Article (Scientific journals)
Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods
Natarajan, Sundararajan; Bordas, Stéphane; Ooi, Ean Tat
2015In International Journal for Numerical Methods in Engineering, 104 (13), p. 1173-1199
Peer reviewed
 

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Keywords :
smoothed finite element method; virtual element method; boundary integration; scaled boundary finite element method; polyhedra
Abstract :
[en] We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally convergent polyhedral FEM.We show that the stiffness matrix computed with one subcell SFEM is identical to the consistency term of the virtual element method, irrespective of the topology of the element, as long as the shape functions vary linearly on the boundary. Using this connection, we propose a new stable approach to strain smoothing for polygonal/polyhedral elements where, instead of using sub-triangulations, we are able to use one single polygonal/polyhedral subcell for each element while maintaining stability. For a similar number of degrees of freedom, the proposed approach is more accurate than the conventional SFEM with triangular subcells. The time to compute the stiffness matrix scales with the O.dof s/1:1 in case of the conventional polygonal FEM, while it scales as O.dof s/0:7 in the proposed approach. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Natarajan, Sundararajan
Bordas, Stéphane ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Ooi, Ean Tat
External co-authors :
yes
Language :
English
Title :
Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods
Publication date :
2015
Journal title :
International Journal for Numerical Methods in Engineering
Volume :
104
Issue :
13
Pages :
1173-1199
Peer reviewed :
Peer reviewed
Focus Area :
Computational Sciences
European Projects :
FP7 - 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery
Funders :
EPSRC under grant EP/G042705/1 Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method
EP/I006494/1 Sustainable domain-specific software generation tools for extremely parallel particle-based simulations
CE - Commission Européenne [BE]
Commentary :
cited By 5 Scopus
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