An adaptive time integration strategy based on displacement history curvature

TL;DR

This paper presents a novel adaptive time integration strategy using displacement history curvature to improve computational efficiency in dynamic simulations, applicable across various numerical methods.

Contribution

It introduces a curvature-based refinement estimator for adaptive time stepping, offering a low-cost, versatile alternative to existing error estimators in dynamic analysis.

Findings

Effective in reducing computational cost

Compatible with multiple integration methods

Maintains accuracy with adaptive time steps

Abstract

This work introduces a time-adaptive strategy that uses a refinement estimator based on the first Frenet curvature. In dynamics, a time-adaptive strategy is a mechanism that interactively proposes changes to the time step used in iterative methods of solution. These changes aim to improve the relation between quality of response and computational cost. The method here proposed is suitable for a variety of numerical time integration problems, e.g., in the study of bodies subjected to dynamical loads. The motion equation in its space-discrete form is used as reference to derive the formulation presented in this paper. Our method is contrasted with other ones based on local error estimator and apparent frequencies. We check the performance of our proposal when employed with the central difference, the explicit generalized-alpha and the Chung-Lee integration methods. The proposed refinement estimator demands low computational resources, being easily applied to several direct integration methods.