Numerical manifold method for dynamic nonlinear analysis of saturated porous media

It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd.     

Plane Symmetric Domain Wall in Lyra Geometry

In this paper general solutions are found for domain walls in Lyra geometry in the plane symmetric spacetime metric given by Taub. Expressions for the energy density and pressure of domain walls are derived in both cases of uniform and time varying displacement field β. It is also shown that the results obtained by Rahaman et al [IJMPD, 10, 735 (2001)] are particular case of our solutions. Finally, the geodesic equations and acceleration of the test particle are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

流形上的空间密度聚类算法研究

研究流形上的聚类分析，针对基于密度的空间聚类引入了流形概念，提出1种基于流形的密度聚类算法，该方法将流形的概念与聚类相结合，可以适用于样本为复杂分布的聚类。文中通过实例证明此算法的有效性。     

Application of the numerical manifold method for stress wave propagation across rock masses

In this paper, the numerical manifold method (NMM) is extended to study wave propagation across rock masses. First, improvements to the system equations, contact treatment, and boundary conditions of the NMM are performed, where new system equations are derived based on the Newmark assumption of the space–time relationship, the edge‐to‐edge contact treatment is further developed for the NMM to handle stress wave propagation across discontinuities, and the viscous non‐reflection boundary condition is derived based on the energy minimisation principle. After the modification, numerical comparisons between the original and improved NMM are presented. The results show that the original system equations result in artificial numerical damping, which can be overcome by the Newmark system equations. Meanwhile, the original contact scheme suffers some calculation problems when modelling stress wave propagation across a discontinuity, which can be solved by the proposed edge‐to‐edge contact scheme. Subsequently, the influence of the mesh size and time step on the improved NMM for stress wave propagation is studied. Finally, 2D wave propagation is modelled, and the model's results are in good agreement with the analytical solution. Copyright © 2013 John Wiley & Sons, Ltd.     

加权空-谱联合保持嵌入的高光谱遥感影像降维方法

高光谱遥感影像数据量大、波段数多,容易导致“维数灾难”。传统流形学习方法一般仅考虑其光谱特征,忽略了空间信息。为此提出一种非监督的基于加权空-谱联合保持嵌入(WSCPE)的维数约简算法。首先采用加权均值滤波(WMF)方法对高光谱影像进行滤波,以消除噪点和背景点的干扰。然后根据遥感影像地物分布的空间一致性,通过采用加权空-谱联合距离(WSCD)来融合像素点的光谱信息和空间信息,有效选取各像素点的空-谱近邻,并根据像素点与其空-谱近邻点之间的坐标距离来有区别的利用其近邻点进行流形重构,提取低维鉴别特征进行地物分类。在PaviaU和Indian Pines数据集上的分类结果表明,总体分类精度分别达到了98.89%和95.47%。该方法在反映影像内部流形结构的同时,有效融合了影像的空间-光谱信息,故能提高影像特征的鉴别性,并提升分类性能。     

抛锚撞击水下管汇的数值模拟研究

船舶抛锚撞击水下管汇会影响到管汇的正常作业,基于ANSYS/LS-DYNA动力学分析软件,建立锚-水下管汇-海床土体的三维有限元模型,对抛锚碰撞水下管汇的过程进行数值仿真。通过求解水下管汇受碰撞后的等效应力、应变的时间历程及受撞击部位的凹陷损伤深度,发现最大等效应力点出现在管汇与锚接触位置处,管汇的碰撞部位最终发生凹痕变形。同时讨论锚与管汇接触面的形状以及海床土体对水下管汇损伤程度的影响,当冲击能量相同时,锚与水下管汇的碰撞接触面积越小,水下管汇的损伤深度就越大;当锚与管汇接触的接触面积相同时,冲击能量越大,水下管汇的损伤变形越大。海床土体的剪切弹性模量对管汇的凹陷损伤深度以及最大等效应力影响与冲击能量有关,海床土体的内摩擦角对管汇的碰撞影响较小。     

Particle manifold method (PMM): A new continuum‐discontinuum numerical model for geomechanics

Particle manifold method (PMM) is a new extension of the numerical manifold method (NMM). PMM uses a mathematical cover system to describe the motion and deformation of a particle‐based physical domain. By introducing the concept of particle into NMM, PMM takes the advantages of easy topological and contact operations with particles. In this article, the methodology, formulations and implementation of the method are presented, together with modelling examples for validation. It is found that good solutions for both continuous and discontinuous problems are obtained by the new developed PMM. Due to the underlying coupled continuum‐discontinuum property of PMM, it has great potential for modelling of geomechanical problems. Copyright © 2012 John Wiley & Sons, Ltd.     

Completely Integrable Systems Connected with Lie Algebras

In a recent paper Ballersteros and Ragnisco (1998) have proposed a new method of constructing integrable Hamiltonian systems. A new class of integrable systems may be devised using the following sequence: , where A is a Lie algebra is a Lie–Poisson structure on R ₃, C is a Casimir for is a reduced Poisson bracket and (A, ▵) is a bialgebra. We study the relation between a Lie-Poisson stucture Λ and a reduced Poisson bracket , which is a key element in using the Lie algebra A to constructing this sequence. New examples of Lie algebras and their related integrable Hamiltonian systems are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

岩土工程数值模拟新方法

论述了岩土工程数值模拟的新进展和近年来新出现的数值模拟方法,重点介绍了无网络伽辽金法（ＥＦＧＭ）和数值流形法（ＭＭ）的原理及其在岩土工程中的应用,指出了今后研究的重点方向。