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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 486171, 11 pages
Research Article

Implicit Damping Iterative Algorithm to Solve Elastoplastic Static and Dynamic Equations

1State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
2Earthquake Engineering Research Center, China Institute of Water Resources and Hydropower Research, Beijing 100048, China
3College of Civil and Transportation Engineering, Hohai University, Jiangsu, Nanjing 210098, China
4Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received 26 May 2014; Revised 6 August 2014; Accepted 6 August 2014; Published 31 August 2014

Academic Editor: Giuseppe Marino

Copyright © 2014 Huaifa Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents an implicit damping iterative algorithm to simultaneously solve equilibrium equations, yield function, and plastic flow equations, without requiring an explicit expression of elastoplastic stiffness matrices and local iteration for “return mapping” stresses to the yield surface. In addition, a damping factor is introduced to improve the stiffness matrix conformation in the nonlinear iterative process. The incremental iterative scheme and whole amount iterative scheme are derived to solve the dynamical and static and dynamical elastoplastic problems. To validate the proposed algorithms, computation procedures are designed and the numerical tests are implemented. The computational results verify the correctness and reliability of the proposed implicit iteration algorithms.