刚体系统的优化方法数值模拟

发布时间：2018-01-18 01:26

本文关键词：刚体系统的优化方法数值模拟　出处：《青岛理工大学》2015年硕士论文　论文类型：学位论文

【摘要】：微分-代数混合方程组是对受约束的多刚体系统建模后得到的动力学方程,在对其进行数值运算及仿真的过程中,往往会遇到以下难点:(1)方程积分过程中出现速度及位移的违约问题;(2)系统方程的质量矩阵奇异问题;(3)冗余约束所导致的约束雅可比矩阵奇异问题等等。本文的目标是研究能够克服上述困难的新的建模方法及数值求解策略,其主要工作如下:(1)基于广义坐标形式的高斯最小拘束原理建立多刚体系统动力学优化形式的数值求解框架,采用智能优化方法中的遗传算法对所构造出的极值函数求出满足条件的最优值,并通过逐步积分法来模拟出系统的运动规律。该方法无需建立系统运动微分方程,且可与优化分析相结合,解决含有控制的动力学问题,同质点形式的高斯最小拘束原理相比,建模方式更加简单且效率更高。(2)研究了将Udwadia和Kalaba所提出的显式方程(简称U-K方法)应用到多刚体系统中。U—K方法给出了系统运动的加速度的显示表达形式,不论所研究的多体系统的约束是否是完整的,所受约束是否理想,它都可以使用,具有广泛的使用范围。在解决复杂的多刚体系统动力学问题方面,U—K方法提供了一种新的建模思路。(3)使用上述两种方法针对位移方程和速度方程的违约以及系统的奇异性问题进行了研究,研究结果表明:同目前经典的微分-代数方程组的求解方法的比较中,该两种方法可以更有效地解决违约问题;针对奇异性问题可以直接建立多刚体系统运动的数学模型,不需要对系统建模方程再次进行修正及对系统的约束条件进行调整,可以直接得出系统运动的加速度,具有更强的通用性。
[Abstract]:Differential algebraic equations of dynamic equations modeling of multi rigid body constrained system after, in the process of calculation and numerical simulation on it, often encounter the following problems: (1) the default speed and displacement equation of the integration process; (2) the quality of the matrix singularity problem system; (3) the redundant constraint constraint Jacobi matrix singularity problem and so on. The goal of this paper is to study the new modeling method to overcome these difficulties and solving strategies, the main work is as follows: (1) the numerical solution of dynamic optimization framework in the form of the Gauss minimum constraint principle of generalized coordinate form of the establishment of a multi rigid body system based on the intelligent optimization genetic algorithm for extremal function constructed to derive the optimal values satisfying the conditions, and through the step-by-step integration method to simulate the system. The movement law of the method To establish the system of differential equations of motion, and the analysis and optimization of the combination of solving dynamics problems with control, compared to the Gauss minimum constraint principle of homogeneous form, modeling method is more simple and more efficient. (2) studied the explicit Udwadia and Kalaba proposed process (U-K method) is applied to.U K method of multi rigid body system is given to show the system motion acceleration expression, whether the multi-body system of whether constraints are complete, the constraints are ideal, it can be used for a wide range of application. To solve the problem of complex multi rigid body system dynamics, provides a a new method for modeling U - K method. (3) the singularity problem using the above two methods for the displacement and velocity equation and the default system was studied, the results show that: with the classical differential generation The calculation method of the number of equations in the two kinds of methods can effectively solve the problem of default; mathematical model for the singular problem can directly establish multi rigid body motion of the system, does not require the modeling of the system equations again correction and constraint on the system to adjust, can directly obtain the system motion acceleration, general which is more.

【学位授予单位】：青岛理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O313.3;O175

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