| 基于刚体平动运动单元的上限有限元研究 |
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| 引用本文： | 杨峰,赵炼恒,张箭,阳军生.基于刚体平动运动单元的上限有限元研究[J].岩土力学,2014,35(6):1782-1786. |
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| 作者姓名： | 杨峰 赵炼恒 张箭 阳军生 |
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| 作者单位： | 中南大学 土木工程学院，长沙 410075 |
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| 基金项目： | 国家自然科学基金项目（No.51008309, No. 51208522）；“十二五”国家科技支撑计划课题（No.2012BAK24B02）。 |
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| 摘 要： | 刚性块体极限分析上限法常应用于岩土工程稳定性研究,然而应用时需假定刚性块体破坏模式并递推繁琐的几何关系。为此,提出一种适应性更广的基于非线性规划模型的刚体平动运动单元上限有限元法,并解决了其优化模型初始值的确定问题。通过引入有限单元思想,将计算区域离散成刚体单元,同时以单元速度和节点坐标作为决策变量,由上限定理建立非线性规划模型获得上限解。利用编制的上限有限元程序进行边坡和浅埋隧道稳定性算例验证,表明运动单元上限有限元法能调整速度间断线至较优方位,所得破坏模式特征鲜明,上限解精度高,可广泛应用于边坡、隧道等稳定性分析研究。
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| 关 键 词： | 极限分析 上限法 刚体运动单元 有限元法 非线性规划 |
| 收稿时间： | 2013-03-10 |
Investigation on finite element upper bound solution based on rigid translatory moving element |
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| YANG Feng,ZHAO Lian-heng,ZHANG Jian,YANG Jun-sheng.Investigation on finite element upper bound solution based on rigid translatory moving element[J].Rock and Soil Mechanics,2014,35(6):1782-1786. |
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| Authors: | YANG Feng ZHAO Lian-heng ZHANG Jian YANG Jun-sheng |
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| Institution: | School of Civil Engineering, Central South University, Changsha 410075, China |
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| Abstract: | Upper bound solution of limit analysis with rigid blocks is widely applied to geotechnical engineering stability analysis. However, rigid blocks failure mechanism and complicated geometric relation are needed to assume and analyze for different geotechnical subjects. In order to banish these restrictions, a finite element upper bound solution with rigid translatory moving elements based on nonlinear programming is presented. And the key problem of determine initial value for nonlinear programming model is also solved. This method firstly discretizes computation domain into rigid elements, then defines the element velocities and nodes coordinate as decision variables, and uses upper bound theory to establish nonlinear programming model to acquire a solution. Corresponding finite element upper bound program is compiled to verify stabilities of slope and shallow tunnel to illustrate that velocity discontinuities of elements adjust automatically into best directions to acquire failure mechanism with distinct characteristics and upper bound solution with high accuracy. The method is expected to be applied widely to stability analysis for slopes, tunnels and other geotechnical subjects. |
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| Keywords: | limit analysis upper bound solution rigid moving element finite element method nonlinear programming |
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