Error estimates and adaptive time stepping for various direct time integration methods

Abstract

In this paper, the global and local error estimates and adaptive time stepping for the various direct time integration in dynamic analysis are presented. A successive quadratic function is used for the locally exact value of the acceleration and the corresponding parameters for the function are obtained from accelerations at three time stations at every time stage. The local error can be estimated simply by comparing the solutions obtained by direct time integration method (Newmark method and Wilson method) with the locally exact solutions. Based on this local error estimate an adaptive time stepping technique in a global sense is proposed. Numerical examples are carried out to verify the performance of the procedure.