New Formulation for Dynamic Analysis of Nonlinear Time-History of Vibrations of Structures under Earthquake Loading

A fast and efficient numerical scheme is presented for time-history analysis of single-degree-of-freedom (SDOF) structural systems undergoing seismic excitation (Chopra, 2003). The new method is called Newton-Cotes-4P-θ Method. It uses the most known 4-point Newton-Cotes quadrature in its body to solve the vibration equation. Nonlinear analysis is covered as well as linear analysis. Any arbitrary external loadings of type force or seismic signals are welcome. The significant advantages of the new formulation are its great simplicity, running speed, and appropriate precision level compared with its counterparts such as Duhamel integral and Newmark-β methods. The accuracy level of the Newton-Cotes-4P-θ is close to the semi-analytical method of Duhamel integration and its speed is similar to the Newmark-β algorithm. Notably, against the nonlinear Newmark-β method, the new method does not require a standalone procedure to handle nonlinear analysis; instead, it simply triggers iteration of the same computation used in its first processing round. Moreover, the Newmark-β method loses its performance dealing with stiff and near-conservative () systems; however, the Newton-Cotes-4P-θ method does not loos its accuracy and keeps its well-performed analysis in this case. Numerical results reveal the superiority of the Newton-Cotes- 4P-θ method against its counterparts such as the Duhamel integral, Newmark-β, and Wilson-θ methods (Babaei et al., 2021; Babaei et al., 2022; Babaei et al., 2023).