<i>A posteriori</i> local error estimation and adaptive time‐stepping for newmark integration in dynamic analysis

Abstract

Abstract A simple a posteriori local error estimate for Newmark time integration schemes in dynamic analysis is presented, based on the concept of a so called ‘post‐processing’ technique. In conjunction with the error estimate, an adaptive time‐stepping algorithm is described, which adjusts the time step size so that the local error of each time step is within a prescribed error tolerance. Numerical examples given in the paper indicate that the error estimate is asymptotically convergent, computationally efficient and convenient, and the adaptive time‐stepping scheme can predict a nearly optimal step size from time to time, thus making the numerical solution reliable in an efficient manner.