Smoothed finite element method (SFEM)

Abstract

In this paper, cell-wise strain smoothing operation is incorporated into conventional finite elements and the smoothed finite element method (SFEM) is proposed for 2D elastic problems. When a constant smoothing function is chosen, area integration becomes line integration along its boundaries and no derivative of shape functions is needed in computing the field gradients. Compared with the conventional FEM, the SFEM achieves more accurate results and generally higher convergence rate in energy without increasing computational cost. In addition, as no mapping or coordinate transformation is performed in the SFEM, the element is allowed to be of arbitrary shape. Hence the well-known issue of the shape distortion of isoparametric elements can be resolved.