中文摘要：

针对多体系统的非线性受约束动态优化设计通用模型，基于连续可微目标函数和一阶、二阶灵敏度分析给出多体系统动力学优化设计的增广Lagrange乘子法。其中基于多体系统动力学方程的一阶设计灵敏度采用伴随变量方法进行计算，二阶设计灵敏度使用混合方法进行计算，在设计变量较多时具有较高的计算效率。最后对曲柄一滑块系统数值算例使用增广Lagrange乘子方法进行约束优化，通过对使用不同方法进行一阶灵敏度分析和二阶灵敏度分析所得的最优值、迭代次数及运行时间的比较，得出一阶灵敏度分析中使用变尺度方法效率较高，而使用二阶灵敏度分析可以进一步提高优化效率。

英文摘要：

Based on the continuous and dffferentiable objective function and the first and second order sensitivity analysis of nonlinear dynamic optimization model of constrained multibody system dynamics, the augmented Lagrange method of general optimization design model of multibody systems was presented. Effective methods based on first order and second order sensitivity analysis, in which the adjoint variable method and hybrid method were introduced respectively, were used in optimization process. The numerical example of a slider-crank mechanism validates the accuracy and efficiency of the methods finally. Through the compare of the best values, iteration numbers and run times by different methods for the first and second order sensitivity analysis, the variable metric method is found to be more effective in the first order sensitivity analysis and the optimization efficiency can be improved by second order sensitivity analysis.