On conservation of energy and kinematic compatibility in dynamics of nonlinear velocity-based three-dimensional beams
On conservation of energy and kinematic compatibility in dynamics of nonlinear velocity-based three-dimensional beams
复制标题
基于非线性速度的三维梁动力学中的能量守恒和运动相容性
DOI：
10.1007/s11071-018-4634-y
复制
发表时间：
2018
影响因子：
5.6
通讯作者：
D. Zupan
中科院分区：
文献类型：
--
作者：
E. Zupan;D. Zupan
在本文中，我们提出了一个原始的能量保持的数值公式为速度为基础的几何精确的三维梁。我们采用代数的四元数作为一个合适的工具来表达的控制方程和相关的旋转与它们的衍生物，而有限元离散化是基于插值的速度在一个固定的框架和角速度在一个移动的框架描述。所提出的控制方程的时间离散化直接将能量守恒约束与时间离散的运动相容性方程联系起来。我们表明，一个合适的选择的主要未知数，以及一个方便的选择的参考系的数量和方程是有益的能量守恒，并允许在一个简单的方式，而无需任何额外的努力近似。本研究的结果是简单有效，但准确和强大的数值模型。
In this paper, we present an original energy-preserving numerical formulation for velocity-based geometrically exact three-dimensional beams. We employ the algebra of quaternions as a suitable tool to express the governing equations and relate rotations with their derivatives, while the finite-element discretization is based on interpolation of velocities in a fixed frame and angular velocities in a moving frame description. The proposed time discretization of governing equations directly relates the energy conservation constraint with the time-discrete kinematic compatibility equations. We show that a suitable choice of primary unknowns together with a convenient choice of the frame of reference for quantities and equations is beneficial for the conservation of energy and enables admissible approximations in a simple manner and without any additional effort. The result of this study is simple and efficient, yet accurate and robust numerical model.