A computational procedure for the dynamics of flexible beams within multibody systems

This dissertation is concerned with the dynamic analysis of three-dimensional elastic beams which experience large rotational and large deformational motions. To this end, the beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which account for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. Due to the inertial reference of the beam kinematics and the convected reference of the beam stresses, the present formulation is easily interfaced with general multibody dynamics methodologies as well as software modules for active control simulations.; The numerical treatment of the beam formulation is considered in detail. A procedure to compute the beam internal force is derived from the continuum formulation. The procedure is proven to be invariant to arbitrary rigid motions of the beam while accurately modeling the beam strain. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems.; The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a spacetime finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.