提出可模拟杆件变形的几何精确模型，保持能量与体积守恒。
Lie Group Variational Integrator for the Geometrically Exact Rod with Circular Cross-Section Incorporating Cross-Sectional Deformation
- 基于李群变分积分法构建含截面变形的三维杆模型
- 离散模型严格保持体积守恒与能量误差有界
- 适用于需要高精度动力学仿真的工程结构分析
本文推导了包含平面截面变形的三维几何精确杆（即Cosserat杆）的连续时空运动方程，并采用李群变分积分方法得到一个同时包含旋转运动和截面变形的离散模型。该离散模型具有多个优良特性：通过局部膨胀因子考虑截面变形，确保离散单元的体积守恒；同时具备变分积分方法带来的优势，如旋转构型保持、能量守恒且误差有界。在多种初始条件下进行的大量数值实验验证了该模型对系统物理行为的准确复现能力。
原文摘要 · Abstract (English)
In this paper, we derive the continuous space-time equations of motion of a three-dimensional geometrically exact rod, or the Cosserat rod, incorporating planar cross-sectional deformation. We then adopt the Lie group variational integrator technique to obtain a discrete model of the rod incorporating both rotational motion and cross-sectional deformation as well. The resulting discrete model possesses several desirable features: it ensures volume conservation of the discrete elements by considering cross-sectional deformation through a local dilatation factor, it demonstrates the beneficial properties associated with the variational integrator technique, such as the preservation of the rotational configuration, and energy conservation with a bounded error. An exhaustive set of numerical results under various initial conditions of the rod demonstrates the efficacy of the model in replicating the physics of the system.
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