In this paper, a three-dimensional arbitrary Lagrangian-Eulerian (ALE) formulation based on the consistent corotational method for flexible structures' large deformation problems is proposed. In contrast with the Lagrangian formulations, the proposed formulation can accurately describe moving boundary and load problems using moving nodes. The ALE formulation for flexible structures with an arbitrarily curved initial geometry is derived for the first time. Moreover, internal and external dampings are integrated into the ALE formulation to consider the energy dissipation induced by the structures' deformation and spatial motion. In addition, the rigid-body motion energy dissipation of the internal damping can be avoided by measuring the element's deformation rate in a corotational frame. Kelvin-Voigt model and the interdependent interpolation element are embedded into the element-independent framework of the corotational method. Then, a general beam element model is established to account for the beam's rotary inertia, viscoelasticity, and shear, bending, torsional, and axial deformations in the ALE formulation. Four examples are provided to validate the proposed formulation. The numerical results obtained using the proposed method are compared with those from the commercial software ANSYS and previously published methods. This comparison illustrates the enhanced efficiency in computation time and computer memory.

中文翻译：

---

用于任意弯曲粘弹性梁的非线性动力学分析的任意拉格朗日-欧拉共旋公式


该文针对柔性结构的大变形问题，提出了一种基于一致共旋法的三维任意拉格朗日-欧拉 （ALE） 公式。与 Lagrangian 公式相比，所提出的公式可以使用移动节点准确描述移动边界和载荷问题。首次推导出了具有任意弯曲初始几何形状的柔性结构的 ALE 公式。此外，内部和外部阻尼被集成到 ALE 公式中，以考虑结构变形和空间运动引起的能量耗散。此外，通过测量同向坐标系中元件的变形速率，可以避免内部阻尼的刚体运动能量耗散。Kelvin-Voigt 模型和相互依赖的插值单元被嵌入到共旋转法的单元独立框架中。然后，在 ALE 公式中，建立了一个通用的梁单元模型，以考虑梁的旋转惯量、粘弹性以及剪切、弯曲、扭转和轴向变形。提供了四个示例来验证所提出的公式。使用所提出的方法获得的数值结果与商业软件 ANSYS 和以前发布的方法的数值结果进行了比较。此比较说明了计算时间和计算机内存效率的提高。