IMHE OpenIR  > 山地灾害与地表过程重点实验室
非连续变形分析和数值流形法的优化与扩展
Language中文
樊火
Thesis Advisor何思明
2016
Degree Grantor中国科学院大学
Place of Conferral北京
Degree Name博士
Degree DisciplineOptimization and Extension of Discontinuous Deformation Analysis and Numerical Manifold Method
Keyword非连续边形分析 数值流形法 S-r分解 广义自由度分解 有限变形 大旋转
Other Abstract

数学家出身的岩石力学专家石根华分别于1988年和1991年提出了非连续变形分析(Discontinuous Deformation Analysis, DDA)和数值流形法(Numerical Manifold Method, NMM)。DDA类似于有限单元法和离散单元法,统一了静力分析和动力分析、正分析与反分析;NMM能用物理覆盖和数学覆盖自然地处理连续和非连续问题。本文对这两种数值方法中存在的一些问题进行了较为深入的分析和研究,相关进展如下:一、针对二维经典DDA中角角接触的不确定性,提出新的在角角接触点处插入两个法向临时弹簧的预处理法和判断可能接触边的方向角法。降低了经典DDA对接触弹簧罚值的敏感性,拓宽了时间步长的取值范围。二、区别二维经典DDA非同时考虑块体旋转和变形的本质,提出了虚功率原理下基于S-R分解的新的动力分析格式,并在DDA的框架下完成其数值实现,建立了新的DDA控制方程。改善了经典DDA描述块体运动的有效性。三、基于二维经典NMM中单元节点位移和广义自由度之间的差异,提出了计算二维混合型应力强度因子的广义自由度分解法,导出了单元刚度偏导数的解析表达式。为经典NMM用于断裂分析提供了相关的理论基础。四、借鉴二维经典DDA中的块体自由度,提出了无线性依赖且在星点处具有连续应力值的高阶NMM,给出了基于S-R分解的单元体积抑制措施和带Bernstein多项式的罚平衡应力后处理法。提高了经典NMM应力的精度。 五、抛弃二维经典NMM中的小应变假设,应用虚位移原理在NMM的框架下实现了基于S-R分解的动力大变形分析格式,构建了新的适合于NMM的控制方程。扩展了经典NMM求解有限变形和大旋转的能力。

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Discontinuous Deformation Analysis (DDA) and Numerical Manifold Method (NMM) are presented respectively in 1988 and 1991 by Genhua Shi, who is a mathematics-trained specialist in rock mechanics. DDA is similar to finite element method or discrete element method and unifies the static analysis and dynamic analysis as well as forward analysis and backward analysis. While, NMM has an ability to deal naturally with the continuous and discontinuous problems by using physical cover and mathematical cover. Some issues existing in the two methods are analyzed and investigated deeply. The related advances are as follows: 1. By aiming at the indeterminacy associated with the corner-corner contact in the classic 2D-DDA, a new pretreatment approach by inserting two normal temporary springs into the contacted vertexes is given and a direction angle method is suggested to determine the possible contact edge. The sensitivity to the contact penalty value is reduced and the range of values of the time size is broadened. 2. By distinguishing the essence of asynchronism in considering the rotation and deformation of blocks in the classic 2D-DDA, based on the S-R decomposition a new dynamic analysis format is proposed by using the virtual power principle, then the new formation is implemented numerically in the framework of DDA. Thus, a new control equation of DDA is built. The effectiveness of describing the block movement is improved. 3. By basing on the difference between node displacement of element and generalized degrees of freedom in the classic 2D-NMM, a decomposition of generalized degrees of freedom is presented for calculating the 2D-mixed-mode stress intensity factor, and the analytical expression for the partial derivative of element stiffness is deduced. The related theoretical basis is provided for applying NMM to the fracture analysis. 4. By referencing degrees of freedom of the classic 2D-DDA, a new high-order NMM possessing the continous stress value at the star points is put forward. A measure based on S-R decomposition is given to suppress the volume expansion of element, and a penalty-equilibrating approach with the Bernstein polynomials is suggested to conduct the stress post-processing. The accuracy of stress given by the classic 2D-NMM is enhanced. 5. By discarding the starin assumption of the classic 2D-NMM, under the context of NMM, a new dynamic large deformation based on the S-R decomposition is decued through employing the virtual displacement principle, and a new governing equation suited for NMM is established. The ability of the classic 2D-NMM to deal with the finite deformation and large rotation is extended. 

Document Type学位论文
Identifierhttp://ir.imde.ac.cn/handle/131551/18893
Collection山地灾害与地表过程重点实验室
Affiliation中国科学院成都山地灾害与环境研究所
Recommended Citation
GB/T 7714
樊火. 非连续变形分析和数值流形法的优化与扩展[D]. 北京. 中国科学院大学,2016.
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