多体系统中的冗余约束

STUDY ON REDUNDANT CONSTRAINTS IN MULTIBODY SYSTEMS

冗余约束主要起因于系统奇异构型以及切断铰约束方程的自动生成,它的存在对多体系统建模和求解都提出了更高的要求.为了使系统运动方程可解,需要从系统约束中分离出一组独立约束,不同的独立约束组往往造成数值分析结果的不同,但该文严格证明了理论上它们是一致的.冗余约束在很大程度上加大了系统奇异构型附近违约量控制的难度.针对这一困难,该文提出了一种将约束稳定化和违约修正相结合的方法,数值算例证明了方法的有效性.鉴于物体的受力分析是实际工程的迫切需要也是多体系统动力学核心任务之一,研究了冗余约束对约束反力的影响,给出了判别铰约束反力是否唯一的实用准则,针对两个铰连接同一对物体而引起的冗余约束,提出了铰合成原理及其求解各自铰内接触力的方法,并通过数值算例说明了方法的可行性.

Resulted from singular configuration and cut joint constraint equations generated in a programmed way,redundant constraints in multibody systems exert great influence on the methods for modeling and solving multibody systems.It is necessary to select a group of independent equations from whole constraint equations in order to keep the system control equation solvable.It is observed that numerical results are usually changed by different choices,but they should be same theoritically as proven rigorously in this paper.Due to constraints violation,many methods for solving DAE lose their effectiveness near by the position corresponding to the singular configuration of multibody systems.Based on the combination of constraints stabilization and elimination of constraint violation,we present a method to overcome such difficulties and testify its validness by an example.It is the greatest negative effect brought by redundant constraints that forces of interaction between bodies may be not unique.A criterion to certify which and when a constraint force would be definite is given.It is known that when a pair of bodies is linked by more than one joint,the reaction forces in those joints would be ambiguous.This paper presented a method of making the reaction forces definite in such case by replacing those joints with a single composed one.