| 弹塑性隐式阻尼迭代法 |
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| 引用本文： | 马怀发,梁国平,周永发.弹塑性隐式阻尼迭代法[J].工程力学,2012,29(10):57-62. |
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| 作者姓名： | 马怀发 梁国平 周永发 |
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| 作者单位： | 1.中国水利水电科学研究院流域水循环模拟与调控国家重点实验室, 北京 100038; |
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| 基金项目： | 国家自然科学基金项目(51079164);863计划项目(2009AA044501);水利部公益专项资助项目(201201053) |
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| 摘 要： | 作者给出了联立求解平衡方程、屈服条件和塑性流动方程的弱解形式, 同时提出了两种位移增量迭代算法:一是以应变增量和塑性因子为独立基本未知量的联立求解迭代算法;二是以应变增量为独立基本未知量的数值求解方法。为了避免弹塑性刚度矩阵的奇异性, 改善迭代收敛速度, 针对上述两种迭代算法本文提出了隐式阻尼迭代法, 并编写了相应脚本文件和计算流程, 并基于有限元程序自动生成系统(FEPG)生成了求解弹塑性问题的有限元源程序。最后, 通过算例验证了所提出的迭代法和计算程序的可靠性和有效性。
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| 关 键 词： | 有限单元法 材料非线性 弹塑性方程 隐式阻尼迭代法 FEPG |
| 收稿时间： | 2011-02-15 |
IMPLICIT DAMPING ITERATION ALGORITHM FOR ELASTOPLASTIC EQUATIONS |
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| MA Huai-fa,LIANG Guo-ping,ZHOU Yong-fa.IMPLICIT DAMPING ITERATION ALGORITHM FOR ELASTOPLASTIC EQUATIONS[J].Engineering Mechanics,2012,29(10):57-62. |
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| Authors: | MA Huai-fa LIANG Guo-ping ZHOU Yong-fa |
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| Affiliation: | 1.State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China;2.Element Computing Technology Co., Ltd, Beijing 100085, China;3.Beijing FEGEN Software Co., Ltd, Beijing 100190, China |
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| Abstract: | Authors present an integral weak form of elastoplastic problem for simultaneously solving equilibrium equations, yield function, and plastic flow equations, and two algorithms for displacement increment iteration: 1) iteration algorithm based on independent unknowns of strain increment and plastic factor; 2) numerical solution based on the only unknowns of strain increment. An implicit damping iteration algorithm is proposed to avoid singularity of elastoplastic matrix and improve convergence speed. Script codes are designed for the iteration process, and finite element programs are generated based on Finite Element Program Generator (FEPG). The programs are verified and computational results agree well with theoretical solutions. |
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