具有完整与非完整约束刚柔耦合非光滑多体系统动力学数值算法研究

In the context of engineering problems about aeronautics, astronautics, mechanical vehicle and the high-rise building, this project is the research on the non-smooth dynamics of rigid-flexible multibody systems with holonomic and nonholonomic constraints, friction and impact,. The dynamic equations of the systems are derived by using the Lagrange equations of the first kind and Routh equations. The deformations of flexible bodies in the systems are described by the absolute nodal coordinate formulation or the method for modal analysis. The non-smooth events (contact and separation, slip and stick) in the systems are detected by the trial-and-error method and linear or nonlinear complementary theory. Using the theory of measure differential inclusion, combined with Baumgarte constraint stabilization method, the numerical method for the dynamical equations of the systems is obtained in order to improve the accuracy of numerical calculation and to keep the stability of the numerical calculation in long-term integration. The research methods and results in the project are necessary tools for modeling and analysing some practical engineering problems，such as vehicle dynamics problems, dynamical analysis of aircraft landing, vibration reduction of high-rise building etc, which are treated as the non-smooth dynamics of rigid-flexible multibody systems with holonomic and nonholonomic constraints, friction and impact..

以航空航天、机械车辆和高层建筑中的工程问题为背景，研究具有完整与非完整约束考虑摩擦与碰撞等非光滑因素的刚柔耦合多体系统动力学问题。利用第一类Lagrange方程和Routh方程建立系统的动力学方程；应用绝对节点坐标法或模态法描述柔性体的变形；应用试算法、线性互补或非线性互补理论给出非光滑事件（接触与分离、滑移与粘滞）的检测方法；利用测度微分包含理论，结合Baumgarte约束稳定化方法，给出具有约束稳定化的该系统动力学方程的数值计算方法，以提高数值计算的精度，使其可保持长期数值计算的稳定性。本项目的研究方法与成果将为分析研究具有完整与非完整约束刚柔耦合非光滑多体系统的某些实际工程问题（如车辆动力学问题、飞机着陆的动力学响应分析、高层建筑物的减振等）提供必要的建模方法和数值计算方法。

以项目申请书立论依据中的工程问题(航空、航天、机械、车辆、建筑)为背景，本项目研究了具有完整与非完整约束包含有摩擦与碰撞刚柔耦合多体系统动力学的数值算法。用第一类Lagrange、Routh方程和Newton-Euler方法，建立上述工程问题中具有完整或非完整约束多刚体或刚柔耦合非光滑多体系统的动力学方程；应用绝对节点坐标法或弹性力学理论描述了柔性体的变形；应用试算法、线性互补或非线性互补理论，给出了非光滑事件（接触与分离、黏滞与滑移）的检测方法；结合Baumgarte约束稳定化方法，利用微分包含理论，给出了求解该类非光滑多体系统动力学方程的数值计算方法，提高了数值计算的精度，可保持长期数值计算的稳定性。本项目的研究方法与成果可用于研究与分析某些实际工程问题，如车辆动力学问题、飞机着陆的动力学分析、具有单边接触非光滑多体系统动力学仿真以及有完整与非完整约束刚柔耦合非光滑多体系统的动力学分析。