An Efficient Nondissipative Higher-Order Single-Step Integration Method for Long-Term Dynamics Simulation

For long-term simulation of dynamic problems, it is desirable for the integration method to capture higher-order accuracy, while maintaining zero numerical damping. To this end, this paper proposes an efficient four-parameter single-step method (FPSM), which only adds two vector operations per step compared with the Newmark method. For linear analysis, these four parameters can be uniquely determined and the generated optimal scheme possesses several desirable attributes, such as nondissipation for undamped systems, fourth-order accuracy and an enough stability interval. Compared with existing nondissipative methods, such as the central difference method and the trapezoidal rule, the present method is recommended for general use due to its high accuracy and efficiency. Finally, several numerical examples are prepared to validate these superiorities of the proposed method.