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A high-order numerical manifold method with nine-node triangular meshes
Fan, Huo1,2,3,4; He, Siming1,2,3; Jiang, Zhongming5
Corresponding AuthorHe, SM
2015
Source PublicationENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
ISSN0955-7997
EISSN1873-197X
Volume61Pages:172-182
SubtypeArticle
AbstractThe numerical manifold method (NMM) is a unified framework that is used to describe continuous and discontinuous problems. The NMM is derived based on the finite cover approximation theory and gains its name after the mathematical notion of manifold. It is also a method based on the partition of unity (PU) and it introduces two cover systems: the mathematical cover (MC) and the physical cover (PC). There are two approaches for constructing high-order approximations. The first approach involves a non-constant PU function and non-constant local approximations. This results in the linear dependence (LD) problem and leads to the singularity in a global matrix. The second approach involves a higher PU function and constant local approximations. The increase in the order of approximations should go along with the increase in star but the LD problem can be avoided completely in theory. In this paper, a new high-order NMM with nine-node triangular meshes is proposed. The upgrade from first-order NMM to high-order NMM is illustrated in detail. Moreover, the initial stress matrix is analyzed in detail. The effectiveness and accuracy of the proposed high-order NMM are validated using several typical examples. The proposed high-order NMM supplements the existing family of non-LD high- and low-order NMM under MC with triangular meshes. (C) 2015 Elsevier Ltd. All rights reserved.
KeywordHigh-order Nmm Non-linear Dependence Nine-node Triangle Initial Stress Matrix Large Deformation
WOS HeadingsScience & Technology ; Technology ; Physical Sciences
DOI10.1016/j.enganabound.2015.07.011
WOS Subject ExtendedEngineering ; Mathematics
Indexed BySCI
WOS KeywordCRACK-PROPAGATION ; PARTITION ; PREDICTION ; SIMULATION ; FLOW
Language英语
Quartile3区
TOP
WOS SubjectEngineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000362308700017
Citation statistics
Cited Times:15[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.imde.ac.cn/handle/131551/11030
Collection山地灾害与地表过程重点实验室
Affiliation1.Chinese Acad Sci, Key Lab Mt Hazards & Surface Proc, Chengdu 610041, Peoples R China
2.Chinese Acad Sci, Inst Mt Hazards & Environm, Chengdu 610041, Peoples R China
3.Chinese Acad Sci, Ctr Excellence Tibetan Plateau Earth Sci, Beijing 100101, Peoples R China
4.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
5.Changsha Univ Sci & Technol, Sch Hydraul Engn, Changsha 410004, Hunan, Peoples R China
First Author Affilication中国科学院水利部成都山地灾害与环境研究所
Recommended Citation
GB/T 7714
Fan, Huo,He, Siming,Jiang, Zhongming. A high-order numerical manifold method with nine-node triangular meshes[J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS,2015,61:172-182.
APA Fan, Huo,He, Siming,&Jiang, Zhongming.(2015).A high-order numerical manifold method with nine-node triangular meshes.ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS,61,172-182.
MLA Fan, Huo,et al."A high-order numerical manifold method with nine-node triangular meshes".ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 61(2015):172-182.
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