有限转动张量的保角参量及在多柔体系统中的应用

PARAMETERS FOR FINITE ROTATIONAL TENSOR AND ITS APPLICATION IN MULTIBODY SYSTEMS

采用保角转动参数描述了多体系统中的大转动张量．该方法消除了传统的欧拉参数描述所必需的约束方程，并且适于大变形部件的建模需要．利用以上结果建立了含大变形梁状部件的多体系统的力学模型．

Large deformation of components in multibody systems is usually caused by relativelylarge rotation between the particles in the component. Finite rotational tensors are used to describelarge rotation. To model the motion of the component with finite element methods, the finiterotational tensor must be approximated by nodal paxameters and shape functions. What kind ofparameters are used to represent finite rotational tensor is a fundamental aspect in formalism ofmultibody systems. Euler parameters are most commonly employed in view of their propertiesof avoiding the singularities. However, Euler parameters are not independent each other, a nonlinear constraint of normality links them. But it is very difficult to find shape functions that canmake Euler parameters satisfy the constraint. Conformal rotation vector obtained by a conformaltransformation on Euler parameters can fully describe finite rotational tensors using three freeparameters. And its singularity of representation only occurs on rare occasions in application.A technique for representing finite rotational tensors, angular velocity vector and angularacceleration vector in terms of conformal rotation parameters is described. The multibody systemwith beam shape components whose deformation may be large is studied. The motion of particleson the cross section of the beam is represented by the translation of the point of the center of massand rotation of the whole cross section. The finite rotational tensor that describes the rotation isrepresented by the conformal rotational parameters. Finally, equations of the motion of multibodysystems are presented.l) The project supported by the National Science Foundation of China (19672011).