BLOCK-DIAGONAL EQUATIONS FOR MULTIBODY ELASTODYNAMICS WITH GEOMETRIC STIFFNESS AND CONSTRAINTS

This paper presents a comprehensive, block-diagonal matrix formulation of the equations of motion of a system of hinge-connected flexible bodies undergoing large rotation and translation together with small elastic vibration. ne formulation compensates for premature linearization of equations, associated with the customary treatment of small elastic displacement, by accounting for geometric stiffness due to inertia as well as interbody forces. The algorithm is first developed for a tree configuration and is then extended to the case of dosed structural loops by cutting the loops and expressing all of the kinematical variables into terms dependent and free of constraint forces/torques. A solution procedure satisfying constraints is given.