An adaptive time integration strategy based on displacement history curvature

摘要

This work introduces a time-adaptive strategy that uses a refinementestimator based on the first Frenet curvature. In dynamics, a time-adaptivestrategy is a mechanism that interactively proposes changes to the time stepused in iterative methods of solution. These changes aim to improve therelation between quality of response and computational cost. The method hereproposed is suitable for a variety of numerical time integration problems,e.g., in the study of bodies subjected to dynamical loads. The motion equationin its space-discrete form is used as reference to derive the formulationpresented in this paper. Our method is contrasted with other ones based onlocal error estimator and apparent frequencies. We check the performance of ourproposal when employed with the central difference, the explicitgeneralized-alpha and the Chung-Lee integration methods. The proposedrefinement estimator demands low computational resources, being easily appliedto several direct integration methods.