A TIME INTEGRATION ALGORITHM FOR FLEXIBLE MECHANISM DYNAMICS - THE DAE ALPHA-METHOD

This paper introduces a new family of second-order methods for solving the index-2 differential-algebraic equations (DAEs) of motion for fle xible mechanism dynamics. These methods, which extend the alpha-method s for ODEs of structural dynamics to DAEs, possess numerical dissipati on that can be controlled by the user. Convergence and stability analy sis is given and verifies that the DAE alpha-methods introduce no addi tional oscillations and preserve the stability of the underlying ODE s ystem. Convergence of the Newton iteration, which can be a source of d ifficulty in solving nonlinear oscillatory systems with large stepsize s, is achieved via a coordinate-split modification to the Newton itera tion. Numerical results illustrate the effectiveness of the new method s for simulation of flexible mechanisms. (C) 1998 Elsevier Science S.A .