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和鲁棒时间积分的无剪切无扭转杆离散公式，该公式由Gebhardt与Romero在文献[20]中引入。通过省略方向矢量作为独立变量场，我们减少了自由度数，并在欧几里得空间(R^3)的多重副本中获取离散解，其维度大于标准Hermite有限元在流形(R^3 x S^2)对应多重副本中获得的解空间。对于隐式时间积分，我们采用与Gebhardt和Romero在文献[20]中相同的积分方案，即中点法和梯形法的混合形式。此外，我们应用了Hiemstra等人在文献[26]中最新提出的异常值消除方法，该方法在不影响精度的条件下降低响应中的高频分量，从而确保了非线性离散公式的鲁棒性。我们通过不同加载条件下的静态和动态杆件实例验证了该非线性离散公式的效能，展示了其在空间、时间及频域的良好精度。数值算例与系泊缆模拟这一实际应用场景相吻合。