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^3xS^2) obtained with standard Hermite finite elements. For implicit time integration, we choose a hybrid form of the mid-point rule and the trapezoidal rule that preserves the linear and angular momentum exactly and approximates the energy accurately. 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的离散公式，该公式源自Gebhardt和Romero在文献[20]中提出的模型。通过省略方向场作为独立变量域，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，该空间大于使用标准Hermite有限元得到的流形(R^3×S^2)的多个对应副本。对于隐式时间积分，我们选择中点法则与梯形法则的混合形式，该形式精确保持线动量与角动量，并准确近似能量。此外，我们应用了Hiemstra等人[26]近期提出的异常值去除方法，该方法在不影响精度的前提下降低响应中的高频成分，从而确保了非线性离散公式的鲁棒性。我们通过不同载荷条件下的静态与瞬态杆算例展示了该公式的效率，验证了其在空间、时间及频域中的良好精度。数值示例与一个实际应用案例——系泊缆仿真——相吻合。