Research Initiation Award: Dynamics and Stability of Multi-Flexible/Rigid-Body Systems Using Geometrically-Exact Theories: Formulation & Computation

本研究是对发展多柔性/刚体系统动力学统一公式的需求的回应，以及对这些系统运动方程的有效集成的计算方法的发展。这种多体动力学公式的统一是建立在几何精确结构理论的概念之上的，这些理论是非线性的，其中变形的几何形状是精确描述的，变形可能很大。提出了几何精确结构公式可以用于处理具有柔性连杆的闭环链，避免了传统方法所带来的非完整约束的困难。为了实现上述目标，本项目探讨了与柔性多体系统相关的几个具体主题。这些包括1)使用几何精确结构模型开发多体系统的统一公式；2)组份数字/代数方程的精度和稳定性特性研究；3)圆柱节点梁几何精确模型的建立；4)将陀螺弹性材料纳入几何精确梁模型；5)研究在并行计算环境下，实现细胞到细胞的映射，以评估几何精确模型的稳定性。这项研究范围广泛，性质基本，内容跨学科。它的成功完成将对前面提到的统一目标产生可衡量的影响。本文开发的工具可用于评估多柔性/刚体系统的动态响应和稳定性，这些系统在机器人、机器设计、高速地面运输车辆、飞机和航天器技术中很普遍。

This research is a response to the need for the development of a unified formulation for the dynamics of multi flexible/rigid body systems, and for the development of computational methods for efficient integration of the equations of motion of such systems. This unification of multibody dynamics formulations is founded upon the concept of geometrically exact structural theories, theories which are nonlinear in character and where the geometry of deformation is exactly described and deformation can be large. The claim is made that the geometrically exact structure formulation can be used to treat closed loop chains with flexible links and avoid the difficulties imposed by non holonomic constraints when traditional methods are employed. To pave the way to the above stated goal, this project explores several specific topics related to flexible multibody systems. These include 1) development of a unified formulation for multi body systems using geometrically exact structural models; 2) study of the accuracy and stability characteristics of component digital/algebraic equations; 3) formulation of geometrically exact models for beams with prismatic joints; 4) incorporation of gyro elastic material into the geometrically exact beam model; 5) study of the implementation of cell to cell mapping to evaluate the stability of geometrically exact models in a parallel computing environment. This research is broad in scope, fundamental in nature, and interdisciplinary in content. Its successful completion will have a measurable impact on the unification goal alluded to earlier. Tools developed herein can be used to assess the dynamic response and stability of multi flexible/rigid body systems which are prevalent in robotics, machine design, high speed ground transportation vehicles, aircraft and spacecraft technologies.