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New strategies for some issues of numerical manifold method in simulation of crack propagation
Zheng, Hong1; Xu, Dongdong2
2014
Source PublicationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
ISSN0029-5981
Volume97Issue:13Pages:986-1010
AbstractAiming to solve, in a unified way, continuous and discontinuous problems in geotechnical engineering, the numerical manifold method introduces two covers, namely, the mathematical cover and the physical cover. In order to reach the goal, some issues in the simulation of crack propagation have to be solved, among which are the four issues to be treated in this study: (1) to reduce the rank deficiency induced by high degree polynomials as local approximation, a new variational principle is formulated, which suppresses the gradient-dependent DOFs; (2) to evaluate the integrals with singularity of 1/r, a new numerical quadrature scheme is developed, which is simpler but more efficient than the existing Duffy transformation; (3) to analyze kinked cracks, a sign convention for argument in the polar system at the crack tip is specified, which leads to more accurate results in a simpler way than the existing mapping technique; and (4) to demonstrate the mesh independency of numerical manifold method in handling strong singularity, a mesh deployment scheme is advised, which can reproduce all singular locations of the crack with regard to the mesh. Corresponding to the four issues, typical examples are given to demonstrate the effectiveness of the proposed schemes. Copyright (c) 2013 John Wiley & Sons, Ltd.
Keywordnumerical manifold method mathematical cover physical cover variational principle stress intensity factor 1 r singularity kinked cracks mesh independency
DOI10.1002/nme.4620
Indexed BySCI
Language英语
WOS Research AreaEngineering ; Mathematics
WOS SubjectEngineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000332952000003
PublisherWILEY-BLACKWELL
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Document Type期刊论文
Identifierhttp://119.78.100.198/handle/2S6PX9GI/3579
Collection岩土力学所知识全产出_期刊论文
国家重点实验室知识产出_期刊论文
Affiliation1.Beijing Univ Technol, Key Lab Urban Secur & Disaster Engn, Minist Educ ;
2.Chinese Acad Sci, Inst Rock & Soil Mech, State Key Lab Geomech & Geotech Engn
Recommended Citation
GB/T 7714
Zheng, Hong,Xu, Dongdong. New strategies for some issues of numerical manifold method in simulation of crack propagation[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING,2014,97(13):986-1010.
APA Zheng, Hong,&Xu, Dongdong.(2014).New strategies for some issues of numerical manifold method in simulation of crack propagation.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING,97(13),986-1010.
MLA Zheng, Hong,et al."New strategies for some issues of numerical manifold method in simulation of crack propagation".INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 97.13(2014):986-1010.
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