A series of energy conserving algorithms for structural dynamics

Abstract

Abstract A series of step‐by‐step integration methods has been effectively developed which does not increase the total number of equations of motion and avoids the use of the derivatives of external force. The well‐known Newmark β method [16] with β = 1/4 is the lowest order of accuracy of this series of methods. All the algorithms of this series are unconditionally stable, without overshoot in displacement or in velocity, and they do not possess any numerical dissipations. The rapid changes of dynamic loading can be automatically overcome. It is also verified that the higher the order of the integration method, the more accurate. Consequently, the higher‐order algorithms of this series allow the use of a large time step in step‐by‐step dynamic analysis. Thus, they are competitive in dynamic analysis, especially when the response of a long duration is of interest.