| 下限问题中基于四边形单元平衡方程的边界积分法 |
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| 引用本文： | 李春光, 朱宇飞, 刘丰, 邓琴, 郑宏. 下限问题中基于四边形单元平衡方程的边界积分法[J]. 工程力学, 2013, 30(8): 127-132. DOI: 10.6052/j.issn.1000-4750.2012.04.0279 |
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| 作者姓名： | 李春光 朱宇飞 刘丰 邓琴 郑宏 |
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| 作者单位： | 中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室，湖北，武汉 430071 |
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| 基金项目： | 国家重点基础研究发展计划(973)项目(2011CB013505)；中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室知识创新工程青年人才领域前沿项目(O713021Q01) |
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| 摘 要： | 相对于三角形单元的下限分析，基于四边形单元的下限分析具有更高的精度和求解效率。该文利用格林公式把平衡方程的弱形式化为边界积分，从而得到简洁的线性方程，取代了以往的数值积分方案，克服了高斯积分中坐标变换等复杂的求解过程。此外还对应力连续性方程进行了简化。该积分方案不仅大大简化了计算，而且更易于编程实现。算例表明该文方法具有较高的精度。
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| 关 键 词： | 下限分析 四边形单元 边界积分 高斯积分 应力连续条件 |
| 收稿时间： | 2013-08-20 |
| 修稿时间： | 2013-08-20 |
BOUNDARY INTEGRAL METHOD FOR EQUILIBRIUM EQUATIONS OF LOWER BOUND PROBLEMS BASED ON QUADRILATERAL ELEMENTS |
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| LI Chun-guang, ZHU Yu-fei, LIU Feng, DENG Qin, ZHENG Hong. BOUNDARY INTEGRAL METHOD FOR EQUILIBRIUM EQUATIONS OF LOWER BOUND PROBLEMS BASED ON QUADRILATERAL ELEMENTS[J]. Engineering Mechanics, 2013, 30(8): 127-132. DOI: 10.6052/j.issn.1000-4750.2012.04.0279 |
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| Authors: | LI Chun-guang ZHU Yu-fei LIU Feng DENG Qin ZHENG Hong |
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| Affiliation: | State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China |
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| Abstract: | For a lower bound analysis, a quadrilateral element is more efficient and accurate, compared with a triangle element. The regional integral resulted from the weak form of equilibrium equations is reduced into a boundary integral through Green's theorem, and linear equilibrium equations are greatly simplified. The numerical integral scheme and coordinate transform in Gaussian integral are avoided. Furthermore, the stress continuity equations are also reduced. The presented method not only simplifies the calculation, but also makes it easy to program. The examples show that the method has higher accuracy. |
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| Keywords: | lower bound analysis quadrilateral element boundary integral Gaussian integral stress continuity condition |
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