Two-Level Consistent Secant Operators for Cyclic Loading of Structures
Publication: Journal of Engineering Mechanics
Volume 144, Issue 8
Abstract
Two-level consistent secant operators are proposed for the nonlinear simulation of structures especially under cyclic loading. At the structural level, the quasi-Newton (Q-N) update of stiffness matrix is used to search the equilibrium of the overall system. At the material level, the general formulas of secant operators are proposed for the nonlinear material model. The consistency between the Q-N stiffness matrix at the structural level and the secant operator at the material level is proposed and considered as a good trade-off between efficiency and robustness. Applications are made to numerical examples that include strain-softening and cyclic loading. Significant improvements are demonstrated in relation to the full Newton methods and the inconsistent secant methods.
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Acknowledgments
Financial support from the National Science Foundation of China (Grant Nos. 51261120374, 51678439, and 51208374) and the Fundamental Research Funds for the Central Universities are sincerely appreciated. The authors also thank Dr. De-Cheng Feng at Southeast University for valuable suggestions and kind help.
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 8 • August 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Apr 16, 2017
Accepted: Feb 12, 2018
Published online: May 31, 2018
Published in print: Aug 1, 2018
Discussion open until: Oct 31, 2018
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