Novel Model-Based Integration Algorithm Based on Generalized-α Method

Weinan Guo, Chuanguo Jia, Min Gan (), Yan Zhang and Yutao Li
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Weinan Guo: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Chuanguo Jia: Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China
Min Gan: Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China
Yan Zhang: School of Intelligent Construction, Chongqing College of Architecture and Technology, Chongqing 401331, China
Yutao Li: School of Civil Engineering, Chongqing University, Chongqing 400045, China

Mathematics, 2025, vol. 13, issue 8, 1-21

Abstract: There exist various methods for solving the dynamic analysis problem in earthquake engineering. While numerical integration techniques are conventionally classified as either explicit or implicit approaches, both categories suffer from fundamental constraints that compromise their general effectiveness. A type of model-based integration algorithm combines explicit and implicit algorithm advantages, making it a hot topic in research. Based on the generalized-α algorithms, this study proposes a model-based integration algorithm by embedding upon Newton iteration to make its displacement solution in explicit form. The root locus method was employed to analyze the stability of the algorithm for single-degree-of-freedom systems containing nonlinear restoring force. Two models were selected to verify the algorithm’s accuracy and stability: three-storey and eight-storey shear-type structural systems with metal dampers. The proposed algorithm, Chang method, and CR method were utilized for the dynamic analysis of the emulated systems. The results indicate that the proposed algorithm has high accuracy and favorable stability for nonlinear dynamic problems.

Keywords: nonlinear structural systems; generalized-α methods; Newton iteration method; dynamic response analysis; dynamic response problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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