A coupled time integration algorithm for discontinuous deformation analysis using the numerical manifold method

2020 ◽  
Vol 44 (8) ◽  
pp. 1145-1169
Author(s):  
Xiaolei Qu ◽  
Guowei Ma ◽  
Chengzhi Qi ◽  
Arcady V. Dyskin ◽  
Chen Xia
Keyword(s):  
Time Integration ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Numerical Manifold Method ◽  
Integration Algorithm ◽  
Time Integration Algorithm ◽  
Discontinuous Deformation ◽  
Numerical Manifold

Study on Application of Numerical Manifold Method

2012 ◽  
Vol 182-183 ◽  
pp. 1194-1199
Author(s):  
Lei Zheng ◽  
Zheng Zhong Shen
Keyword(s):  
Continuum Mechanics ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Numerical Manifold Method ◽  
Analysis Method ◽  
Continuous Problems ◽  
Discontinuous Deformation ◽  
Numerical Manifold ◽  
Cover Function ◽  
The Continuum

Numerical manifold method (NMM) is based on the blocky theory which absorbed the advantages of finite element method based on the continuum mechanics, discontinuous deformation analysis method based on the non-continuum mechanics and analytic method. According to the finite covering technology of modern manifold analysis method, uniform solving format on continuous-non-continuous problems is established by taking the continuous and discontinuous cover function which can be used for the numerical simulation of large deformation and continuous-discontinuous deformation. The calculation program is worked out based on the method above and it is applied to the actual project.

STABILITY ANALYSES FOR ANCIENT MASONRY STRUCTURES USING DISCONTINUOUS DEFORMATION ANALYSIS AND NUMERICAL MANIFOLD METHOD

2011 ◽  
Vol 08 (02) ◽  
pp. 247-275 ◽  
Author(s):  
TAKESHI SASAKI ◽  
IKUO HAGIWARA ◽  
KASTUJI SASAKI ◽  
RYUNOSHIN YOSHINAKA ◽  
YUZO OHNISHI ◽  
...  
Keyword(s):  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Numerical Manifold Method ◽  
Masonry Structures ◽  
Stress Distributions ◽  
Isoparametric Element ◽  
Discontinuous Deformation ◽  
The Stability ◽  
Numerical Manifold ◽  
Physical Phenomena

In this paper, the stability including stress distribution of two ancient masonry structures, the pyramid of the Pharaoh Khufu, Egypt and the Pont of Gard, were analyzed using discontinuous deformation analysis (DDA) and numerical manifold method (NMM). For the simulation using NMM, the newly developed four-node isoparametric element was used. The stress distributions/concentration were calculated and compared between the two methods. The calculated results show qualitative agreement with observations. DDA and NMM are applicable to simulate the physical phenomena of masonry structures.

DEVELOPMENT OF COUPLED DISCONTINUOUS DEFORMATION ANALYSIS AND NUMERICAL MANIFOLD METHOD (NMM–DDA)

2010 ◽  
Vol 07 (01) ◽  
pp. 131-150 ◽  
Author(s):  
SHIGERU MIKI ◽  
TAKESHI SASAKI ◽  
TOMOFUMI KOYAMA ◽  
SATOSHI NISHIYAMA ◽  
YOZO OHNISH OHNISHI
Keyword(s):  
Rigid Body ◽  
Slope Failure ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Response Analysis ◽  
Numerical Manifold Method ◽  
Body Rotation ◽  
Rigid Body Rotation ◽  
Discontinuous Deformation ◽  
Numerical Manifold

Discontinuous Deformation Analysis (DDA) and Numerical Manifold Method (NMM) have been widely used for the analyses of discontinuous rock masses. Recently, these discontinuum-based numerical methods have been applied to the simulations for slope failure due to earthquakes, where one of the key issues is the estimation of traveling velocities and distances for the collapsed rock blocks. For the dynamic response analysis of rock slopes, it is necessary to consider the local variation of seismic forces, especially when the slope size is large and/or the slope geometry becomes complicated. In DDA, there is difficulty to consider the local displacements and stress condition of the single block for the basement because of mathematical principle (in DDA, the displacement function is defined at the gravity center of the blocks and the strain in the block is uniform). On the other hand, NMM can simulate both continuous and discontinuous deformation of the block systems. However, the rigid body rotation of blocks cannot be treated properly because NMM does not deal with the rigid body rotation in explicit form. According to the above-mentioned features and drawbacks, it is reasonable to combine DDA and NMM from practical point of view. In this paper, the formulation for the coupled NMM and DDA (NMM–DDA) was presented. For the formulation, NMM and DDA can be easily combined by choosing displacements of the DDA blocks and NMM cover nodes as unknowns, because the processes to establish the equilibrium equations (minimizing total potential energy) and kinematics for block system are same between DDA and NMM. In this paper, some applications of the NMM–DDA to both dynamic and static problems were also presented and the validity and applicability of newly developed DDA–MM were discussed.

DEVELOPMENT OF 3D NUMERICAL MANIFOLD METHOD

2010 ◽  
Vol 07 (01) ◽  
pp. 107-129 ◽  
Author(s):  
LEI HE ◽  
GUOWEI MA
Keyword(s):  
Virtual Work ◽  
Three Dimensional ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Numerical Manifold Method ◽  
Block System ◽  
Structure Description ◽  
Operation Rule ◽  
Discontinuous Deformation ◽  
Numerical Manifold

The numerical manifold method (NMM) is a combination of the finite element method (FEM) and discontinuous deformation analysis (DDA) method. It provides a robust numerical solution to a solid medium with dense discontinuities. This paper extends NMM to the three-dimensional domain based on the 2D fundamentals. The general framework of the 3D NMM is introduced, including the cover geometry patterns (GP) with division structure from hexahedron to tetrahedron, and general formulations based on the virtual work principle. The block cutting process to generate discrete blocks are discussed through the topological structure description of blocks, and the operation rule of blocks is explained. The proposed 3D block generation algorithm allows for any arbitrary discrete structure or block system. Three numerical examples are presented to demonstrate that the developed 3D numerical manifold code is effective and applicable to 3D continuum solids. Further developments aim to incorporate contact models to simulate complicated discrete block system.

THE NUMERICAL MANIFOLD METHOD: A REVIEW

2010 ◽  
Vol 07 (01) ◽  
pp. 1-32 ◽  
Author(s):  
GUOWEI MA ◽  
XINMEI AN ◽  
LEI HE
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Distinct Element ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Integration Scheme ◽  
Numerical Manifold Method ◽  
Strong Discontinuities ◽  
Numerical Manifold ◽  
Element Method

This paper presents a review on the numerical manifold method (NMM), which covers the basic theories of the NMM, such as NMM components, NMM displacement approximation, formulations of the discrete system of equations, integration scheme, imposition of the boundary conditions, treatment of contact problems involved in the NMM, and also the recent developments and applications of the NMM. Modeling the strong discontinuities within the framework of the NMM is specially emphasized. Several examples demonstrating the capability of the NMM in modeling discrete block system, strong discontinuities, as well as weak discontinuities are given. The similarities and distinctions of the NMM with various other numerical methods such as the finite element method (FEM), the extended finite element method (XFEM), the generalized finite element method (GFEM), the discontinuous deformation analysis (DDA), and the distinct element method (DEM) are investigated. Further developments on the NMM are suggested.

A Risk Evaluation Modeling upon Discontinuous Deformation Analysis and Hydraulic Computation for Aged Dam

2011 ◽  
Vol 121-126 ◽  
pp. 4307-4314
Author(s):  
Hsueh Chun Lin ◽  
Yao Ming Hong ◽  
Wen Pei Sung ◽  
Ying Chih Chen ◽  
Yao Chiang Kan
Keyword(s):  
Risk Evaluation ◽  
Discontinuous Deformation Analysis ◽  
Evaluation Methodology ◽  
Earth Dam ◽  
Evaluation Procedure ◽  
Deformation Analysis ◽  
Flow Equations ◽  
Discontinuous Deformation ◽  
Numerical Manifold ◽  
Energy Convergence

This study aims to generate a risk evaluation methodology for the aged dam structure by coupling the micro and macro models created by hydraulic computation and discontinuous deformation analysis (DDA) with numerical manifold method (NMM), respectively. For the macro analysis, DDA+NMM is an energy-convergence algorithm and can be utilized to estimate critical loading based on the potential joints existing within the discontinuous block system. Due to the micro view, the relationship of groundwater level and precipitation can be studied by using hydraulic computation based on the groundwater flow equations. The proposed method presents an evaluation procedure for modeling an aged earth dam with efficient and economic open-source programs. As the result, the simulation can help determining the criterion of risk factors and the prevention strategy.

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