Header menu link for other important links
X
Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods
, Stéphane PA Bordas, Ean Tat Ooi
Published in John Wiley and Sons Ltd
2015
Volume: 104
   
Issue: 13
Pages: 1173 - 1199
Abstract

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(dofs)1.1 in case of the conventional polygonal FEM, while it scales as O(dofs)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. © 2015 John Wiley & Sons, Ltd.

About the journal
JournalData powered by TypesetInternational Journal for Numerical Methods in Engineering
PublisherData powered by TypesetJohn Wiley and Sons Ltd
ISSN00295981
Open AccessNo
Concepts (13)
  •  related image
    Degrees of freedom (mechanics)
  •  related image
    Matrix algebra
  •  related image
    Stiffness
  •  related image
    Stiffness matrix
  •  related image
    Bench-mark problems
  •  related image
    Convergence properties
  •  related image
    LINEAR ELASTICITY
  •  related image
    POLYHEDRA
  •  related image
    SCALED BOUNDARY FINITE ELEMENT METHOD
  •  related image
    SMOOTHED FINITE ELEMENT METHOD
  •  related image
    SMOOTHED FINITE ELEMENTS
  •  related image
    VIRTUAL ELEMENT METHOD
  •  related image
    Finite element method