Nonlinear structural dynamics via Newton and quasi-Newton methods

Abstract This paper is an attempt to compare Newton and quasi-Newton methods in nonlinear structural dynamics. After a review of the classical iterative methods, several quasi-Newton updates are presented and tested. Special attention is devoted to the solution of large sparse systems for which two original procedures are described: a substructure correction and a vectorial correction. The numerical examples presented include the dynamic analyses of geometrical, material and combined nonlinearities. All the results are assorted with a complete discussion of the different methods used, of the convergence rates and of the associated computer costs. From the present results, Newton's methods appear to exhibit the best convergence rates when an efficient computational strategy is adopted. Nevertheless computational costs for the solution of large systems can be reduced drastically by using convenient quasi-Newton updates.