Computational Mechanics

, Volume 39, Issue 6, pp 859–877

A Smoothed Finite Element Method for Mechanics Problems

Original Paper


In the finite element method (FEM), a necessary condition for a four-node isoparametric element is that no interior angle is greater than 180° and the positivity of Jacobian determinant should be ensured in numerical implementation. In this paper, we incorporate cell-wise strain smoothing operations into conventional finite elements and propose the smoothed finite element method (SFEM) for 2D elastic problems. It is found that a quadrilateral element divided into four smoothing cells can avoid spurious modes and gives stable results for integration over the element. Compared with original FEM, the SFEM achieves more accurate results and generally higher convergence rate in energy without increasing computational cost. More importantly, as no mapping or coordinate transformation is involved in the SFEM, its element is allowed to be of arbitrary shape. Hence the restriction on the shape bilinear isoparametric elements can be removed and problem domain can be discretized in more flexible ways, as demonstrated in the example problems.


Finite element method (FEM) Smoothed finite element method (SFEM) Strain smoothing Isoparametric element Gauss quadrature 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Center for Advanced Computations in Engineering Science (ACES), Department of Mechanical EngineeringNational University of SingaporeSingaporeSingapore
  2. 2.Singapore-MIT Alliance (SMA)SingaporeSingapore

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