A Novel Numerical Method for Nonlinear Time History Analysis of MDOF Structures: Newton-Cotes-Hermite-4Point

Articles in Press

Document Type : Original Article

Authors

1 Assistant professor, Department of Civil Engineering, University of Bonab, Bonab, Iran

2 M.S. of Structural Engineering, Department of Civil Engineering, University of Bonab, Bonab, Iran

3 M.S. Student of Construction Management and Engineering, Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran

10.22065/jsce.2023.400538.3134

Abstract

This paper presents an efficient numerical analysis method called the Newton-Cotes-Hermite-Four-Point (NCH-4P) method for the time history analysis of structural systems with one and multiple degrees of freedom under earthquake effect. The method combines the numerical integration formula of the Newton-Cotes four-point method with the Hermite interpolation formulas to form a new algorithm for solving the vibration equation. The method can handle both linear and nonlinear systems, as well as different types of loading, such as external forces and earthquake excitation. The method is developed for the first time for the analysis of linear and nonlinear damped and undamped structural systems with one and multiple degrees of freedom. The method shows remarkable performance superiority in terms of accuracy, speed, convergence and simplicity compared to the pseudo-analytical Newmark-beta method and the semi-analytical Duhamel integral method. The method modifies the differential equation of motion to have a suitable form for numerical integration. Unlike the nonlinear Newmark-beta method, the method does not require an independent process such as Newton’s iteration to account for nonlinear effects; instead, a series of simple repeated calculations leads to the convergence of the response in nonlinear behavior. The numerical results demonstrate the efficiency of the method in estimating the response of systems under the famous EL-Centro record.

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Main Subjects

Journal of Structural and Construction Engineering

Articles in Press, Accepted Manuscript
Available Online from 17 November 2023

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History

  • Receive Date: 09 June 2023
  • Revise Date: 19 October 2023
  • Accept Date: 17 November 2023

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