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

这项研究是对发展一种 多柔/刚体动力学的统一公式 系统，并为计算方法的发展， 有效地整合这些系统的运动方程。 这种统一的多体动力学公式是建立在 根据几何精确结构理论的概念， 这些理论在性质上是非线性的， 变形的精确描述和变形可以是大的。 有人声称，几何上精确的结构 配方可用于处理具有柔性的闭环链， 链接和避免非完整性带来的困难 在使用传统方法时， 铺平 为了实现上述目标，本项目探讨了几个 与柔性多体系统相关的特定主题。 这些 包括：1）建立多体统一计算公式 使用几何精确结构模型的系统; 2）研究 元件精度和稳定性特性 数字/代数方程; 3）几何公式 棱柱形节点梁的精确模型; 4） 陀螺仪弹性材料的几何精确梁模型; 5） 研究细胞到细胞映射的实施，以评估 几何精确模型的稳定性 计算环境 这项研究的范围很广， 本质上是基础性的，内容上是跨学科的。 其 成功完成将对 前面提到的统一目标。 在此开发的工具可以 可用于评估多个系统的动态响应和稳定性 在机器人技术中普遍存在的柔性/刚性体系统， 机械设计，高速地面运输车辆， 飞机和航天器技术。

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.