romero在文献[20]中提出。通过省略指向矢作为独立变量场，我们减少了自由度数量，并在欧几里得空间（R^3）的多个副本中获得离散解，该解空间大于采用标准Hermite有限元方法所对应的流形（R^3 × S^2）多个副本。对于隐式时间积分，我们采用与文献[20]中相同的积分格式，即中点法则与梯形法则的混合形式。此外，我们应用了Hiemstra等人在文献[26]中近期提出的异常值消除方法，该方法能在不影响精度的前提下降低响应中的高频成分，从而确保非线性离散化公式的鲁棒性。我们通过静态与瞬态杆在不同载荷条件下的算例，验证了所提非线性离散化公式的有效性，其在空间、时间及频域均表现出良好的精度。我们的数值算例对应一个典型应用场景——系泊缆索的仿真模拟。