Journal article
A unified stability analysis of meshless particle methods
International journal for numerical methods in engineering, Vol.48(9), pp.1359-1400
07/30/2000
DOI: 10.1002/1097-0207(20000730)48:9<1359::AID-NME829>3.0.CO;2-U
Abstract
A unified stability analysis of meshless methods with Eulerian and Lagrangian kernels is presented. Three types of instabilities were identified in one dimension: an instability due to rank deficiency, a tensile instability and a material instability which is also found in continua. The stability of particle methods with Eulerian and Lagrangian kernels is markedly different: Lagrangian kernels do not exhibit the tensile instability. In both kernels, the instability due to rank deficiency can be suppressed by stress points. In two dimensions the stabilizing effect of stress points is dependent on their locations. It was found that the best approach to stable particle discretizations is to use Lagrangian kernels with stress points. The stability of the least‐squares stabilization was also studied. Copyright © 2000 John Wiley & Sons, Ltd.
Details
- Title: Subtitle
- A unified stability analysis of meshless particle methods
- Creators
- Ted BelytschkoYong GuoWing Kam LiuShao Ping Xiao
- Resource Type
- Journal article
- Publication Details
- International journal for numerical methods in engineering, Vol.48(9), pp.1359-1400
- Publisher
- John Wiley & Sons, Ltd; Chichester, UK
- DOI
- 10.1002/1097-0207(20000730)48:9<1359::AID-NME829>3.0.CO;2-U
- ISSN
- 0029-5981
- eISSN
- 1097-0207
- Number of pages
- 42
- Grant note
- Army Research Office Army High Performance Computing Research Center (DAAH04‐95‐2‐003/Contract DAAH04‐95‐C‐0008) Office of Naval Research
- Language
- English
- Date published
- 07/30/2000
- Academic Unit
- Mechanical Engineering; Iowa Technology Institute
- Record Identifier
- 9984064558302771
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