Linear implicit algorithm with embedded Newton iteration and its application in nonlinear dynamic analysis of structures

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (9) : 177-188.

JIA Chuanguo1,2, ZHAO Jinji2, LI Xing2, GOU Yingqi2

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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.

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nonlinear structures / the average acceleration method / Newton iteration method / dynamic response / analysis

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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[J]. Journal of Vibration and Shock, 2023, 42(9): 177-188

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