Extension of numerical manifold method for coupled fluid flow and fracturing problems     

Zhijun Wu  Louis Ngai Yuen Wong 《国际地质力学数值与分析法杂志》2014,38(18):1990-2008

The present study extends the numerical manifold method to include the hydro‐mechanical model to investigate the effect of water flow in fractures on the stability of rock structures, particularly slopes. The proposed flow model is verified by a simple 2‐D flow problem in a homogeneous aquifer. Combining the water flow model with the earlier developed fracture evolution technique, the entire failure process of the rock slope due to a heavy rain is simulated. The results illustrate that the developed numerical manifold method can not only determine the trigger factor of the crack initiation but also model the failure processes related to crack initiation, propagation, block formation, detachment and sliding due to the water effect successfully. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

Non-Existence of Five Dimensional Perfect Fluid Cosmological Model in Lyra Manifold     

G. Mohanty  K. L. Mahanta  R. R. Sahoo 《Astrophysics and Space Science》2006,306(4):269-272

In this paper we have taken an attempt to construct a five dimensional perfect fluid cosmological model within the framework of Lyra manifold. It is found that neither perfect fluid nor dust distributions survive. Finally the exact solutions of the vacuum field equations are obtained.  相似文献   

数值流形法中“质量守恒”的探讨     

林兴超  汪小刚  王玉杰  李旭  韩鑫晔 《岩土力学》2011,32(10):3065-3070

数值流形法是至少包含流形法(NMM)、有限元法(FEM)和非连续变形分析(DDA)的数值方法体系。将数值流形法中物理单元与数学单元完全重合,去掉接触理论,流形元能够回归到有限元,将通过简单的板压缩数值试验验证这一点。在以前的数值流形法法中,质量守恒问题一直被忽视,物理单元的质量会随着单元体积改变,计算结果存在一定的误差。通过改变计算过程中单元密度实现计算过程中的"质量守恒",完善了现有数值流形法的理论基础。  相似文献   

Motions close to escapes in the rhomboidal four body problem     

Ernesto A. Lacomba  Ernesto Pérez-Chavela 《Celestial Mechanics and Dynamical Astronomy》1993,57(3):411-437

In this work we study escape and capture orbits in the planar rhomboidal 4-body problem in a level of constant negative energy. There are only two different values of the masses here. By using numerical analysis, we show certain transversal intersections of the invariant manifolds of parabolic orbits. We then introduce Symbolic Dynamics when the mass ratio is small, and when it is close to one. In the first case the escapes or captures predominate in the direction of one of the diagonals of the rhombus, while in the second case we find solutions escaping or being captured in the direction of both possible diagonals.  相似文献   

一类高阶位涡反演的算法及其应用     

甘璐  赵南  沈新勇 《气象学报》2011,69(3):412-422

从位涡反演的基本定义和性质出发讨论了它的发展,指出基于非线性平衡(Chamey平衡)来进行位涡反演的局限性,要准确地反演中尺度系统还有待于发展高阶位涡反演算子.文中通过分析位涡反演算子的构造得出,高阶位涡反演算子的存在性问题最终归结为探讨高阶平衡流表达式,即高阶平衡方程的存在性问题.然而,平衡流在运动过程中对惯性重力波...  相似文献   

变系数紧耦合波动方程组的非线性边界镇定     

雷娟 《南京气象学院学报》2011,(2):172-183

利用黎曼几何方法和乘子技巧,讨论了带变系数和非线性边界扩散反馈项的紧耦合波动方程组的镇定,得到了解能量的衰减估计.  相似文献   

The Tetrahedral 4‐Body Problem with Rotation     

Claudio Vidal 《Celestial Mechanics and Dynamical Astronomy》1998,71(1):15-33

We consider four bodies in space with same masses forming two binaries, each one symmetric with respect to a fixed axis and moving under Newtonian gravitation in opposite directions about this axis. It is given a direct proof that all singularities of this model are due to collisions, and it is proved that the singularities due to simultaneous double collisions are regularizable. The set of equilibrium points on the total collision manifold is studied as well as the possible connections among them. We show that the set of initial conditions on a given energy surface going to quadruple collision is a union of twenty submanifolds: twelve of them have dimension 2 and the others have dimension 3. Similarly for ejection orbits from quadruple collision. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

Demonstration and application of NMM‐based fractured porous medium flow model     

Qi‐Hua Zhang  Shao‐Zhong Lin  Hai‐Dong Su  Gen‐Hua Shi 《国际地质力学数值与分析法杂志》2021,45(1):132-153

In natural rock masses, the shapes of three‐dimensional (3‐D) blocks cut by arbitrary fracture networks may be very complex. Owing to the geometric complexity and difficulty of mesh discretization of 3‐D blocks and fracture facets, explicit consideration of fracture networks in flow analysis of fractured porous medium (FPM) is very challenging. Using the numerical manifold method based on independent covers (NMMIC), an FPM flow model was proposed that can deal with very complex 3‐D fracture networks. In this paper, the convergence of NMMIC was first demonstrated. The theoretical basis of the arbitrary refinement of computational meshes was proven. Moreover, three peculiarities of NMMIC meshes, that is, arbitrary shape, arbitrary connection, and arbitrary refinement of independent covers, were concluded. Finally, some two‐dimensional (2‐D) tunnel flow examples were analyzed and the numerical results were compared with the analytical results. 3‐D examples with complex fracture distributions were also analyzed. In addition, the computational scale of the developed program was tested by increasing the number of computational elements. The results show that our model can accurately analyze the groundwater flow of rocks surrounding tunnels with complex fracture distributions.  相似文献   

海底管道沉箱基础的复合承载力包络面研究     

周素静  张艳  王栋 《海洋通报》2019,38(6):727-733

当负压沉箱被用作深水管汇或管道终端基础时,其长径比常介于1～2之间,而目前的沉箱复合承载力包络面表达式大都针对长径比不超过1的情况,少数覆盖长径比大于1的研究又不适用于土体表层强度非零的情况。采用有限元方法,模拟竖向力、水平力和弯矩共同作用下沉箱基础的响应,采用Probe加载模式获得沉箱的复合承载力包络面。进行大量变动参数分析,针对长径比为1～2的沉箱,讨论了长径比和土体强度分布对单向承载力和包络面的影响,并给出了预测沉箱复合承载力的归一化表达式。  相似文献   

开挖模拟在数值流形方法中的实现     

焦健  乔春生  徐干成 《岩土力学》2010,31(9):2951-2957

针对数值流形方法特有的覆盖剖分方式,提出了一种模拟岩土工程中开挖过程的算法。该算法采取某种措施,在覆盖剖分过程中将开挖面视为特殊的不连续面,这种不连续面将其所在的数学网格剖分成不同的流形单元,但却不对所在的数学覆盖作剖分。这样,开挖面两侧虽分属不同的流形单元,但开挖面两侧同一数学网格内的流形单元却具有相同的物理覆盖。采用该算法,无需对开挖面处的单元进行特殊处理,可在整个分析域采用统一的网格形式;同时,打破了原有数值流形方法的限制,将开挖面的位置完全当作连续介质来处理,避免了因将其视为不连续面而产生的误差。验证了算法的可靠性后,将其应用于某假想隧道的开挖模拟,计算结果表明该算法具有一定的应用前景。  相似文献