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

G. F. Zhao  X. B. Zhao  J. B. Zhu 《国际地质力学数值与分析法杂志》2014,38(1):92-110

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.  相似文献   

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

L. Sun  G.F. Zhao  J. Zhao 《国际地质力学数值与分析法杂志》2013,37(12):1711-1736

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.  相似文献   

Investigation on strength and stability of jointed rock mass using three‐dimensional numerical manifold method     

L. He  X. M. An  X. B. Zhao  Z. Y. Zhao 《国际地质力学数值与分析法杂志》2013,37(14):2348-2366

This paper proposes a numerical model for jointed rock masses within the 3‐D numerical manifold method (NMM) framework equipped with a customized contact algorithm. The strength of rock sample containing a few sets of discontinuities is first investigated. The results of models with simple geometries are compared with the available analytical solutions to verify the developed computer code, whereas models with complex geometries are simulated to better understand the fundamental behavior and failure mechanism of jointed rock mass. Furthermore, the stability of jointed rock mass in an underground excavation is studied, where rock failure process is determined by the 3‐D NMM simulation. The simulation results provide valuable guidance on excavation process design and stabilization design in rock engineering practice. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

抛锚撞击水下管汇的数值模拟研究          下载免费PDF全文

娄敏  王艳红  明海芹 《海洋工程》2016,34(4):38-46

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。  相似文献   

Numerical manifold method for dynamic nonlinear analysis of saturated porous media     

H. W. Zhang  L. Zhou 《国际地质力学数值与分析法杂志》2006,30(9):927-951

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.  相似文献   

A compact model for the planar rhomboidal 4-body problem     

Ernesto A. Lacomba  Ernesto Pérez-Chavela 《Celestial Mechanics and Dynamical Astronomy》1992,54(4):343-355

We obtain a compact model for the global study of the planar rhomboidal 4-body problem in a level of constant negative energy. This model is a variation of the non compact model obtained through a McGehee blow up transformation. but compactness permits to obtain results which are not clear in the other case.  相似文献   

Wilson非协调数值流形方法   总被引：1，自引：0，他引：1  

魏高峰  冯伟 《岩土力学》2006,27(2):189-192

三维数值流形方法中，当数学覆盖取六面体体单元时流形单元总体位移函数中所包含的多项式并不是完全的，非完全的高次项非但对改善精度不起作用，而且还可能起相反的作用。为此，基于Wilson非协调元理论，推导了附加非协调位移基本项的流形元通用公式，通过内参静力凝聚处理，导出了消除单元内参后的单元应变矩阵、单元刚度矩阵，建立了非协调数值流形方法。数值试验表明，在规则数学网格覆盖下它们能够保证收敛，有较高的精度，从而证明所建方法的可行性。  相似文献   

Completely Integrable Systems Connected with Lie Algebras     

Stanisław P. Kasperczuk 《Celestial Mechanics and Dynamical Astronomy》2000,76(4):215-227

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.  相似文献   

Plane Symmetric Cosmic Strings In Lyra Manifold     

D.?R.?K.?ReddyEmail author 《Astrophysics and Space Science》2005,300(4):381-386

Static and non-static plane symmetric string cosmological models are obtained in Lyra [Mathematische Zeitsehrift 54, 52, 1951] manifold. Some properties of the models are also discussed.  相似文献   

岩土工程数值模拟新方法   总被引：13，自引：1，他引：12  

唐辉明  滕伟福 《地质科技情报》1998,(Z2)

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。  相似文献