Two dynamic explicit methods based on double time steps

Abstract

The primary purpose of this paper is to develop novel fast dynamic methods for large-scale problems of structural dynamics at the least computational efforts. The explicit method of double time steps (EMDTS) is proposed through integration with the assumption of linear acceleration in two time steps. The corrected explicit method of double time steps (CEMDTS) is obtained after correcting the EMDTS. The analyses of stability, accuracy, numerical dissipation and dispersion are performed on the proposed methods. Finally, both linear and nonlinear numerical examples are utilised for the comparison of the two new methods and the established methods. The results show that the EMDTS is unstable in undamped linear systems; however, the CEMDTS has a nondissipative property and the same stability condition as the explicit central difference method (ECDM). The amplitude error of the EMDTS is greater than that of the CEMDTS and the ECDM when the time step is large. The CEMDTS possesses excellent comprehensive properties with less damping ratio error and periodic error than the ECDM in the case of small time steps at almost the same computational efforts. Three numerical examples manifest that the CEMDTS is better than the EMDTS, and endowed with good accuracy and stable properties.