Linear implicit algorithm with embedded Newton iteration and its application in nonlinear dynamic analysis of structures
JIA Chuanguo1,2, ZHAO Jinji2, LI Xing2, GOU Yingqi2
1.Key Laboratory of New Technology for Construction of Cities in Mountain Area, Ministry of Education, Chongqing University, Chongqing 400045, China;
2.School of Civil Engineering, Chongqing University, Chongqing 400045, China
Abstract：In this paper, the strategy of Newton iteration is introduced into the average acceleration method. A novel linear implicit numerical integration algorithm is derived by embedding once Newton iteration in the method with the acceleration term as the iteration variable. Then, according to discrete control theory and root locus method, the conditions for maintaining stability of the novel algorithm is derived when the novel algorithm is used to solve the structure with nonlinear restoring forces and nonlinear damping forces. Meanwhile, a single-degree-of-freedom shear- type structure is used to exam the stability of the novel algorithm in solving the problem with nonlinear restoring forces and nonlinear damping forces. Finally, the applicability and reliability of the novel algorithm in solving problems of multi-degree-of-freedom structures with nonlinear restoring forces and nonlinear damping forces is proved through numerical simulations.
贾传果1,2，赵进级2，李兴2，苟英旗2. 内嵌牛顿迭代的线性隐式算法及其在结构非线性动力分析中的应用[J]. 振动与冲击, 2023, 42(9): 177-188.
JIA Chuanguo1,2, ZHAO Jinji2, LI Xing2, GOU Yingqi2. Linear implicit algorithm with embedded Newton iteration and its application in nonlinear dynamic analysis of structures. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(9): 177-188.
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