具有多种非光滑接触刚柔耦合多体系统动力学的建模与算法研究

In the context of engineering problems about aeronautics, astronautics, machinery and vibration,.this project is the research on the non-smooth multibody dynamics of rigid-flexible systems with point-surface contact, line-surface contact, surface-surface contact and 1D&2D friction. The contact force models are given using the modern theories of contact mechanics and tribology. flexible bodies in the system are discretized using the method of finite element or ANCF. The multibody dynamic equations of rigid-flexible systems with multiple non-smooth contact are obtained by the method for multibody dynamics with unilateral contacts. The algorithms for detecting the non-smooth events such as stick-slip and contact-separation are presented using differential inclusion, complementarity theory and modern computing technology. According to motion characteristics of the system, such as structural vibration and the large motion of rigid-flexible systems, the methods for solving dynamic equations of the systems are given using modern computing methods (implicit algorithm，explicit algorithm, optimization algorithm and parallel algorithm）and these methods have high calculate precision, high calculate speed and computing stability during long time. The models and methods in this projiect are validated by numeircal simulations and physical experiments. The research methods and results in this project are necessary tools for studying the dynamics of rigid-flexible systems with multiple non-smooth contacts in engineering practice.

本项目以航空、航天、机械和振动等领域中的工程问题为背景，研究具有点与面接触、线（棱）与面接触和面与面接触且含一维和二维摩擦(含干摩擦)刚柔耦合多体系统动力学的建模方法与数值算法。应用现代接触力学和摩擦学的相关理论，建立点、线、面多种接触状态的接触力学模型；用有限元法和绝对节点坐标法等，建立柔性体的力学模型；用单边接触多体动力学方法，建立具有多种非光滑接触的刚柔耦合多体系统动力学方程；基于微分包含和互补理论，以及现代计算技术，给出非光滑事件（滑移与粘滞、接触与分离）的检测算法；利用现代数值计算方法（显式算法、隐式算法、优化算法和并行算法等），根据系统的特点（结构振动、刚柔耦合大范围运动）给出动力学方程的数值算法，使其具有计算精度高、速度快且能保持长期数值计算的稳定性。用数值仿真和物理实验验证模型与方法的合理性。相关成果将为研究具有多种非光滑接触刚柔耦合系统动力学的实际工程问题提供必要的工具。

在机械系统中普遍存在多种非光滑接触力，当物体间出现接触-分离和黏滞-滑移现象时，接触力呈现出非光滑特性，给动力学方程的建立及其数值计算带来困难。基于扩展的Hertz接触模型、Coulomb摩擦模型、LuGre摩擦模型，建立了多体系统的力学模型；用第一类或第二类Lagrange方程或牛顿-欧拉方法得到了该系统的动力学方程；结合LCP、DAE、ALE等方法给出非光滑动力学方程的显式或隐式的数值计算方法，能有效地揭示机械系统中非光滑转动铰和移动铰的接触与分离、黏滞与滑移现象，可提高计算的精度和速度，有助于分析浮放物体、被动行走器、环形机器人、振动驱动机器人、两轮无人自行车和绳索驱动机械臂的动力学特性。在项目执行期间，发表期刊论文18篇，4名博士研究生和4名硕士研究生毕业，17人次参加国际和国内会议，2名教师晋升为教授。