An n-sided polygonal edge-based smoothed finite element method (nES-FEM) for solid mechanics

An edge‐based smoothed finite element method (ES‐FEM) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the elastic solid mechanics problems. In this paper the ES‐FEM is further extended to a more gen...

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Published inInternational journal for numerical methods in biomedical engineering Vol. 27; no. 9; pp. 1446 - 1472
Main Authors Nguyen-Thoi, T., Liu, G. R., Nguyen-Xuan, H.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.09.2011
Wiley
Subjects
Convergence
edge-based smoothed finite element method (ES-FEM)
Exact sciences and technology
Exact solutions
Finite element method
finite element method (FEM)
Fundamental areas of phenomenology (including applications)
Interpolation
Mathematical analysis
Mathematical models
node-based smoothed finite element method (NS-FEM)
numerical methods
Physics
polygonal element
smoothed finite element methods (S-FEM)
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Solid mechanics
Averaging method
edge-based smoothed finite element method (ES-FEM)
numerical methods
Triangular finite element
node-based smoothed finite element method (NS-FEM)
finite element method (FEM)
Modeling
Exact solution
Finite element method
Smoothing
polygonal element
Polynomial interpolation
Convergence rate
smoothed finite element methods (S-FEM)
Polygon
Online AccessGet full text
ISSN2040-7939
2040-7947
2040-7947
DOI10.1002/cnm.1375

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Abstract An edge‐based smoothed finite element method (ES‐FEM) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the elastic solid mechanics problems. In this paper the ES‐FEM is further extended to a more general case, n‐sided polygonal edge‐based smoothed finite element method (nES‐FEM), in which the problem domain can be discretized by a set of polygons, each with an arbitrary number of sides. The simple averaging point interpolation method is suggested to construct nES‐FEM shape functions. In addition, a novel domain‐based selective scheme of a combined nES/NS‐FEM model is also proposed to avoid volumetric locking. Several numerical examples are investigated and the results of the nES‐FEM are found to agree well with exact solutions and are much better than those of others existing methods. Copyright © 2010 John Wiley & Sons, Ltd.
AbstractList An edge‐based smoothed finite element method (ES‐FEM) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the elastic solid mechanics problems. In this paper the ES‐FEM is further extended to a more general case, n ‐sided polygonal edge‐based smoothed finite element method ( n ES‐FEM), in which the problem domain can be discretized by a set of polygons, each with an arbitrary number of sides. The simple averaging point interpolation method is suggested to construct n ES‐FEM shape functions. In addition, a novel domain‐based selective scheme of a combined n ES/NS‐FEM model is also proposed to avoid volumetric locking. Several numerical examples are investigated and the results of the n ES‐FEM are found to agree well with exact solutions and are much better than those of others existing methods. Copyright © 2010 John Wiley & Sons, Ltd.
An edge-based smoothed finite element method (ES-FEM) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the elastic solid mechanics problems. In this paper the ES-FEM is further extended to a more general case, n-sided polygonal edge-based smoothed finite element method (nES-FEM), in which the problem domain can be discretized by a set of polygons, each with an arbitrary number of sides. The simple averaging point interpolation method is suggested to construct nES-FEM shape functions. In addition, a novel domain-based selective scheme of a combined nES/NS-FEM model is also proposed to avoid volumetric locking. Several numerical examples are investigated and the results of the nES-FEM are found to agree well with exact solutions and are much better than those of others existing methods.
An edge‐based smoothed finite element method (ES‐FEM) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the elastic solid mechanics problems. In this paper the ES‐FEM is further extended to a more general case, n‐sided polygonal edge‐based smoothed finite element method (nES‐FEM), in which the problem domain can be discretized by a set of polygons, each with an arbitrary number of sides. The simple averaging point interpolation method is suggested to construct nES‐FEM shape functions. In addition, a novel domain‐based selective scheme of a combined nES/NS‐FEM model is also proposed to avoid volumetric locking. Several numerical examples are investigated and the results of the nES‐FEM are found to agree well with exact solutions and are much better than those of others existing methods. Copyright © 2010 John Wiley & Sons, Ltd.
Author Nguyen-Thoi, T.
Nguyen-Xuan, H.
Liu, G. R.
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  surname: Nguyen-Xuan
  fullname: Nguyen-Xuan, H.
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Issue 9
Keywords Solid mechanics
Averaging method
edge-based smoothed finite element method (ES-FEM)
numerical methods
Triangular finite element
node-based smoothed finite element method (NS-FEM)
finite element method (FEM)
Modeling
Exact solution
Finite element method
Smoothing
polygonal element
Polynomial interpolation
Convergence rate
smoothed finite element methods (S-FEM)
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2007; 39
2007; 301
2009; 45
2009; 25
2009; 87
2004; 60
2000; 47
2009; 80
2006; 13
2000; 50
2009
2009; 198
2009; 199
2008; 56
1996
2008; 79
2003; 16
2008; 5
2006; 3
2007; 71
2007; 72
2008; 55
2008; 74
2003
1992
1970
2002
2007; 12
2009; 78
2009; 77
2000
2008; 28
2008; 25
1987
2009; 320
2008; 23
2009; 6
2005; 2
2007; 43
2008; 198
2008; 197
2009; 18
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Snippet An edge‐based smoothed finite element method (ES‐FEM) using triangular elements was recently proposed to improve the accuracy and convergence rate of the...
An edge-based smoothed finite element method (ES-FEM) using triangular elements was recently proposed to improve the accuracy and convergence rate of the...
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SubjectTerms Convergence
edge-based smoothed finite element method (ES-FEM)
Exact sciences and technology
Exact solutions
Finite element method
finite element method (FEM)
Fundamental areas of phenomenology (including applications)
Interpolation
Mathematical analysis
Mathematical models
node-based smoothed finite element method (NS-FEM)
numerical methods
Physics
polygonal element
smoothed finite element methods (S-FEM)
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Title An n-sided polygonal edge-based smoothed finite element method (nES-FEM) for solid mechanics
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https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fcnm.1375
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https://www.proquest.com/docview/1671456837
Volume 27
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