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==Abstract==
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Reproducing Kernel Particle Method (RKPM) has been applied to many large deformation problems [<span id='cite-1'></span>[[#1|1]],<span id='cite-2'></span>[[#2|2]]]. RKPM relies on polynomial reproducing conditions to yield desired accuracy and convergence properties, but requires appropriate kernel support coverage of neighboring particles to ensure kernel stability [<span id='cite-3'></span>[[#3|3]]]. This kernel stability condition is difficult to achieve for problems with large particle motion such as the fragment-impact processes commonly exist in many extreme events. A new reproducing kernel formulation with “quasi-linear” reproducing conditions is introduced. In this approach, the first order polynomial reproducing conditions are approximately enforced to yield a nonsingular moment matrix. With proper error control of the first completeness, nearly 2 nd order convergence rate in L2 norm can be achieved while maintaining kernel stability. The effectiveness of this new quasi-linear RKPM formulation is demonstrated by modelling fragment-impact and penetration extreme events.
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== Recording of the presentation ==
 
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| {{#evt:service=youtube|id=https://youtu.be/FncBGiebqWk | alignment=center}}
 
|- style="text-align: center;"  
 
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| Location: Technical University of Catalonia (UPC), Vertex Building.  
 
| Location: Technical University of Catalonia (UPC), Vertex Building.  
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| Date: 28 - 30 September 2015, Barcelona, Spain.
 
| Date: 28 - 30 September 2015, Barcelona, Spain.
 
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== General Information ==
 
== General Information ==
 
* Location: Technical University of Catalonia (UPC), Barcelona, Spain.
 
* Location: Technical University of Catalonia (UPC), Barcelona, Spain.
 
* Date: 28 - 30 September 2015
 
* Date: 28 - 30 September 2015
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* Secretariat: [//www.cimne.com/ CIMNE] Centre Internacional de Metodes Numerics.
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* Secretariat: [//www.cimne.com/ International Center for Numerical Methods in Engineering (CIMNE)].
  
 
== External Links ==
 
== External Links ==
 
* [//congress.cimne.com/particles2015/frontal/default.asp Particles 2015] Official Website of the Conference.
 
* [//congress.cimne.com/particles2015/frontal/default.asp Particles 2015] Official Website of the Conference.
 
* [//www.cimnemultimediachannel.com/ CIMNE Multimedia Channel]
 
* [//www.cimnemultimediachannel.com/ CIMNE Multimedia Channel]
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==References==
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<div id="1"></div>
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[[#cite-1|[1]]] S. W. Chi, C. H. Lee, J. S. Chen, and P. C. Guan, “A Level Set Enhanced Natural Kernel
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Contact Algorithm for Impact and Penetration Modeling,” International Journal for Numerical
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Methods in Engineering, 102, 839–866 (2015).
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<div id="2"></div>
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[[#cite-2|[2]]] C. Guan, S. W. Chi, J. S. Chen, T. R. Slawson, M. J. Roth, “Semi-Lagrangian Reproducing
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Kernel Particle Method for Fragment-Impact Problems,” International Journal of Impact
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Engineering, 38, 1033-1047 (2011).
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<div id="3"></div>
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[[#cite-3|[3]]] J. S. Chen, C. Pan, C. T. Wu, and W. K. Liu, "Reproducing Kernel Particle Methods for Large
 +
Deformation Analysis of Nonlinear Structures," Computer Methods in Applied Mechanics and
 +
Engineering, 139, 195-227 (1996).

Latest revision as of 11:24, 20 July 2016

Abstract

Reproducing Kernel Particle Method (RKPM) has been applied to many large deformation problems [1,2]. RKPM relies on polynomial reproducing conditions to yield desired accuracy and convergence properties, but requires appropriate kernel support coverage of neighboring particles to ensure kernel stability [3]. This kernel stability condition is difficult to achieve for problems with large particle motion such as the fragment-impact processes commonly exist in many extreme events. A new reproducing kernel formulation with “quasi-linear” reproducing conditions is introduced. In this approach, the first order polynomial reproducing conditions are approximately enforced to yield a nonsingular moment matrix. With proper error control of the first completeness, nearly 2 nd order convergence rate in L2 norm can be achieved while maintaining kernel stability. The effectiveness of this new quasi-linear RKPM formulation is demonstrated by modelling fragment-impact and penetration extreme events.

Recording of the presentation

Location: Technical University of Catalonia (UPC), Vertex Building.
Date: 28 - 30 September 2015, Barcelona, Spain.

General Information

External Links

References

[1] S. W. Chi, C. H. Lee, J. S. Chen, and P. C. Guan, “A Level Set Enhanced Natural Kernel Contact Algorithm for Impact and Penetration Modeling,” International Journal for Numerical Methods in Engineering, 102, 839–866 (2015).

[2] C. Guan, S. W. Chi, J. S. Chen, T. R. Slawson, M. J. Roth, “Semi-Lagrangian Reproducing Kernel Particle Method for Fragment-Impact Problems,” International Journal of Impact Engineering, 38, 1033-1047 (2011).

[3] J. S. Chen, C. Pan, C. T. Wu, and W. K. Liu, "Reproducing Kernel Particle Methods for Large Deformation Analysis of Nonlinear Structures," Computer Methods in Applied Mechanics and Engineering, 139, 195-227 (1996).

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