Abstract: The hierachical finite element technique has been applied in the time domain and a step-by-step integration method with high accuracy has been developed in this paper. The degrees of the hierachical finite element can be raised freely using the technique to reach the prescribed accuracy.It is a very effective method for some engineering problems. Wilson-θ method and the Sun Huanzhun method are special cases of this method.

Key words: hierachical finite element, finite element in time do-main, dynamic response.