The integration of nonlinear equations of motion particularly in relation with friction-impact phenomena

The central objective of our investigations into the integration of non-linear equations of motion was to reduce the computing time required for the dynamic analysis of PWR fuel assemblies based on series models. Consequently, our statements below apply primarily to non-linear equations of motion which are set up in this context, Furthermore, however, they comprise considerable information value for other problems in which friction and impact elements are present. It is usual to integrate non-linear equations of motion numerically with the aid of explicit or implicit algorithms (Runge-Kutta algorithm, Newmark algorithm, Houbolt algorithm, Predictor-Corrector procedures). First it is demonstrated that explicit algorithms are superior to the implicit in motion phenomena characterized by a large number of impacts. A Runge-Kutta algorithm of the 4th order requires 4 function evaluations per time increment. The Predictor-Corrector procedures afford far greater ease of calculation where the number of function evaluations is concerned. All in all however, even these algorithms do not possess any decisive advantages over the Runge-Kutta algorithm of the 4th order. (orig./GL)