Assessment of Finite Element Approximations for Nonlinear Flexible Multibody Dynamics

Systematic investigation is made of effects of kinematic assumptions and finite element approximations in the context of nonlinear flexible multibody dynamics. Two nonlinear beam finite elements are consistently derived from virtual work principle using Bernoulli Euler and Timoshenko beam kinematics. Initial assessment is made by studying convergence properties of element formulations with eigenvalue problems free vibration, static buckling, and dynamic buckling. Equations of motion are derived for rigid central body with flexible appendage using virtual work principle. Virtual work principle allows natural and consistent discretization of flexible appendage using finite element method. Nonlinearities in flexibility are explored through dynamics examples using beam finite elements. Application of dynamics formulation is made to a realistic scenario involving space shuttle remote manipulator arm with attached payload. Contribution of nonlinear theory, in both formulation and solution, is assessed.