An Unconditionally Stable Integration Method for Structural Nonlinear Dynamic Problems

• Published in: Mathematics (Basel) Vol. 11; no. 13; p. 2987
• Main Authors: Jia, Chuanguo, Su, Hongchen, Guo, Weinan, Li, Yutao, Wu, Biying, Gou, Yingqi
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.07.2023
• Subjects: Accuracy; Algorithms; Analysis; Control theory; Dampers; Dynamic response; Empirical analysis; Equations of motion; Frame structures; Iterative methods; linearly implicit algorithm; Methods; Motion stability; Newmark-β method; Newton iteration method; nonlinear dynamic problem-solving; Nonlinear dynamics; Root locus; structural nonlinear dynamic problems; Velocity; Viscous damping
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math11132987

This paper presents an unconditionally stable integration method, which introduces a linearly implicit algorithm featuring an explicit displacement expression. The technique that is being considered integrates one Newton iteration into the mean acceleration method. The stability of the proposed algorithm in solving equations of motion containing nonlinear restoring force and nonlinear damping force is analyzed using the root locus method. The objective of this investigation was to assess the accuracy and consistency of the proposed approach in contrast to the Chang method and the CR method. This is achieved by analyzing the dynamic response of three distinct structures: a three-layer shear structure model outfitted with viscous dampers, a three-layer shear structure model featuring metal dampers, and an eight-story planar frame structure. Empirical evidence indicates that the algorithm in question exhibits a notable degree of precision and robustness when applied to nonlinear dynamic problem-solving.