A unified scheme for nonlinear dynamic direct time integration methods: a comparative study on the application of multi-point methods

In this article, we first present a unified scheme to apply nonlinear dynamic time integration methods. The unified scheme covers many existing time integration methods as exceptional cases. This paper has investigated time integration methods, including the Newmark, Wilson, Houbolt, and rho(infinity)-Bathemethod. We then implement the multi-point methods as the nonlinear solution schemes along with the direct time integration methods in nonlinear dynamic analysis. Also, a unified scheme for applying single-point and multi-point methods is presented. Finally, we demonstrate with numerical examples that the unified scheme provides a framework for comparing direct time integration methods. We also investigate the performance of multi-point methods as nonlinear solution methods in detail.