Spatial Dynamics of Deformable Multibody Systems With Variable Kinematic Structure: Part 1—Dynamic Model

In this paper a method for the spatial kinematic and dynamic analysis of deformable multibody systems that are subject to topology changes is presented. A pieced interval analysis scheme that accounts for the change in the spatial system topology due to the changes in the connectivity between bodies is developed. Deformable bodies in the system are discretized using the finite element method and accordingly a finite set of deformation modes is employed to characterize the system vibration. Even though there are infinitely many arrangements for deformable body axes, computational difficulties may be encountered due to the use of a limited number of deformation modes. Therefore, the deformable body references have to be carefully selected, and accordingly as the system topology changes, new bases for the configuration space have to be identified. In order to guarantee a smooth transition from one configuration space to another, a set of spatial interface conditions or compatibility conditions that are formulated using a set of nonlinear algebraic equations are developed and solved in this paper. The solution of these equations uniquely define the spatial configuration of the deformable multibody system after the change in the system kinematic structure.