多体系统动力学动态最优化设计与灵敏度分析

基于多体系统的动态最优化设计过程包括传统的多体系统仿真分析、系统设计灵敏度分析、 系统最优化设计等过程, 针对多体系统运动学、用二阶常微分方程和微分代数方程描述 的动力学，基于含设计参数的通用数学模型及通用的积分型目标函数，采用高效的系统灵 敏度分析伴随变量方法及易于实施的惩罚函数最优设计方法，建立了多体系统最优设计数学 模型和算法. 通过双摆系统、曲柄-滑块系统、弹簧/阻尼器-滑块系统3个算例对上述 算法的有效性进行了验证.

Dynamic Optimization of Multibody System Dynamics and Adjoint Variable Method for Design Sensitivity Analysis

Dynamic optimization based on multibody system dynamics is a complex process, which composed of traditional analysis and simulation of multibody system dynamics, design sensitivity analysis and iterative processes of optimization. A penalty function method for multibody system dynamic optimization is presented based on kinematics described by algebraic equations and dynamics described by second order ordinary differential equations or differential/algebraic equations which include design parameters. Based on the above equations and a general objective functions of integral type, the corresponding adjoint variable methods for sensitivity analysis are constructed. Finally, three numerical examples include double pendulum, slide-crank system and spring-mass system validate the method presented in this paper.