Flexible multibody dynamic simulation

Formulations and numerical algorithms for dynamic simulation of flexible multibody systems are developed. For bodies that undergo large gross motion accompanied by small elastic deformation, a modal body formulation is developed, using deformation mode coordinates in conjunction with lumped inertia models. An optimal inertia lumping method and a system-level component mode approach are developed for use with the modal body formulation. The optimal inertia lumping method uses modal mass matrices obtained from structural analysis and minimizes error in approximating modal momentum of a flexible body. System-level component modes are component modes that are derived using a complete system finite element model. Extraction of rigid-body modes from the system-level component modes is carried out by maximizing strain energy, for unit displacement norm. Dependency, or near dependency, in the resulting set of deformation modes is identified and removed using a method based on singular value decomposition.; For bodies that undergo large gross motion and large, geometric and material nonlinear deformation, a general body formulation is presented. This formulation allows use of existing nonlinear finite element technology and can be implemented in a multibody dynamic simulation.; Finally, the rigid body formulation, modal body formulation, and general body formulation are synthesized to obtain a general flexible multibody dynamics formulation. Nonlinear kinematic constraints between bodies are enforced using the Lagrange multiplier method. Linear kinematic constraints between bodies are enforced by eliminating dependent generalized coordinates in a assembly process. The resulting differential-algebraic equations are solved using a method that is based on the generalized coordinate partitioning algorithm. The formulation and solution methods are implemented by developing a software that integrates a spatial multibody dynamic analysis software and a pilot nonlinear finite element analysis code.; For each of the formulations and computational algorithms developed, numerical examples are provided to demonstrate their validity.