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Multi‐scale methods
Author(s) -
Liu Wing Kam,
Hao Su,
Belytschko Ted,
Li Shaofan,
Chang Chin Tang
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(20000310)47:7<1343::aid-nme828>3.0.co;2-w
Subject(s) - scale (ratio) , dilation (metric space) , meshfree methods , computer science , smoothing , partition of unity , multiresolution analysis , scale analysis (mathematics) , algorithm , mathematics , kernel (algebra) , mathematical optimization , finite element method , geometry , artificial intelligence , structural engineering , wavelet , engineering , mechanics , wavelet transform , computer vision , physics , discrete wavelet transform , quantum mechanics , combinatorics
In this paper four multiple scale methods are proposed. The meshless hierarchical partition of unity is used as a multiple scale basis. The multiple scale analysis with the introduction of a dilation parameter to perform multiresolution analysis is discussed. The multiple field based on a 1‐D gradient plasticity theory with material length scale is also proposed to remove the mesh dependency difficulty in softening/localization problems. A non‐local (smoothing) particle integration procedure with its multiple scale analysis are then developed. These techniques are described in the context of the reproducing kernel particle method. Results are presented for elastic‐plastic one‐dimensional problems and 2‐D large deformation strain localization problems to illustrate the effectiveness of these methods. Copyright © 2000 John Wiley & Sons, Ltd.