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Application of Polygonal Finite Elements to Two-Dimensional Mechanical and Electro-Mechanically Coupled Problems

Kaliappan, Jayabal and Menzel, Andreas LU (2011) In CMES: Computer Modeling in Engineering and Sciences 73(2). p.183-207
Abstract
Naturally evolving Voronoi discretisation of two-dimensional plane domains renders representative microstructures that turn out to be useful for the modelling and simulation of polycrystalline materials. Hybrid finite element approaches are employed on such polygonal discretisations to solve, for instance, mechanical and electromechanical problems within a finite element context. In view of solving mechanical problems, varying order of polynomial functions are suggested in the literature to sufficiently approximate stresses within the polygonal finite elements. These are, in addition to the order of the approximation functions for the displacements, characterised by the number of edges in the polygonal elements. It appears, as demonstrated... (More)
Naturally evolving Voronoi discretisation of two-dimensional plane domains renders representative microstructures that turn out to be useful for the modelling and simulation of polycrystalline materials. Hybrid finite element approaches are employed on such polygonal discretisations to solve, for instance, mechanical and electromechanical problems within a finite element context. In view of solving mechanical problems, varying order of polynomial functions are suggested in the literature to sufficiently approximate stresses within the polygonal finite elements. These are, in addition to the order of the approximation functions for the displacements, characterised by the number of edges in the polygonal elements. It appears, as demonstrated in this work, that the naturally evolving Voronoi discretisations exhibit a specific property when combined with a hybrid polygonal finite element approach. This property allows the choice of stress approximating functions in polygonal finite elements to be based only on the order of the displacement approximating functions regardless of the number of edges in the element. Such a relation also appears to hold in coupled electromechanical problems between the approximating functions for the electric displacements and the electric potential. The realisation of such a property is demonstrated through several standard numerical examples and also with an application on a representative piezoceramic microstructure. (Less)
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author
organization
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Contribution to journal
publication status
published
subject
keywords
Polygonal finite element, Voronoi discretisations, approximation, functions, electromechanically coupled problems, piezoceramics
in
CMES: Computer Modeling in Engineering and Sciences
volume
73
issue
2
pages
183 - 207
publisher
Tech Science Press
external identifiers
  • wos:000292362300004
  • scopus:79959857917
ISSN
1526-1506
DOI
10.3970/cmes.2011.073.183
language
English
LU publication?
yes
id
6cf438ca-e93a-4516-bc78-8d4edb3bda98 (old id 2032322)
date added to LUP
2011-07-26 15:05:28
date last changed
2017-01-01 03:49:10
@article{6cf438ca-e93a-4516-bc78-8d4edb3bda98,
  abstract     = {Naturally evolving Voronoi discretisation of two-dimensional plane domains renders representative microstructures that turn out to be useful for the modelling and simulation of polycrystalline materials. Hybrid finite element approaches are employed on such polygonal discretisations to solve, for instance, mechanical and electromechanical problems within a finite element context. In view of solving mechanical problems, varying order of polynomial functions are suggested in the literature to sufficiently approximate stresses within the polygonal finite elements. These are, in addition to the order of the approximation functions for the displacements, characterised by the number of edges in the polygonal elements. It appears, as demonstrated in this work, that the naturally evolving Voronoi discretisations exhibit a specific property when combined with a hybrid polygonal finite element approach. This property allows the choice of stress approximating functions in polygonal finite elements to be based only on the order of the displacement approximating functions regardless of the number of edges in the element. Such a relation also appears to hold in coupled electromechanical problems between the approximating functions for the electric displacements and the electric potential. The realisation of such a property is demonstrated through several standard numerical examples and also with an application on a representative piezoceramic microstructure.},
  author       = {Kaliappan, Jayabal and Menzel, Andreas},
  issn         = {1526-1506},
  keyword      = {Polygonal finite element,Voronoi discretisations,approximation,functions,electromechanically coupled problems,piezoceramics},
  language     = {eng},
  number       = {2},
  pages        = {183--207},
  publisher    = {Tech Science Press},
  series       = {CMES: Computer Modeling in Engineering and Sciences},
  title        = {Application of Polygonal Finite Elements to Two-Dimensional Mechanical and Electro-Mechanically Coupled Problems},
  url          = {http://dx.doi.org/10.3970/cmes.2011.073.183},
  volume       = {73},
  year         = {2011},
}