A Novel Family of Two-Stage Implicit Time Integration Schemes for Structural Dynamics

In this paper, a new family of composite implicit time schemes is developed to overcome some shortcomings of the existing composite schemes. In the development, unconventional time approximations are used for the displacement and velocity vectors. The algorithmic parameters of the approximations are optimized to have improved numerical characteristics. This study also explains some difficulties of the existing implicit composite schemes in dealing with some special types of external force vectors when the splitting ratio is varied over the range of current time interval. Some drawbacks of the existing composite schemes due to the adjustable splitting ratio are resolved in the newly proposed family through different algorithmic parameters. The new schemes can handle the externally applied forces as simple as the Newmark method does, which is impossible in the existing composite schemes. Impact and excitation of elastic bar problems are numerically solved by using the new and existing two-stage schemes, and numerical results are analyzed, illustrating the merit of the proposed schemes.