| 下限分析有限单元法的非线性规划求解 |
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| 引用本文： | 赵明华,张 锐,刘 猛.下限分析有限单元法的非线性规划求解[J].岩土力学,2015,36(12):3589-3597. |
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| 作者姓名： | 赵明华 张 锐 刘 猛 |
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| 作者单位： | 湖南大学 岩土工程研究所，湖南 长沙 410082 |
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| 基金项目： | 国家自然科学基金项目（No. 51278187）。 |
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| 摘 要： | 下限分析有限单元法将下限定理这一数学变分问题转化为一个数学规划问题，克服了人为构造可静应力场的困难，在实际工程中具有广阔的应用前景。通过有限元离散得到的非线性下限规划模型中包含大量的优化变量与约束条件，常规优化算法难以求解。为此，在分析非线性下限规划模型自身特点的基础上，引入可行弧技术和Wolfe非精确搜索技术改进其优化求解效率。算例分析表明，基于可行弧技术和Wolfe非精确搜索技术，下限分析有限单元法优化求解程序的收敛速度和步长搜索效率得到明显的提升，并且其数值稳定性良好、计算精度较高，可以较好地适应实际工程问题的计算。
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| 关 键 词： | 下限法 有限单元法 非线性规划 可行弧内点算法 Wolfe非精确搜索技术 |
| 收稿时间： | 2014-05-04 |
Nonlinear programming of lower bound finite element method |
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| ZHAO Ming-hua,ZHANG Rui,LIU Meng.Nonlinear programming of lower bound finite element method[J].Rock and Soil Mechanics,2015,36(12):3589-3597. |
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| Authors: | ZHAO Ming-hua ZHANG Rui LIU Meng |
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| Institution: | Institute of Geotechnical Engineering, Hunan University, Changsha, Hunan 410082, China |
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| Abstract: | Lower bound finite element method converts the mathematical variation problem of lower bound theorem into an mathematical programming one, which can overcome the difficulty of artificially constructing a statically admissible stress field; thus, it has a broad prospect in engineering practice. The lower bound programming model arising from finite element discretization of stress field contains a large number of optimization variables and constraints; therefore, it is hard to be solved by traditional optimization methods. By analyzing characteristics of the nonlinear lower bound programming model, feasible arc technique and Wolfe’s inaccurate search technique are introduced to enhance the optimization efficiency of this model. Example analysis shows that, based on feasible arc technique and Wolfe’s inaccurate search technique, the convergent speed and step-length searching efficiency of optimization procedure of lower bound finite element method are evidently improved; and numerical stability and good accuracy are acquired. As a result, the new method is more adaptable to engineering practice. |
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| Keywords: | lower bound method finite element method nonlinear programming feasible arc interior point algorithm Wolfe’s inaccurate search technique |
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