首页 | 本学科首页   官方微博 | 高级检索  
     检索      

数值流形方法及其在岩石力学中的应用
引用本文:李树忱,程玉民.数值流形方法及其在岩石力学中的应用[J].力学进展,2004,34(4):446-454.
作者姓名:李树忱  程玉民
作者单位:上海大学上海市应用数学与力学研究所
摘    要:数值流形方法是目前岩石力学分析的主要方法之一.该方法起源于不连续变形分析,主要用于统一求解连续和非连续问题,其核心技术是在分析时采用了双重网格:数学网格提供的节点形成求解域的有限覆盖和权函数;而物理网格为求解的积分域.数学网格被用来建立数学覆盖,数学覆盖与物理网格的交集定义为物理覆盖,由物理覆盖的交集形成流形单元.流形方法的优点在于它使用了独立的数学和物理网格,具有和有限元明显不同的定义形式,且数学网格对于同一问题不同的求解精度的需求可以很方便地细化.由于该方法考虑了块体运动学,可以模拟节理岩体裂隙的开裂和闭合过程,因而在岩石力学中得到了广泛应用,近年来许多学者对该方法进行了研究.本文简要叙述了节理岩体的数值方法从连续到非连续的发展过程,详细地介绍了数值流形方法的组成和数值流形方法在岩石力学及其相关领域的研究和发展概况,最后就作者所关心的一些问题,如三维问题的数值流形方法、数值流形方法在物理非线性问题和裂纹扩展问题中的应用、相关的耦合方法等进行了探讨.

关 键 词:数值流形  不连续变形分析  岩石力学  裂纹扩展

NUMERICAL MANIFOLD METHOD AND ITS APPLICATIONS IN ROCK MECHANICS
LI Shuchen CHENG Yumin.NUMERICAL MANIFOLD METHOD AND ITS APPLICATIONS IN ROCK MECHANICS[J].Advances in Mechanics,2004,34(4):446-454.
Authors:LI Shuchen CHENG Yumin
Institution:LI Shuchen CHENG YuminShanghai Institute of Applied Math and Mech,Shanghai University,Shanghai 200072,China
Abstract:The Numerical Manifold Method (NMM) is one of important numerical methods to model rock mechanics problems at present. The NMM comes from the discontinuous deformation analysis, and is mainly used to combine continuous and discontinuous mechanics into a system. Two meshes are employed in the method: the mathematical mesh enables the nodes to build a finite cover system of the solution domain and the weighted functions, while the physical mesh provides the sub-domains of integration. The mathematical mesh is used to form mathematical covers. The physical covers are defined by the intersection of the mathematical covers and the physical mesh. And an element in the manifold method is defined by the intersection of physical covers. The advantages of the NMM are that the mathematical mesh and the physical mesh are generally independent, and that the manifold element is different from the finite element, and the mathematical mesh can be easily re-meshed to obtain a better accuracy of the solution. The NMM can simulate the open and close process of crack in the fractured rockmass due to the fact that the kinematics theory of the block system is considered in it. Therefore the method has been widely used in rock mechanics, and has been studied by many scholars in recent years. In the paper, the advances of the numerical methods of the fractured rockmass from continuous to discontinuous domains are discussed. The components of the numerical manifold method and its applications in rock mechanics and the advances in corresponding fields are discussed in detail. Finally, some problems, such as the NMM for three-dimension problems, physical nonlinear problems, crack propagation, related coupled methods etc., are discussed.
Keywords:numerical manifold method  discontinuous deformation analysis  rock mechanics  crack growth  large deformation
本文献已被 CNKI 维普 万方数据 等数据库收录!
点击此处可从《力学进展》浏览原始摘要信息
点击此处可从《力学进展》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号