摘要
现代计算技术在计算能力和存储容量上的革命仅仅提供了计算更复杂问题的有效工具,而程序的高效性是我们永恒的追求。本文试图从两方面着手,应用面向对象的程序设计方法来提高程序的开发和维护效率;在有限元分析中纳入无界单元以减小岩土工程的计算区域,从而提高程序的计算效率,最终为脆塑性岩石破坏后区力学特性的数值模拟服务。本文分别对面向对象的程序设计方法、无界单元方法以及岩石破坏后区力学特性进行了系统的研究,主要工作如下:
1、在系统地研究了面向对象程序设计方法的基础上,建立了有限元三维非线性分析的面向对象模型。
2、采用面向对象的程序设计语言Visual C++,嵌入Matlab数学库,利用其强大的矩阵运算功能,开发了运行于Windowsxp/2000/NT操作系统的,适用于岩土工程二维和三维有限元分析的面向对象有限元分析软件EBPFEM。该软件能进行弹塑性或弹脆塑性有限元计算,能较好的模拟脆塑性岩石的力学性能,可以考虑开挖卸荷;程序中加入了节理单元,可以模拟岩体中的不连续面;程序中还纳入了无界单元,可以模拟岩土工程中经常涉及到的无限和半无限域问题。
3、在对无界单元方法进行了系统而全面的回顾与总结的基础上,分别阐述了映射无界元和衰减无界元的基本原理及其形函数的具体构造方法,总结了几种常用的映射无界元和衰减无界元的形函数,并且详细推导了一种简单而又非常实用的无界单元—6节点三维无界元的形函数以及其它相关计算公式。
4、在前人工作的基础上,对岩石的应力应变全过程曲线分类进行了有益的探讨;应用塑性位势理论,详细推导了对应于不同屈服准则的应力脆性跌落过程塑性流动因子的确定方法,并且给出了非理想脆塑性模型应力脆性跌落过程中产生的非零位移增量的一种简便的近似处理方法。
5、分别对大理岩、红砂岩和花岗岩等几种脆性比较明显的岩石进行了应力脆性跌落系数的试验研究。研究表明脆塑性岩石的脆性是相对的,随着围压的增大,岩石逐渐由脆性向延性转化;脆塑性岩石的应力脆性跌落在围压不大的情形下发生,其应力脆性跌落系数是围压的函数;并给出了大理岩和红砂岩的应力脆性跌落系数与围压的关系表达式。
6、对非线性有限元分析中不同屈服条件进行了对比研究。研究表明,在三维情形下,采用不同的广义Von Mises条件来逼近莫尔—库仑条件时,Drucker-Prager条件偏于保守,真正的逼近Mohr-Coulomb条件应该介于内角圆和外角圆之间,内角圆偏于保守而外角圆偏于危险,所以等面积圆是相对合适的折中选择。
7、将应用面向对象方法开发的三维弹-脆-塑性有限元与无界元耦合分析软件EBPFEM对小湾水电站地下洞室群的围岩稳定性进行了不同屈服条件下的分析。证明了本文所设计的分析软件的有效性和实用性,对类似的工程具有一定的参考意义。
The revolutions of the computational power and memory capacity of modern computing technology offer us a valid implement to calculate more complicated problems only, and the high efficiency of program is our perpetual seek. This thesis tries to act from two aspects: applies object-oriented programming method to advance the development and maintenance efficiencies of programs; applies finite elements coupled with infinite elements to reduce the computational domain of geotechnical engineering so as to advance the calculation efficiency of programs, and service to the numerical simulation of the post-failure mechanical properties of brittle-plastic rocks finally. Therefore, object-oriented programming method, infinite element method and the post-failure properties of brittle-plastic rocks are the themes of this paper. Recapitulatively, several aspects are studied as follows:
1. Based on the systemic research of object-oriented programming method, a three-dimensional object-oriented non-linear brittle-plastic finite element analysis model is constructed.
2. Applies object-oriented program design language visual C++, embeds Matlab math library and utilizes its powerful matrix operation functions, a geotechnical FEM software (named as EBPFEM) based on Windows98/2000/NT is designed to deal with two or three dimensional problems. This software can execute elastic-plastic and brittle-plastic finite analysis, can preferably simulate mechanical properties of brittle-plastic rocks, can preferably simulate excavation, and can preferably simulate discontinuity between rock mass as well. What’s more, this software can simulate infinite or semi-infinite calculate zone which is often involved in geotechnical engineering because infinite elements are incorporated.
3. Based on the systemic and comprehensive review and summarize of infinite element method, the fundamental principles of mapping or attenuation infinite elements and the specific construction methods of their shape functions are elaborated respectively, and then shape functions of several mapping or attenuation infinite elements in common use are summarized, and the shape function and some other correlation formulas of a simple and utility infinite element- three dimensional 6 node infinite element are deduced particularly as well.
4. Based on the works of predecessors, the classification of complete stress-strain curves of rocks is discussed beneficially. Applies plastic potential theory, the methods of determinations of plastic flow factors between brittle stress drop under different yield criterions are deduced, and a simple and approximate treatment method of the non-zero displacement increment generated between the brittle stress drop when the non-ideal brittle-plastic model involved in is put forward.
5. Tests aims to research on the coefficient of brittle stress drop of several brittle rocks such as marble, red sandstone and granite are performed. The researches show: the brittleness of brittle- plastic rocks is relative, and can change to ductility accompanied by the increasing confining stress; the brittle stress drop of brittle-plastic rocks only takes place when the confining stress is small, and the coefficient of brittle stress drop is a function of the confining stress, and such relation expressions about marble and red sandstone are given as well.
6. The results of contrast research on different yield criterions of non-linear finite analysis show: in the condition of three-dimension, using different general Von Mises criterions to approximate Morh-Coulomb criterion, Drucker-Prager condition is inclined to conservative, and the accurate one which approximated to Morh-Coulomb criterion is between interior and exterior vertex circle. Interior vertex circle is inclined to be conservative and exterior vertex circle is inclined to be dangerous as well, and so, the equal area circle is the relative well-founded compromise choice.
7. The application in the stability of underground excavation of Xiaowan Hydropower Project with different yield criterions proves validity and practicability of the three dimensional elastic-brittle-plastic finite elements coupled with infinite elements analysis software (named as EBPFEM), which can be of beneficial reference to analogous projects.
引文
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