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An Explicit and Highly Accurate Runge-Kutta Family | ||
| Civil Engineering Infrastructures Journal | ||
| دوره 56، شماره 1، شهریور 2023، صفحه 51-78 اصل مقاله (2.07 M) | ||
| نوع مقاله: Research Papers | ||
| شناسه دیجیتال (DOI): 10.22059/ceij.2022.330788.1792 | ||
| نویسندگان | ||
| Mohammad Rezaiee-Pajand* 1؛ S. AH. Esfehani2؛ H. Ehsanmanesh3 | ||
| 1Professor, Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran. | ||
| 2M.Sc., Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran. | ||
| 3B.Sc., Department of Electrical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran. | ||
| چکیده | ||
| In this paper, an explicit family with higher-order of accuracy is proposed for dynamic analysis of structural and mechanical systems. By expanding the analytical amplification matrix into Taylor series, the Runge-Kutta family with stages can be presented. The required coefficients ( ) for different stages are calculated through a solution of nonlinear algebraic equations. The contribution of the new family is the equality between its accuracy order, and the number of stages used in a single time step ( ). As a weak point, the stability of the proposed family is conditional, so that the stability domain for each of the first three orders ( 5, 6, and 7) is smaller than that for the classic fourth-order Runge-Kutta method. However, as a positive point, the accuracy of the family boosts as the order of the family increases. As another positive point, any arbitrary order of the family can be easily achieved by solving the nonlinear algebraic equations. The robustness and ability of the authors’ schemes are illustrated over several useful time integration methods, such as Newmark linear acceleration, generalized-𝛼, and explicit and implicit Runge-Kutta methods. Moreover, various numerical experiments are utilized to show higher performances of the explicit family over the other methods in accuracy and computation time. The results demonstrate the capability of the new family in analyzing nonlinear systems with many degrees of freedom. Further to this, the proposed family achieves accurate results in analyzing tall building structures, even if the structures are under realistic loads, such as ground motion loads. | ||
| کلیدواژهها | ||
| Accuracy؛ Linear and Nonlinear Dynamic Systems؛ Stability؛ Tall Building Structure؛ Taylor Series | ||
| مراجع | ||
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