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**A smoothed finite element method for mechanics problems.**
*(English)*
Zbl 1169.74047

Summary: In the finite element method (FEM), a necessary condition for a four-node isoparametric element is that no interior angle is greater than \(180^\circ \) 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 of bilinear isoparametric elements can be removed and problem domain can be discretized in more flexible ways, as demonstrated in the example problems.

### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

74K20 | Plates |

### Software:

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\textit{G. R. Liu} et al., Comput. Mech. 39, No. 6, 859--877 (2007; Zbl 1169.74047)

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