A simple local error estimator and an adaptive time‐stepping procedure for direct integration method in dynamic analysis

Abstract

AbstractA simple a posteriori local error estimator for time discretization in structural dynamic analysis is presented. It is derived from the difference of the solutions between an ordinary integration method (the Newmark scheme) and another higher‐order one which assumes that the derivatives of accelerations vary linearly within each time step. It may be obtained directly without resolving new equations, so the additional computational cost is small and the implementation is convenient. Furthermore, it is shown that this error estimator may also be obtained by Taylor expansion or by a post‐processing technique. Accordingly, an adaptive time‐stepping procedure, which automatically adjusts the time‐step size so that the local error at each time step is within a prescribed accuracy, is described. Numerical examples, including two single‐DOF problems, a two‐DOF problem and a multi‐DOF model, are presented. The results show that the presented local error estimator is simple, reliable and accurate.