This research is a response to the need for the development of a unified formulation for the dynamics of multi flexible/rigid body systems, and for the development of computational methods for efficient integration of the equations of motion of such systems. This unification of multibody dynamics formulations is founded upon the concept of geometrically exact structural theories, theories which are nonlinear in character and where the geometry of deformation is exactly described and deformation can be large. The claim is made that the geometrically exact structure formulation can be used to treat closed loop chains with flexible links and avoid the difficulties imposed by non holonomic constraints when traditional methods are employed. To pave the way to the above stated goal, this project explores several specific topics related to flexible multibody systems. These include 1) development of a unified formulation for multi body systems using geometrically exact structural models; 2) study of the accuracy and stability characteristics of component digital/algebraic equations; 3) formulation of geometrically exact models for beams with prismatic joints; 4) incorporation of gyro elastic material into the geometrically exact beam model; 5) study of the implementation of cell to cell mapping to evaluate the stability of geometrically exact models in a parallel computing environment. This research is broad in scope, fundamental in nature, and interdisciplinary in content. Its successful completion will have a measurable impact on the unification goal alluded to earlier. Tools developed herein can be used to assess the dynamic response and stability of multi flexible/rigid body systems which are prevalent in robotics, machine design, high speed ground transportation vehicles, aircraft and spacecraft technologies.
